a shopkeeper sold an article offering a discount of 5 % and earned a profit of 31.1 % . what would have been the percentage of profit earned if no discount had been offered ?

Explanation: "giving no discount to customer implies selling the product on printed price . suppose the cost price of the article is 100 . then printed price = 100 ã — ( 100 + 31.1 ) / ( 100 â ˆ ’ 5 ) = 138 hence , required % profit = 138 â € “ 100 = 38 % answer a"

subtract(divide(multiply(add(const_100, 31.1), const_100), subtract(const_100, 5)), const_100)

<gadget id="calculator">100 + 31.1</gadget>
<output>131.1</output>
<gadget id="calculator">131.1 * 100</gadget>
<output>13_110</output>
<gadget id="calculator">100 - 5</gadget>
<output>95</output>
<gadget id="calculator">13_110 / 95</gadget>
<output>138</output>
<gadget id="calculator">138 - 100</gadget>
<output>38</output>
<result>38</result>


what will be the difference between simple and compound interest at 14 % per annum on a sum of rs . 1000 after 4 years ?

Explanation: "s . i . = ( 1000 * 14 * 4 ) / 100 = rs . 560 c . i . = [ 1000 * ( 1 + 14 / 100 ) 4 - 1000 ] = rs . 689 difference = ( 689 - 560 ) = rs . 129 answer : a"

subtract(subtract(multiply(1000, power(add(divide(14, const_100), const_1), 4)), 1000), multiply(multiply(1000, divide(14, const_100)), 4))


there are 28 stations between hyderabad and bangalore . how many second class tickets have to be printed , so that a passenger can travel from any station to any other station ?

Explanation: "the total number of stations = 30 from 30 stations we have to choose any two stations and the direction of travel ( i . e . , hyderabad to bangalore is different from bangalore to hyderabad ) in 3 ⁰ p ₂ ways . 30 p ₂ = 30 * 29 = 870 . answer : c"

multiply(add(28, const_1), add(add(28, const_1), const_1))

<gadget id="calculator">28 + 1</gadget>
<output>29</output>
<gadget id="calculator">29 + 1</gadget>
<output>30</output>
<gadget id="calculator">29 * 30</gadget>
<output>870</output>
<result>870</result>


the sum of all the integers s such that - 26 < s < 24 is

Explanation: "easy one - - 25 , - 24 , - 23 , - 22 , . . . . . . - 1,0 , 1 , 2 . . . . , 22 , 23 cancel everyhitng and we ' re left with - - 25 and - 24 s = - 49 . d is the answer ."

add(add(negate(26), const_1), add(add(negate(26), const_1), const_1))

<gadget id="calculator">-26</gadget>
<output>-26</output>
<gadget id="calculator">(-26) + 1</gadget>
<output>-25</output>
<gadget id="calculator">(-25) + 1</gadget>
<output>-24</output>
<gadget id="calculator">(-25) + (-24)</gadget>
<output>-49</output>
<result>-49</result>


a full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet . oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck ' s tank is completely filled . if the truck ' s tank has a radius of 6 feet and a height of 10 feet , how far ( in feet ) did the oil level drop in the stationary tank ?

Explanation: "the volume of oil pumped to the tank = the volume of oil taken away from stationary cylinder . pi * 36 * 10 = pi * h * 100 * 100 ( h is distance that the oil level dropped ) h = 360 / 10,000 = 36 / 1000 = 0.036 ft the answer is a ."

<gadget id="calculator">pi * (6 ** 2) * 10</gadget>
<output>360*pi = around 1_130.973355</output>
<gadget id="calculator">pi * (100 ** 2)</gadget>
<output>10000*pi = around 31_415.926536</output>
<gadget id="calculator">(360*pi) / (10000*pi)</gadget>
<output>9/250 = around 0.036</output>
<result>9/250 = around 0.036</result>


if n is an integer and 101 n ^ 2 is less than or equal to 10000 , what is the greatest possible value of n ?

Explanation: "101 * n ^ 2 < = 10000 n ^ 2 < = 10000 / 101 which will be less than 100 since 10000 / 100 = 100 which is the square of 9 next closest value of n where n ^ 2 < = 100 is 9 ans c"

<gadget id="calculator">10_000 / 101</gadget>
<output>10_000/101 = around 99.009901</output>
<gadget id="calculator">(10_000/101) ** (1/2)</gadget>
<output>100*sqrt(101)/101 = around 9.950372</output>
<gadget id="calculator">floor(100*sqrt(101)/101)</gadget>
<output>9</output>
<result>9</result>


the percentage profit earned by selling an article for rs . 1920 is equal to the percentage loss incurred by selling the same article for rs . 1280 . at what price should the article be sold to make 40 % profit ?

Explanation: "let c . p . be rs . x . then , ( 1920 - x ) / x * 100 = ( x - 1280 ) / x * 100 1920 - x = x - 1280 2 x = 3200 = > x = 1600 required s . p . = 140 % of rs . 1600 = 140 / 100 * 1600 = rs . 2240 . answer : e"

multiply(divide(add(const_100, 40), const_100), divide(add(1920, 1280), const_2))

<gadget id="calculator">100 + 40</gadget>
<output>140</output>
<gadget id="calculator">140 / 100</gadget>
<output>7/5 = around 1.4</output>
<gadget id="calculator">1_920 + 1_280</gadget>
<output>3_200</output>
<gadget id="calculator">3_200 / 2</gadget>
<output>1_600</output>
<gadget id="calculator">(7/5) * 1_600</gadget>
<output>2_240</output>
<result>2_240</result>


running at the same constant rate , 6 identical machines can produce a total of 360 bottles per minute . at this rate , how many bottles could 10 such machines produce in 4 minutes ?

Explanation: "let the required number of bottles be x . more machines , more bottles ( direct proportion ) more minutes , more bottles ( direct proportion ) machines 6 : 10 : : 360 : x time ( in minutes ) 1 : 4 6 x 1 x x = 10 x 4 x 360 x = ( 10 x 4 x 360 ) / ( 6 ) x = 2400 . answer : c"

multiply(multiply(divide(360, 6), 4), 10)

<gadget id="calculator">360 / 6</gadget>
<output>60</output>
<gadget id="calculator">60 * 4</gadget>
<output>240</output>
<gadget id="calculator">240 * 10</gadget>
<output>2_400</output>
<result>2_400</result>


there are 1000 buildings in a street . a sign - maker is contracted to number the houses from 1 to 1000 . how many zeroes will he need ?

Explanation: divide as ( 1 - 100 ) ( 100 - 200 ) . . . . ( 900 - 1000 ) total 192 answer : c

add(add(divide(1000, const_10), multiply(subtract(const_10, 1), const_10)), const_2)

<gadget id="calculator">1_000 / 10</gadget>
<output>100</output>
<gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">9 * 10</gadget>
<output>90</output>
<gadget id="calculator">100 + 90</gadget>
<output>190</output>
<gadget id="calculator">190 + 2</gadget>
<output>192</output>
<result>192</result>


Explanation: "? % of 360 = 108 or , ? = 108 × 100 / 360 = 30 answer a"

<gadget id="calculator">108 * 100</gadget>
<output>10_800</output>
<gadget id="calculator">10_800 / 360</gadget>
<output>30</output>
<result>30</result>


a train running at the speed of 120 km / hr crosses a pole in 18 seconds . what is the length of the train ?

Explanation: "speed = ( 120 x ( 5 / 18 ) m / sec = ( 100 / 3 ) m / sec . length of the train = ( speed x time ) . length of the train = ( ( 100 / 3 ) x 18 ) m = 600 m e"

multiply(divide(multiply(120, const_1000), const_3600), 18)

<gadget id="calculator">120 * 1_000</gadget>
<output>120_000</output>
<gadget id="calculator">120_000 / 3_600</gadget>
<output>100/3 = around 33.333333</output>
<gadget id="calculator">(100/3) * 18</gadget>
<output>600</output>
<result>600</result>


a train 100 meters long completely crosses a 300 meters long bridge in 45 seconds . what is the speed of the train is ?

Explanation: "s = ( 100 + 300 ) / 45 = 400 / 45 * 18 / 5 = 32 answer : a"

divide(divide(add(100, 300), const_1000), divide(45, const_3600))

<gadget id="calculator">100 + 300</gadget>
<output>400</output>
<gadget id="calculator">400 / 1_000</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">45 / 3_600</gadget>
<output>1/80 = around 0.0125</output>
<gadget id="calculator">(2/5) / (1/80)</gadget>
<output>32</output>
<result>32</result>


each month a retailer sells 100 identical items . on each item he makes a profit of $ 40 that constitutes 10 % of the item ' s price to the retailer . if the retailer contemplates giving a 5 % discount on the items he sells , what is the least number of items he will have to sell each month to justify the policy of the discount ?

Explanation: "for this question , we ' ll need the following formula : sell price = cost + profit we ' re told that the profit on 1 item is $ 20 and that this represents 10 % of the cost : sell price = cost + $ 40 sell price = $ 400 + $ 40 thus , the sell price is $ 440 for each item . selling all 100 items gives the retailer . . . 100 ( $ 40 ) = $ 2,000 of profit if the retailer offers a 5 % discount on the sell price , then the equation changes . . . 5 % ( 440 ) = $ 22 discount $ 418 = $ 400 + $ 18 now , the retailer makes a profit of just $ 18 per item sold . to earn $ 2,000 in profit , the retailer must sell . . . . $ 18 ( x ) = $ 2,000 x = 2,000 / 18 x = 222.222222 items you ' ll notice that this is not among the answer choices . . . . 221 and 223 are . selling 221 items would get us 9 ( 221 ) = $ 1989 which is not enough money . to get back to at least $ 2,000 , we need to sell 223 items . final answer : d"

divide(multiply(100, 40), subtract(40, divide(multiply(add(divide(multiply(100, 40), 10), 40), 5), 100)))

<gadget id="calculator">100 * 40</gadget>
<output>4_000</output>
<gadget id="calculator">4_000 / 10</gadget>
<output>400</output>
<gadget id="calculator">400 + 40</gadget>
<output>440</output>
<gadget id="calculator">440 * 5</gadget>
<output>2_200</output>
<gadget id="calculator">2_200 / 100</gadget>
<output>22</output>
<gadget id="calculator">40 - 22</gadget>
<output>18</output>
<gadget id="calculator">4_000 / 18</gadget>
<output>2_000/9 = around 222.222222</output>
<result>2_000/9 = around 222.222222</result>


bookman purchased 55 copies of a new book released recently , 10 of which are hardback and sold for $ 20 each , and rest are paperback and sold for $ 10 each . if 14 copies were sold and the total value of the remaining books was 460 , how many paperback copies were sold ?

Explanation: "the bookman had 10 hardback ad 55 - 10 = 45 paperback copies ; 14 copies were sold , hence 55 - 14 = 41 copies were left . let # of paperback copies left be p then 10 p + 20 ( 41 - p ) = 460 - - > 10 p = 360 - - > p = 36 # of paperback copies sold is 45 - 36 = 9 answer : e"

divide(subtract(subtract(add(multiply(subtract(55, 10), 10), multiply(10, 20)), 460), multiply(gcd(55, 10), 20)), 10)

<gadget id="calculator">55 - 10</gadget>
<output>45</output>
<gadget id="calculator">45 * 10</gadget>
<output>450</output>
<gadget id="calculator">10 * 20</gadget>
<output>200</output>
<gadget id="calculator">450 + 200</gadget>
<output>650</output>
<gadget id="calculator">650 - 460</gadget>
<output>190</output>
<gadget id="calculator">gcd(55, 10)</gadget>
<output>5</output>
<gadget id="calculator">5 * 20</gadget>
<output>100</output>
<gadget id="calculator">190 - 100</gadget>
<output>90</output>
<gadget id="calculator">90 / 10</gadget>
<output>9</output>
<result>9</result>


diana is painting statues . she has 1 / 2 of a gallon of paint remaining . each statue requires 1 / 16 gallon of paint . how many statues can she paint ?

Explanation: "number of statues = all the paint ÷ amount used per statue = 1 / 2 ÷ 1 / 16 = 8 / 16 * 16 / 1 = 8 / 1 = 8 answer is a ."

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 / 16</gadget>
<output>1/16 = around 0.0625</output>
<gadget id="calculator">(1/2) / (1/16)</gadget>
<output>8</output>
<result>8</result>


if the price of gasoline increases by 25 % and a driver intends to spend only 20 % more on gasoline , by how much percent should the driver reduce the quantity of gasoline that he buys ?

Explanation: "let x be the amount of gasoline the driver buys originally . let y be the new amount of gasoline the driver should buy . let p be the original price per liter . ( 1.25 * p ) y = 1.2 ( p * x ) y = ( 1.2 / 1.25 ) x = 0.96 x which is a reduction of 4 % . the answer is c ."

multiply(divide(subtract(add(25, const_100), add(20, const_100)), add(25, const_100)), const_100)

<gadget id="calculator">25 + 100</gadget>
<output>125</output>
<gadget id="calculator">20 + 100</gadget>
<output>120</output>
<gadget id="calculator">125 - 120</gadget>
<output>5</output>
<gadget id="calculator">5 / 125</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">(1/25) * 100</gadget>
<output>4</output>
<result>4</result>


an art gallery has only paintings and sculptures . currently , 1 / 3 of the pieces of art are displayed , and 1 / 6 of the pieces on display are sculptures . if 1 / 3 of the pieces not on display are paintings , and 1000 sculptures are not on display , how many pieces of art does the gallery have ?

Explanation: too many words and redundant info there . ( i ) 1 / 3 of the pieces of art are displayed , hence 2 / 3 of the pieces of art are not displayed . ( ii ) 1 / 6 of the pieces on display are sculptures , hence 5 / 6 of the pieces on display are paintings . ( iii ) 1 / 3 of the pieces not on display are paintings , hence 2 / 3 of the pieces not on display are sculptures . 1000 sculptures are not on display , so according to ( iii ) 2 / 3 * { not on display } = 1000 - - > { not on display } = 1500 . according to ( i ) 2 / 3 * { total } = 1500 - - > { total } = 2250 . answer : b .

divide(divide(1000, subtract(const_1, divide(1, 3))), subtract(const_1, divide(1, 3)))

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 - (1/3)</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">1_000 / (2/3)</gadget>
<output>1_500</output>
<gadget id="calculator">1_500 / (2/3)</gadget>
<output>2_250</output>
<result>2_250</result>


john and ingrid pay 30 % and 40 % tax annually , respectively . if john makes $ 60000 and ingrid makes $ 72000 , what is their combined tax rate ?

Explanation: "( 1 ) when 30 and 40 has equal weight or weight = 1 / 2 , the answer would be 35 . ( 2 ) when 40 has larger weight than 30 , the answer would be in between 35 and 40 . unfortunately , we have 2 answer choices d and e that fit that condition so we need to narrow down our range . ( 3 ) get 72000 / 132000 = 6 / 11 . 6 / 11 is a little above 6 / 12 = 1 / 2 . thus , our answer is just a little above 35 . answer : d"

multiply(divide(add(multiply(divide(30, const_100), 60000), multiply(divide(40, const_100), 72000)), add(72000, 60000)), const_100)

<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(3/10) * 60_000</gadget>
<output>18_000</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) * 72_000</gadget>
<output>28_800</output>
<gadget id="calculator">18_000 + 28_800</gadget>
<output>46_800</output>
<gadget id="calculator">72_000 + 60_000</gadget>
<output>132_000</output>
<gadget id="calculator">46_800 / 132_000</gadget>
<output>39/110 = around 0.354545</output>
<gadget id="calculator">(39/110) * 100</gadget>
<output>390/11 = around 35.454545</output>
<result>390/11 = around 35.454545</result>


the lenght of a room is 5.5 m and width is 4 m . find the cost of paving the floor by slabs at the rate of rs . 900 per sq . metre .

Explanation: "area of the floor = ( 5.5 ã — 4 ) m 2 = 22 m 2 . cost of paving = rs . ( 900 ã — 22 ) = rs . 19800 answer : option a"

<gadget id="calculator">5.5 * 4</gadget>
<output>22</output>
<gadget id="calculator">900 * 22</gadget>
<output>19_800</output>
<result>19_800</result>


a corporation double its annual bonus to 100 of its employees . what percent of the employees ’ new bonus is the increase ?

Explanation: let the annual bonus be x . a corporation double its annual bonus . so new bonus = 2 x . increase = 2 x - x = x the increase is what percent of the employees ’ new bonus = ( x / 2 x ) * 100 = 50 % hence a .

multiply(divide(subtract(const_2, const_1), const_2), 100)

<gadget id="calculator">2 - 1</gadget>
<output>1</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * 100</gadget>
<output>50</output>
<result>50</result>


calculate the ratio between x and y if 30 % of x equal to 50 % of y ?

Explanation: "explanation : 30 x = 50 y x : y = 30 : 50 = 3 : 5 answer : b"

<gadget id="calculator">30 / 50</gadget>
<output>3/5 = around 0.6</output>
<result>3/5 = around 0.6</result>


three walls have wallpaper covering a combined area of 300 square meters . by overlapping the wallpaper to cover a wall with an area of 180 square meters , the area that is covered by exactly two layers of wallpaper is 34 square meters . what is the area that is covered with three layers of wallpaper ?

Explanation: "300 - 180 = 120 sq m of the wallpaper overlaps ( in either two layers or three layers ) if 36 sq m has two layers , 120 - 34 = 86 sq m of the wallpaper overlaps in three layers . 86 sq m makes two extra layers hence the area over which it makes two extra layers is 43 sq m . answer ( a ) ."

divide(subtract(subtract(300, 180), 34), const_2)

<gadget id="calculator">300 - 180</gadget>
<output>120</output>
<gadget id="calculator">120 - 34</gadget>
<output>86</output>
<gadget id="calculator">86 / 2</gadget>
<output>43</output>
<result>43</result>


a trader bought a car at 20 % discount on its original price . he sold it at a 40 % increase on the price he bought it . what percent of profit did he make on the original price ?

Explanation: "original price = 100 cp = 80 s = 80 * ( 140 / 100 ) = 112 100 - 112 = 12 % answer : c"

multiply(subtract(divide(divide(multiply(subtract(const_100, 20), add(const_100, 40)), const_100), const_100), const_1), const_100)

<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">100 + 40</gadget>
<output>140</output>
<gadget id="calculator">80 * 140</gadget>
<output>11_200</output>
<gadget id="calculator">11_200 / 100</gadget>
<output>112</output>
<gadget id="calculator">112 / 100</gadget>
<output>28/25 = around 1.12</output>
<gadget id="calculator">(28/25) - 1</gadget>
<output>3/25 = around 0.12</output>
<gadget id="calculator">(3/25) * 100</gadget>
<output>12</output>
<result>12</result>


what is the unit digit in the product ( 3 ^ 65 x 6 ^ 59 x 7 ^ 71 ) ?

Explanation: explanation : unit digit in 3 ^ 4 = 1 unit digit in ( 3 ^ 4 ) 16 = 1 unit digit in 3 ^ 65 = unit digit in [ ( 3 ^ 4 ) 16 x 3 ] = ( 1 x 3 ) = 3 unit digit in 6 ^ 59 = 6 unit digit in 7 ^ 4 unit digit in ( 7 ^ 4 ) 17 is 1 . unit digit in 7 ^ 71 = unit digit in [ ( 7 ^ 4 ) 17 x 73 ] = ( 1 x 3 ) = 3 required digit = unit digit in ( 3 x 6 x 3 ) = 4 e

subtract(multiply(multiply(3, 6), 3), subtract(multiply(multiply(3, 6), 3), const_4))

<gadget id="calculator">3 * 6</gadget>
<output>18</output>
<gadget id="calculator">18 * 3</gadget>
<output>54</output>
<gadget id="calculator">54 - 4</gadget>
<output>50</output>
<gadget id="calculator">54 - 50</gadget>
<output>4</output>
<result>4</result>


a start walking from a place at a uniform speed of 6 kmph in a particular direction . after half an hour , b starts from the same place and walks in the same direction as a at a uniform speed and overtakes a after 1 hour 48 minutes . find the speed of b .

Explanation: "distance covered by a in 30 min = 1 km b covers extra 1 km in 1 hour 48 minutes ( 9 / 5 hr ) i . e . relative speed of b over a = 1 / ( 9 / 5 ) = 5 / 9 so the speed of b = speed of a + 5 / 9 = 6 + 5 / 9 = 6.55 answer b"

add(divide(1, divide(add(const_60, 48), const_60)), 6)

<gadget id="calculator">60 + 48</gadget>
<output>108</output>
<gadget id="calculator">108 / 60</gadget>
<output>9/5 = around 1.8</output>
<gadget id="calculator">1 / (9/5)</gadget>
<output>5/9 = around 0.555556</output>
<gadget id="calculator">(5/9) + 6</gadget>
<output>59/9 = around 6.555556</output>
<result>59/9 = around 6.555556</result>


oak street begins at pine street and runs directly east for 2 kilometers until it ends when it meets maple street . oak street is intersected every 400 meters by a perpendicular street , and each of those streets other than pine street and maple street is given a number beginning at 1 st street ( one block east of pine street ) and continuing consecutively ( 2 nd street , 3 rd street , etc . . . ) until the highest - numbered street one block west of maple street . what is the highest - numbered street that intersects oak street ?

Explanation: 2 km / 400 m = 5 . however , the street at the 2 - km mark is not 5 th street ; it is maple street . therefore , the highest numbered street is 4 th street . the answer is a .

subtract(divide(multiply(2, const_1000), 400), const_1)

<gadget id="calculator">2 * 1_000</gadget>
<output>2_000</output>
<gadget id="calculator">2_000 / 400</gadget>
<output>5</output>
<gadget id="calculator">5 - 1</gadget>
<output>4</output>
<result>4</result>


50 percent of the members of a study group are women , and 30 percent of those women are lawyers . if one member of the study group is to be selected at random , what is the probability that the member selected is a woman lawyer ?

Explanation: "say there are 100 people in that group , then there would be 0.5 * 0.30 * 100 = 15 women lawyers , which means that the probability that the member selected is a woman lawyer is favorable / total = 15 / 100 . answer : e"

multiply(divide(50, multiply(multiply(const_5, const_5), const_4)), divide(30, multiply(multiply(const_5, const_5), const_4)))

<gadget id="calculator">5 * 5</gadget>
<output>25</output>
<gadget id="calculator">25 * 4</gadget>
<output>100</output>
<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(1/2) * (3/10)</gadget>
<output>3/20 = around 0.15</output>
<result>3/20 = around 0.15</result>


the cost of one photocopy is $ 0.02 . however , a 25 % discount is offered on orders of more than 100 photocopies . if arthur and david have to make 80 copies each , how much will each of them save if they submit a single order of 160 copies ?

Explanation: "if arthur and david submit separate orders , each would be smaller than 100 photocopies , so no discount . each would pay ( 80 ) * ( $ 0.02 ) = $ 1.60 , or together , a cost of $ 3.20 - - - that ' s the combined no discount cost . if they submit things together as one big order , they get a discount off of that $ 3.20 price - - - - 25 % or 1 / 4 of that is $ 0.80 , the discount on the combined sale . they each effective save half that amount , or $ 0.40 . answer = ( b ) ."

divide(subtract(multiply(const_2, multiply(80, 0.02)), multiply(multiply(160, divide(subtract(100, 25), 100)), 0.02)), const_2)

<gadget id="calculator">80 * 0.02</gadget>
<output>1.6</output>
<gadget id="calculator">2 * 1.6</gadget>
<output>3.2</output>
<gadget id="calculator">100 - 25</gadget>
<output>75</output>
<gadget id="calculator">75 / 100</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">160 * (3/4)</gadget>
<output>120</output>
<gadget id="calculator">120 * 0.02</gadget>
<output>2.4</output>
<gadget id="calculator">3.2 - 2.4</gadget>
<output>0.8</output>
<gadget id="calculator">0.8 / 2</gadget>
<output>0.4</output>
<result>0.4</result>


if 6 men and 8 women can do a piece of work in 10 days while 26 men and 48 women can do the same in 2 days , the time taken by 15 men and 20 women in doing the same type of work will be ?

Explanation: let 1 man ' s 1 day ' s work = x and 1 women ' s 1 day ' s work = y . then , 6 x + 8 y = 1 and 26 x + 48 y = 1 . 10 2 solving these two equations , we get : x = 1 and y = 1 . 100 200 ( 15 men + 20 women ) ' s 1 day ' s work = 15 + 20 = 1 . 100 200 4 15 men and 20 women can do the work in 4 days . hence answer will be b

divide(multiply(add(divide(8, divide(subtract(multiply(48, 2), multiply(8, 10)), subtract(multiply(6, 10), multiply(26, 2)))), 6), 10), add(divide(20, divide(subtract(multiply(48, 2), multiply(8, 10)), subtract(multiply(6, 10), multiply(26, 2)))), 15))

<gadget id="calculator">48 * 2</gadget>
<output>96</output>
<gadget id="calculator">8 * 10</gadget>
<output>80</output>
<gadget id="calculator">96 - 80</gadget>
<output>16</output>
<gadget id="calculator">6 * 10</gadget>
<output>60</output>
<gadget id="calculator">26 * 2</gadget>
<output>52</output>
<gadget id="calculator">60 - 52</gadget>
<output>8</output>
<gadget id="calculator">16 / 8</gadget>
<output>2</output>
<gadget id="calculator">8 / 2</gadget>
<output>4</output>
<gadget id="calculator">4 + 6</gadget>
<output>10</output>
<gadget id="calculator">10 * 10</gadget>
<output>100</output>
<gadget id="calculator">20 / 2</gadget>
<output>10</output>
<gadget id="calculator">10 + 15</gadget>
<output>25</output>
<gadget id="calculator">100 / 25</gadget>
<output>4</output>
<result>4</result>


the maximum number of students among them 1345 pens and 775 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :

Explanation: "explanation : required number of students = h . c . f of 1345 and 775 = 5 . answer : d"

<gadget id="calculator">gcd(1_345, 775)</gadget>
<output>5</output>
<result>5</result>


a sum of rs . 1360 has been divided among a , b and c such that a gets 2 / 3 of what b gets and b gets 1 / 4 of what c gets . b ' s share is :

Explanation: "let c ' s share = rs . x then , b ' s share = rs . x / 4 ; a ' s share = rs . 2 / 3 * x / 4 = rs . x / 6 therefore x / 6 + x / 4 + x = 1360 17 x / 12 = 1360 x = 1360 * 12 / 17 = rs . 960 hence , b ' s share = rs . 960 / 4 = rs . 240 answer : c"

subtract(subtract(multiply(divide(1360, const_10), const_2), const_12), const_12)

<gadget id="calculator">1_360 / 10</gadget>
<output>136</output>
<gadget id="calculator">136 * 2</gadget>
<output>272</output>
<gadget id="calculator">272 - 12</gadget>
<output>260</output>
<gadget id="calculator">260 - 12</gadget>
<output>248</output>
<result>248</result>


two - third of a positive number and 16 / 216 of its reciprocal are equal . find the positive number .

Explanation: "explanation : let the positive number be x . then , 2 / 3 x = 16 / 216 * 1 / x x 2 = 16 / 216 * 3 / 2 = 16 / 144 x = √ 16 / 144 = 4 / 12 . answer : a"

sqrt(divide(multiply(16, const_3), multiply(216, const_2)))

<gadget id="calculator">16 * 3</gadget>
<output>48</output>
<gadget id="calculator">216 * 2</gadget>
<output>432</output>
<gadget id="calculator">48 / 432</gadget>
<output>1/9 = around 0.111111</output>
<gadget id="calculator">(1/9) ** (1/2)</gadget>
<output>1/3 = around 0.333333</output>
<result>1/3 = around 0.333333</result>


find large number from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder

Explanation: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 large number = 270 + 1365 = 1635 d"

multiply(divide(subtract(1365, 15), subtract(6, const_1)), 6)

<gadget id="calculator">1_365 - 15</gadget>
<output>1_350</output>
<gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">1_350 / 5</gadget>
<output>270</output>
<gadget id="calculator">270 * 6</gadget>
<output>1_620</output>
<result>1_620</result>


in a recent election , james received 0.5 percent of the 2,000 votes cast . to win the election , a candidate needed to receive more than 50 percent of the vote . how many additional votes would james have needed to win the election ?

Explanation: james = ( 0.5 / 100 ) * 2000 = 10 votes to win = ( 50 / 100 ) * total votes + 1 = ( 50 / 100 ) * 2000 + 1 = 1001 remaining voted needed to win election = 1001 - 10 = 991 answer : option d

subtract(add(const_1000, const_1000), multiply(add(const_1000, const_1000), 0.5))

<gadget id="calculator">1_000 + 1_000</gadget>
<output>2_000</output>
<gadget id="calculator">2_000 * 0.5</gadget>
<output>1_000</output>
<gadget id="calculator">2_000 - 1_000</gadget>
<output>1_000</output>
<result>1_000</result>


what least number must be subtracted from 3832 so that the remaining number is divisible by 5 ?

Explanation: "on dividing 3832 by 5 , we get remainder = 2 . required number be subtracted = 2 answer : b"

subtract(3832, multiply(floor(divide(3832, 5)), 5))

<gadget id="calculator">3_832 / 5</gadget>
<output>3_832/5 = around 766.4</output>
<gadget id="calculator">floor(3_832/5)</gadget>
<output>766</output>
<gadget id="calculator">766 * 5</gadget>
<output>3_830</output>
<gadget id="calculator">3_832 - 3_830</gadget>
<output>2</output>
<result>2</result>


find the length of the wire required to go 14 times round a square field containing 5625 m 2 .

Explanation: "a 2 = 5625 = > a = 75 4 a = 300 300 * 14 = 4200 answer : c"

<gadget id="calculator">5_625 ** (1/2)</gadget>
<output>75</output>
<gadget id="calculator">4 * 75</gadget>
<output>300</output>
<gadget id="calculator">300 * 14</gadget>
<output>4_200</output>
<result>4_200</result>


how many bricks , each measuring 25 cm x 11.25 cm x 6 cm , will be needed to build a wall of 1 m x 2 m x 20 cm ?

Explanation: "number of bricks = volume of the wall / volume of 1 brick = ( 100 x 200 x 20 ) / ( 25 x 11.25 x 6 ) = 237 . answer : option c"

divide(multiply(multiply(multiply(1, const_100), multiply(2, const_100)), 20), multiply(multiply(25, 11.25), 6))

<gadget id="calculator">1 * 100</gadget>
<output>100</output>
<gadget id="calculator">2 * 100</gadget>
<output>200</output>
<gadget id="calculator">100 * 200</gadget>
<output>20_000</output>
<gadget id="calculator">20_000 * 20</gadget>
<output>400_000</output>
<gadget id="calculator">25 * 11.25</gadget>
<output>281.25</output>
<gadget id="calculator">281.25 * 6</gadget>
<output>1_687.5</output>
<gadget id="calculator">400_000 / 1_687.5</gadget>
<output>237.037037</output>
<result>237.037037</result>


spanish language broadcast records last 90 min on each of two sides . if it takes 3 hours to translate one hour of broadcast , how long will it take to translate 16 full records ?

Explanation: records last 90 min on each of 2 sides , = = > record last 90 * 2 = 180 min = 3 hours 16 full records - - > 16 * 3 = 48 hour broadcast given , 3 hours to translate 1 hour of broadcast let x be the time required to translate 48 hour broadcast ( 16 full records ) x = 48 * 3 = 144 hours answer : a

multiply(multiply(divide(multiply(90, const_2), const_60), 16), 3)

<gadget id="calculator">90 * 2</gadget>
<output>180</output>
<gadget id="calculator">180 / 60</gadget>
<output>3</output>
<gadget id="calculator">3 * 16</gadget>
<output>48</output>
<gadget id="calculator">48 * 3</gadget>
<output>144</output>
<result>144</result>


a can do a piece of work in 4 hours ; b and c together can do it in 3 hours , which a and c together can do it in 2 hours . how long will b alone take to do it ?

Explanation: "a ' s 1 hour work = 1 / 4 ; ( b + c ) ' s 1 hour work = 1 / 3 ; ( a + c ) ' s 1 hour work = 1 / 2 ( a + b + c ) ' s 1 hour work = ( 1 / 4 + 1 / 3 ) = 7 / 12 b ' s 1 hour work = ( 7 / 12 + 1 / 2 ) = 1 / 12 b alone will take 12 hours to do the work . answer : c"

divide(const_1, subtract(divide(const_1, 3), subtract(divide(const_1, 2), divide(const_1, 4))))

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/2) - (1/4)</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/3) - (1/4)</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">1 / (1/12)</gadget>
<output>12</output>
<result>12</result>


how many seconds will a 650 meter long train moving with a speed of 63 km / hr take to cross a man walking with a speed of 3 km / hr in the direction of the train ?

Explanation: "explanation : here distance d = 650 mts speed s = 63 - 3 = 60 kmph = 60 x 5 / 18 m / s time t = = 39 sec . answer : d"

divide(650, multiply(subtract(63, 3), const_0_2778))

<gadget id="calculator">63 - 3</gadget>
<output>60</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">60 * (5/18)</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">650 / (50/3)</gadget>
<output>39</output>
<result>39</result>


today is thursday . i came home from a trip 3 days before the day after last monday . how many days have i been home ?

Explanation: d 6 days the day after last monday was tuesday . if i came home 3 days before that , i came home on saturday , sunday , monday , tuesday , wednesday , and thursday = 6 days .

<gadget id="calculator">3 + 1</gadget>
<output>4</output>
<gadget id="calculator">4 + 2</gadget>
<output>6</output>
<result>6</result>


in one hour , a boat goes 19 km along the stream and 5 km against the stream . the speed of the boat in still water ( in km / hr ) is :

Explanation: "sol . speed in still water = 1 / 2 ( 19 + 5 ) kmph = 12 kmph . answer d"

<gadget id="calculator">19 + 5</gadget>
<output>24</output>
<gadget id="calculator">24 / 2</gadget>
<output>12</output>
<result>12</result>


a profit of rs . 900 is divided between x and y in the ratio of 1 / 2 : 1 / 3 . what is the difference between their profit shares ?

Explanation: a profit of rs . 900 is divided between x and y in the ratio of 1 / 2 : 1 / 3 or 3 : 2 . so profits are 540 and 360 . difference in profit share = 540 - 360 = 180 answer : b

subtract(divide(divide(900, add(divide(1, 2), divide(1, 3))), 2), divide(divide(900, add(divide(1, 2), divide(1, 3))), 3))

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/2) + (1/3)</gadget>
<output>5/6 = around 0.833333</output>
<gadget id="calculator">900 / (5/6)</gadget>
<output>1_080</output>
<gadget id="calculator">1_080 / 2</gadget>
<output>540</output>
<gadget id="calculator">1_080 / 3</gadget>
<output>360</output>
<gadget id="calculator">540 - 360</gadget>
<output>180</output>
<result>180</result>


a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 27 , the how old is b ?

Explanation: "explanation : let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 27 ⇒ 5 x = 25 ⇒ x = 5 . hence , b ' s age = 2 x = 10 years . answer : e"

divide(multiply(subtract(27, const_2), const_2), add(const_4, const_1))

<gadget id="calculator">27 - 2</gadget>
<output>25</output>
<gadget id="calculator">25 * 2</gadget>
<output>50</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">50 / 5</gadget>
<output>10</output>
<result>10</result>


calculate the share of y , if rs . 2880 is divided among x , y and z in the ratio 3 : 5 : 8 ?

Explanation: 3 + 5 + 8 = 16 2880 / 16 = 180 so y ' s share = 3 * 180 = 540 answer : a

multiply(divide(2880, add(add(3, 5), 8)), 3)

<gadget id="calculator">3 + 5</gadget>
<output>8</output>
<gadget id="calculator">8 + 8</gadget>
<output>16</output>
<gadget id="calculator">2_880 / 16</gadget>
<output>180</output>
<gadget id="calculator">180 * 3</gadget>
<output>540</output>
<result>540</result>


3 years ago , paula was 3 times as old as karl . in 9 years , paula will be twice as old as karl . what is the sum of their ages now ?

Explanation: "p - 3 = 3 ( k - 3 ) and so p = 3 k - 6 p + 9 = 2 ( k + 9 ) ( 3 k - 6 ) + 9 = 2 k + 18 k = 15 p = 39 p + k = 54 the answer is d ."

add(subtract(multiply(add(negate(subtract(9, multiply(9, const_2))), subtract(multiply(3, 3), 3)), 3), subtract(multiply(3, 3), 3)), add(negate(subtract(9, multiply(9, const_2))), subtract(multiply(3, 3), 3)))

<gadget id="calculator">9 * 2</gadget>
<output>18</output>
<gadget id="calculator">9 - 18</gadget>
<output>-9</output>
<gadget id="calculator">-(-9)</gadget>
<output>9</output>
<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">9 - 3</gadget>
<output>6</output>
<gadget id="calculator">9 + 6</gadget>
<output>15</output>
<gadget id="calculator">15 * 3</gadget>
<output>45</output>
<gadget id="calculator">45 - 6</gadget>
<output>39</output>
<gadget id="calculator">39 + 15</gadget>
<output>54</output>
<result>54</result>


if soundharya rows 49 km upstream and 77 km down steam taking 7 hours each , then the speed of the stream

Explanation: speed upstream = 49 / 7 = 7 kmph speed down stream = 77 / 7 = 11 kmph speed of stream = ½ ( 11 - 7 ) = 2 kmph answer : c

divide(subtract(77, 49), multiply(7, const_2))

<gadget id="calculator">77 - 49</gadget>
<output>28</output>
<gadget id="calculator">7 * 2</gadget>
<output>14</output>
<gadget id="calculator">28 / 14</gadget>
<output>2</output>
<result>2</result>


the digital sum of a number is the sum of its digits . for how many of the positive integers 24 - 140 inclusive is the digital sum a multiple of 7 ?

Explanation: is there other way than just listing ? 25 34 43 52 59 61 68 70 77 86 95 106 115 124 133 15 ways . . d

<gadget id="calculator">24 - 7</gadget>
<output>17</output>
<gadget id="calculator">17 - 2</gadget>
<output>15</output>
<result>15</result>


20 beavers , working together in a constant pace , can build a dam in 6 hours . how many hours will it take 12 beavers that work at the same pace , to build the same dam ?

Explanation: "total work = 20 * 6 = 120 beaver hours 12 beaver * x = 120 beaver hours x = 120 / 12 = 10 answer : a"

<gadget id="calculator">6 * 20</gadget>
<output>120</output>
<gadget id="calculator">120 / 12</gadget>
<output>10</output>
<result>10</result>


if a student loses 6 kilograms , he will weigh twice as much as his sister . together they now weigh 126 kilograms . what is the student ' s present weight in kilograms ?

Explanation: "let x be the weight of the sister . then the student ' s weight is 2 x + 6 . x + ( 2 x + 6 ) = 126 3 x = 120 x = 40 kg then the student ' s weight is 86 kg . the answer is c ."

subtract(126, divide(subtract(126, 6), const_3))

<gadget id="calculator">126 - 6</gadget>
<output>120</output>
<gadget id="calculator">120 / 3</gadget>
<output>40</output>
<gadget id="calculator">126 - 40</gadget>
<output>86</output>
<result>86</result>


a person buys an article at rs . 575 . at what price should he sell the article so as to make a profit of 15 % ?

Explanation: "cost price = rs . 575 profit = 15 % of 575 = rs . 86.25 selling price = cost price + profit = 575 + 86.25 = 661.25 answer : d"

add(575, multiply(575, divide(15, const_100)))

<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">575 * (3/20)</gadget>
<output>345/4 = around 86.25</output>
<gadget id="calculator">575 + (345/4)</gadget>
<output>2_645/4 = around 661.25</output>
<result>2_645/4 = around 661.25</result>


two consultants can type up a report in 12.5 hours and edit it in 7.5 hours . if mary needs 30 hours to type the report and jim needs 12 hours to edit it alone , how many t hours will it take if jim types the report and mary edits it immediately after he is done ?

Explanation: "break down the problem into two pieces : typing and editing . mary needs 30 hours to type the report - - > mary ' s typing rate = 1 / 30 ( rate reciprocal of time ) ( point 1 in theory below ) ; mary and jim can type up a report in 12.5 and - - > 1 / 30 + 1 / x = 1 / 12.5 = 2 / 25 ( where x is the time needed for jim to type the report alone ) ( point 23 in theory below ) - - > x = 150 / 7 ; jim needs 12 hours to edit the report - - > jim ' s editing rate = 1 / 12 ; mary and jim can edit a report in 7.5 and - - > 1 / y + 1 / 12 = 1 / 7.5 = 2 / 15 ( where y is the time needed for mary to edit the report alone ) - - > y = 20 ; how many t hours will it take if jim types the report and mary edits it immediately after he is done - - > x + y = 150 / 7 + 20 = ~ 41.4 answer : a ."

add(inverse(subtract(divide(const_1, 12.5), divide(const_1, 30))), inverse(subtract(divide(const_1, 7.5), divide(const_1, 12))))

<gadget id="calculator">1 / 12.5</gadget>
<output>0.08</output>
<gadget id="calculator">1 / 30</gadget>
<output>1/30 = around 0.033333</output>
<gadget id="calculator">0.08 - (1/30)</gadget>
<output>0.046667</output>
<gadget id="calculator">1 / 0.046667</gadget>
<output>21.428418</output>
<gadget id="calculator">1 / 7.5</gadget>
<output>0.133333</output>
<gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">0.133333 - (1/12)</gadget>
<output>0.05</output>
<gadget id="calculator">1 / 0.05</gadget>
<output>20</output>
<gadget id="calculator">21.428418 + 20</gadget>
<output>41.428418</output>
<result>41.428418</result>


an amount of rs . 1638 was divided among a , b and c , in the ratio 1 / 2 : 1 / 3 : 1 / 4 . find the share of a ?

Explanation: let the shares of a , b and c be a , b and c respectively . a : b : c = 1 / 2 : 1 / 3 : 1 / 4 let us express each term with a common denominator which is the last number divisible by the denominators of each term i . e . , 12 . a : b : c = 6 / 12 : 4 / 12 : 3 / 12 = 6 : 4 : 3 . share of a = 6 / 13 * 1638 = rs . 756 answer : c

multiply(divide(1638, add(add(2, 3), 4)), 4)

<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">5 + 4</gadget>
<output>9</output>
<gadget id="calculator">1_638 / 9</gadget>
<output>182</output>
<gadget id="calculator">182 * 4</gadget>
<output>728</output>
<result>728</result>


in two triangles , the ratio of the areas is 4 : 3 and the ratio of their heights is 3 : 4 . find the ratio of their bases .

Explanation: sol . let the bases of the two triangles be x and y and their heights be 3 h and 4 h respectively . then , ( ( 1 / 2 ) x xx 3 h ) / ( 1 / 2 ) x y x 4 h ) = 4 / 3  x / y = ( 4 / 3 x 4 / 3 ) = 16 / 9 required ratio = 16 : 9 . ans : c

multiply(divide(4, 3), inverse(divide(3, 4)))

<gadget id="calculator">4 / 3</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">1 / (3/4)</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">(4/3) * (4/3)</gadget>
<output>16/9 = around 1.777778</output>
<result>16/9 = around 1.777778</result>


a trader sells 40 metres of cloth for rs . 8200 at a profit of rs . 15 per metre of cloth . how much profit will the trder earn on 40 metres of cloth ?

Explanation: "explanation : sp of 1 metre cloth = 8200 / 40 = rs . 205 . cp of 1 metre cloth = rs . 205 – 15 = rs . 190 cp on 40 metres = 190 x 40 = rs . 7600 profit earned on 40 metres cloth = rs . 8200 – rs . 7600 = rs . 600 . answer : option c"

<gadget id="calculator">15 * 40</gadget>
<output>600</output>
<result>600</result>


a thief goes away with a santro car at a speed of 50 kmph . the theft has been discovered after half an hour and the owner sets off in a bike at 60 kmph when will the owner over take the thief from the start ?

Explanation: "explanation : | - - - - - - - - - - - 20 - - - - - - - - - - - - - - - - - - - - | 60 50 d = 20 rs = 60 – 50 = 10 t = 20 / 10 = 2 hours answer : option a"

subtract(divide(multiply(divide(const_1, const_2), 50), subtract(60, 50)), divide(const_1, const_2))

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * 50</gadget>
<output>25</output>
<gadget id="calculator">60 - 50</gadget>
<output>10</output>
<gadget id="calculator">25 / 10</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">(5/2) - (1/2)</gadget>
<output>2</output>
<result>2</result>


the average weight of 18 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg . find the average weights of all the boys in the class .

Explanation: "explanation : average weight of 18 boys = 50.25 total weight of 18 boys = 50.25 × 18 average weight of remaining 8 boys = 45.15 total weight of remaining 8 boys = 45.15 × 8 total weight of all boys in the class = ( 50.25 × 18 ) + ( 45.15 × 8 ) total boys = 18 + 8 = 26 average weight of all the boys = ( 50.25 × 18 ) + ( 45.15 × 8 ) / 26 = 48.68077 answer : option a"

<gadget id="calculator">18 * 50.25</gadget>
<output>904.5</output>
<gadget id="calculator">8 * 45.15</gadget>
<output>361.2</output>
<gadget id="calculator">904.5 + 361.2</gadget>
<output>1_265.7</output>
<gadget id="calculator">18 + 8</gadget>
<output>26</output>
<gadget id="calculator">1_265.7 / 26</gadget>
<output>48.680769</output>
<result>48.680769</result>


the ratio of the area of a square to that of the square drawn on its diagonal is

Explanation: answer : a ) 1 : 2

<gadget id="calculator">2 ** (1/2)</gadget>
<output>sqrt(2) = around 1.414214</output>
<gadget id="calculator">1 / (sqrt(2))</gadget>
<output>sqrt(2)/2 = around 0.707107</output>
<gadget id="calculator">(sqrt(2)/2) ** 2</gadget>
<output>1/2 = around 0.5</output>
<result>1/2 = around 0.5</result>


a 4 digit number divisible by 7 becomes divisible by 3 when 19 is added to it . the largest such number is :

Explanation: out of all the 5 options , only 4487 is not divisible by 3 . all others are divisible so answer = d ( no further calculation required ) addition of any two non - divisible numbers by 3 gives the resultant divisible by 3 19 is non - divisible by 3 ; we are adding a number to that so that the resultant becomes divisible by 3 applying the above rule , it means that the number which we are going to add should be non - divisible by 3 so comes the answer = 4487 answer : d

add(multiply(multiply(multiply(4, 7), multiply(3, 19)), const_2), subtract(multiply(multiply(4, 7), multiply(3, 19)), multiply(const_2, const_100)))

<gadget id="calculator">4 * 7</gadget>
<output>28</output>
<gadget id="calculator">3 * 19</gadget>
<output>57</output>
<gadget id="calculator">28 * 57</gadget>
<output>1_596</output>
<gadget id="calculator">1_596 * 2</gadget>
<output>3_192</output>
<gadget id="calculator">2 * 100</gadget>
<output>200</output>
<gadget id="calculator">1_596 - 200</gadget>
<output>1_396</output>
<gadget id="calculator">3_192 + 1_396</gadget>
<output>4_588</output>
<result>4_588</result>


what is the probability for a family with 3 children to have a girl and two boys ( assuming the probability of having a boy or a girl is equal ) ?

Explanation: one possible case is : girl - boy - boy the probability of this is 1 / 2 * 1 / 2 * 1 / 2 = 1 / 8 there are 3 c 2 = 3 such cases so we should multiply by 3 . p ( one girl and two boys ) = 3 / 8 the answer is d .

divide(subtract(const_1, multiply(power(divide(const_1, const_2), 3), const_2)), const_2)

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) ** 3</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">(1/8) * 2</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 - (1/4)</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(3/4) / 2</gadget>
<output>3/8 = around 0.375</output>
<result>3/8 = around 0.375</result>


a manufacturer produces a certain men ' s athletic shoe in integer sizes from 8 to 17 . for this particular shoe , each unit increase in size corresponds to a 1 / 5 - inch increase in the length of the shoe . if the largest size of this shoe is 30 % longer than the smallest size , how long , in inches , is the shoe in size 15 ?

Explanation: "let x be the length of the size 8 shoe . then 0.3 x = 9 / 5 x = 90 / 15 = 6 inches the size 15 shoe has a length of 6 + 7 / 5 = 7.4 inches the answer is b ."

add(divide(multiply(divide(1, 5), subtract(17, 8)), divide(30, const_100)), multiply(subtract(15, 8), divide(1, 5)))

<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">17 - 8</gadget>
<output>9</output>
<gadget id="calculator">(1/5) * 9</gadget>
<output>9/5 = around 1.8</output>
<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(9/5) / (3/10)</gadget>
<output>6</output>
<gadget id="calculator">15 - 8</gadget>
<output>7</output>
<gadget id="calculator">7 * (1/5)</gadget>
<output>7/5 = around 1.4</output>
<gadget id="calculator">6 + (7/5)</gadget>
<output>37/5 = around 7.4</output>
<result>37/5 = around 7.4</result>


a 240 m long train running at the speed of 120 km / hr crosses another train running in opposite direction at the speed of 80 km / hr in 9 sec . what is the length of the other train ?

Explanation: "relative speed = 120 + 80 = 200 km / hr . = 200 * 5 / 18 = 500 / 9 m / sec . let the length of the other train be x m . then , ( x + 240 ) / 9 = 500 / 9 = > x = 260 . answer : option a"

subtract(multiply(multiply(add(120, 80), const_0_2778), 9), 240)

<gadget id="calculator">120 + 80</gadget>
<output>200</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">200 * (5/18)</gadget>
<output>500/9 = around 55.555556</output>
<gadget id="calculator">(500/9) * 9</gadget>
<output>500</output>
<gadget id="calculator">500 - 240</gadget>
<output>260</output>
<result>260</result>


34 . the side surface of a cylinder is rolled with a rectangular plate . if the perimeter of the circular base is 9 feet , and the diagonal of the rectangular plate was 15 ft . what is height of the of the cylinder ?

Explanation: think of a pringles can . if you took off the bottom and top and cut a slit down the length , it would flatten to a rectangle . the dimensions of the rectangle are the height of the can and the circumference of the circle . since you know both , one side and thehypothenuse use pythagoreans theorem or properties of 3 - 4 - 5 triangles to solve for the other side , 12 . correct answer a

sqrt(subtract(power(15, const_2), power(9, const_2)))

<gadget id="calculator">15 ** 2</gadget>
<output>225</output>
<gadget id="calculator">9 ** 2</gadget>
<output>81</output>
<gadget id="calculator">225 - 81</gadget>
<output>144</output>
<gadget id="calculator">144 ** (1/2)</gadget>
<output>12</output>
<result>12</result>


what quantity of water should be added to reduce 9 liters of 50 % acidic liquid to 30 % acidic liquid ?

Explanation: acid in 9 liters = 50 % of 9 = 4.5 liters suppose x liters of water be added . then 4.5 liters of acid in 9 + x liters of diluted solution 30 % of 9 + x = 4.5 27 + 3 x = 45 x = 6 liters answer is a

subtract(divide(multiply(multiply(9, divide(50, const_100)), const_100), 30), 9)

<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">9 * (1/2)</gadget>
<output>9/2 = around 4.5</output>
<gadget id="calculator">(9/2) * 100</gadget>
<output>450</output>
<gadget id="calculator">450 / 30</gadget>
<output>15</output>
<gadget id="calculator">15 - 9</gadget>
<output>6</output>
<result>6</result>


the average weight of 20 persons sitting in a boat had some value . a new person added to them whose weight was 46 kg only . due to his arrival , the average weight of all the persons decreased by 5 kg . find the average weight of first 20 persons ?

Explanation: "20 x + 46 = 21 ( x – 5 ) x = 59 answer : e"

subtract(multiply(add(20, const_1), 5), 46)

<gadget id="calculator">20 + 1</gadget>
<output>21</output>
<gadget id="calculator">21 * 5</gadget>
<output>105</output>
<gadget id="calculator">105 - 46</gadget>
<output>59</output>
<result>59</result>


a and b can together finish a work in 40 days . they worked together for 10 days and then b left . after another 18 days , a finished the remaining work . in how many days a alone can finish the job ?

Explanation: a + b 10 days work = 10 * 1 / 40 = 1 / 4 remaining work = 1 - 1 / 4 = 3 / 4 3 / 4 work is done by a in 18 days whole work will be done by a in 18 * 4 / 3 = 24 days answer is b

divide(multiply(18, 40), subtract(40, 10))

<gadget id="calculator">18 * 40</gadget>
<output>720</output>
<gadget id="calculator">40 - 10</gadget>
<output>30</output>
<gadget id="calculator">720 / 30</gadget>
<output>24</output>
<result>24</result>


a student gets 55 % in one subject , 65 % in the other . to get an overall of 55 % how much should get in third subject .

Explanation: "let the 3 rd subject % = x 55 + 65 + x = 3 * 55 120 + x = 165 x = 165 - 120 = 45 answer : c"

subtract(multiply(55, const_3), add(55, 65))

<gadget id="calculator">55 * 3</gadget>
<output>165</output>
<gadget id="calculator">55 + 65</gadget>
<output>120</output>
<gadget id="calculator">165 - 120</gadget>
<output>45</output>
<result>45</result>


in an election between two candidates , the winner has a margin of 10 % of the votes polled . if 4000 people change their mind and vote for the loser , the loser would have won by a margin of 10 % of the votes polled . find the total number of votes polled in the election ?

Explanation: "winner - looser 55 % - 45 % if 4000 people change their mind and vote for the loser : winner - looser 45 % - 55 % thus 4,000 people compose 25 % of all voters , which means that the total number of votes is 40,000 answer : c"

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">4_000 / (1/10)</gadget>
<output>40_000</output>
<result>40_000</result>


there are 28 stations between ernakulam and chennai . how many second class tickets have to be printed , so that a passenger can travel from one station to any other station ?

Explanation: "the total number of stations = 30 from 30 stations we have to choose any two stations and the direction of travel ( ernakulam to chennai is different from chennai to ernakulam ) in 30 p 2 ways . 30 p 2 = 30 * 29 = 870 answer : d"

multiply(add(28, const_2), subtract(add(28, const_2), const_1))

<gadget id="calculator">28 + 2</gadget>
<output>30</output>
<gadget id="calculator">30 - 1</gadget>
<output>29</output>
<gadget id="calculator">30 * 29</gadget>
<output>870</output>
<result>870</result>


the wages earned by robin is 40 % more than that earned by erica . the wages earned by charles is 60 % more than that earned by erica . how much percent is the wages earned by charles more than that earned by robin ?

Explanation: "let wage of erica = 10 wage of robin = 1.4 * 10 = 14 wage of charles = 1.6 * 10 = 16 percentage by which wage earned by charles is more than that earned by robin = ( 16 - 14 ) / 14 * 100 % = 2 / 14 * 100 % = 14 % answer a"

multiply(divide(subtract(add(const_100, 60), add(const_100, 40)), add(const_100, 40)), const_100)

<gadget id="calculator">100 + 60</gadget>
<output>160</output>
<gadget id="calculator">100 + 40</gadget>
<output>140</output>
<gadget id="calculator">160 - 140</gadget>
<output>20</output>
<gadget id="calculator">20 / 140</gadget>
<output>1/7 = around 0.142857</output>
<gadget id="calculator">(1/7) * 100</gadget>
<output>100/7 = around 14.285714</output>
<result>100/7 = around 14.285714</result>


25 is subtracted from 75.00001 % of a number , the result is 50 . find the number ?

Explanation: "( 75 / 100 ) * x â € “ 25 = 50 7.5 x = 750 x = 100 answer : e"

<gadget id="calculator">25 + 50</gadget>
<output>75</output>
<gadget id="calculator">75.00001 / 100</gadget>
<output>0.75</output>
<gadget id="calculator">75 / 0.75</gadget>
<output>100</output>
<result>100</result>


half a number plus 7 is 11 . what is the number ?

Explanation: "let x be the number . always replace ` ` is ' ' with an equal sign ( 1 / 2 ) x + 7 = 11 ( 1 / 2 ) x = 11 - 7 ( 1 / 2 ) x = 4 x = 8 correct answer is a"

<gadget id="calculator">11 - 7</gadget>
<output>4</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<result>8</result>


of the total amount that jill spent on a shopping trip , excluding taxes , she spent 25 percent on clothing , 25 percent on food , and 50 percent on other items . if jill paid a 10 percent tax on the clothing , no tax on the food , and an 2 percent tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ?

Explanation: "assume she has $ 200 to spend . tax clothing = 25 % = $ 50 = $ 5 food = 25 % = $ 50 = $ 0.00 items = 50 % = $ 100 = $ 2.00 total tax = $ 20.00 % of total amount = 7 / 200 * 100 = 3.5 % answer d"

multiply(divide(add(multiply(25, divide(10, const_100)), multiply(50, divide(2, const_100))), const_100), const_100)

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">25 * (1/10)</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">2 / 100</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">50 * (1/50)</gadget>
<output>1</output>
<gadget id="calculator">(5/2) + 1</gadget>
<output>7/2 = around 3.5</output>
<gadget id="calculator">(7/2) / 100</gadget>
<output>7/200 = around 0.035</output>
<gadget id="calculator">(7/200) * 100</gadget>
<output>7/2 = around 3.5</output>
<result>7/2 = around 3.5</result>


in a certain pond , 55 fish were caught , tagged , and returned to the pond . a few days later , 55 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what ` s the approximate number of fish in the pond ?

Explanation: "the percent of tagged fish in the second catch is 2 / 55 * 100 = 3.64 % . we are told that 3.64 % approximates the percent of tagged fish in the pond . since there are 55 tagged fish , then we have 0.036 x = 55 - - > x = 1,528 . answer : d ."

<gadget id="calculator">2 / 55</gadget>
<output>2/55 = around 0.036364</output>
<gadget id="calculator">55 / (2/55)</gadget>
<output>3_025/2 = around 1_512.5</output>
<result>3_025/2 = around 1_512.5</result>


how many 1 / 6 s are there in 37 1 / 2 ?

Explanation: required number = ( 75 / 2 ) / ( 1 / 6 ) = ( 75 / 2 x 6 / 1 ) = 225 . answer : a

divide(add(37, divide(1, 2)), divide(1, 6))

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">37 + (1/2)</gadget>
<output>75/2 = around 37.5</output>
<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(75/2) / (1/6)</gadget>
<output>225</output>
<result>225</result>


the ratio between the present ages of a and b is 7 : 3 respectively . the ratio between a ' s age 4 years ago and b ' s age 4 years hence is 1 : 1 . what is the ratio between a ' s age 4 years hence and b ' s age 4 years ago ?

Explanation: "let the present ages of a and b be 7 x and 3 x years respectively . then , ( 7 x - 4 ) / ( 3 x + 4 ) = 1 / 1 4 x = 8 = > x = 2 required ratio = ( 5 x + 4 ) : ( 3 x - 4 ) = 18 : 2 = 9 : 1 . answer : c"

divide(add(multiply(7, divide(add(7, 7), subtract(7, 3))), 7), subtract(multiply(3, divide(add(7, 7), subtract(7, 3))), 7))

<gadget id="calculator">7 + 7</gadget>
<output>14</output>
<gadget id="calculator">7 - 3</gadget>
<output>4</output>
<gadget id="calculator">14 / 4</gadget>
<output>7/2 = around 3.5</output>
<gadget id="calculator">7 * (7/2)</gadget>
<output>49/2 = around 24.5</output>
<gadget id="calculator">(49/2) + 7</gadget>
<output>63/2 = around 31.5</output>
<gadget id="calculator">3 * (7/2)</gadget>
<output>21/2 = around 10.5</output>
<gadget id="calculator">(21/2) - 7</gadget>
<output>7/2 = around 3.5</output>
<gadget id="calculator">(63/2) / (7/2)</gadget>
<output>9</output>
<result>9</result>


two vessels contains equal number of mixtures milk and water in the ratio 3 : 2 and 4 : 1 . both the mixtures are now mixed thoroughly . find the ratio of milk to water in the new mixture so obtained ?

Explanation: "the ratio of milk and water in the new vessel is = ( 3 / 5 + 4 / 5 ) : ( 2 / 5 + 1 / 5 ) = 7 / 5 : 3 / 5 = 7 : 3 answer is d"

divide(add(multiply(3, divide(add(4, 1), add(3, 2))), 4), add(multiply(2, divide(add(4, 1), add(3, 2))), 1))

<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">5 / 5</gadget>
<output>1</output>
<gadget id="calculator">3 * 1</gadget>
<output>3</output>
<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">2 * 1</gadget>
<output>2</output>
<gadget id="calculator">2 + 1</gadget>
<output>3</output>
<gadget id="calculator">7 / 3</gadget>
<output>7/3 = around 2.333333</output>
<result>7/3 = around 2.333333</result>


if sharon ' s weekly salary increased by 15 percent , she would earn $ 460 per week . if instead , her weekly salary were to increase by 10 percent , how much would she earn per week ?

Explanation: soln : - 460 / 115 ) 110 = 385 in this case long division does not take much time . ( 4 / 1 ) 110 = rs . 440 answer : b

add(divide(460, add(const_1, divide(15, const_100))), multiply(divide(10, const_100), divide(460, add(const_1, divide(15, const_100)))))

<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">1 + (3/20)</gadget>
<output>23/20 = around 1.15</output>
<gadget id="calculator">460 / (23/20)</gadget>
<output>400</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) * 400</gadget>
<output>40</output>
<gadget id="calculator">400 + 40</gadget>
<output>440</output>
<result>440</result>


a fruit seller had some oranges . he sells 10 % oranges and still has 360 oranges . how many oranges he had originally ?

Explanation: "explanation : he sells 10 % of oranges and still there are 360 oranges remaining = > 90 % of oranges = 360 ⇒ ( 90 × total oranges ) / 100 = 360 ⇒ total oranges / 100 = 4 ⇒ total oranges = 4 × 100 = 400 answer : option d"

add(360, multiply(360, divide(10, const_100)))

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">360 * (1/10)</gadget>
<output>36</output>
<gadget id="calculator">360 + 36</gadget>
<output>396</output>
<result>396</result>


because he ’ s taxed by his home planet , mork pays a tax rate of 40 % on his income , while mindy pays a rate of only 20 % on hers . if mindy earned 4 times as much as mork did , what was their combined tax rate ?

Explanation: "say morks income is - 100 so tax paid will be 40 say mindys income is 4 * 100 = 400 so tax paid is 20 % * 400 = 80 total tax paid = 40 + 80 = 120 . combined tax % will be 120 / 100 + 400 = 24 %"

multiply(const_100, divide(add(divide(40, const_100), multiply(4, divide(20, const_100))), add(const_1, 4)))

<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">4 * (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(2/5) + (4/5)</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">(6/5) / 5</gadget>
<output>6/25 = around 0.24</output>
<gadget id="calculator">100 * (6/25)</gadget>
<output>24</output>
<result>24</result>


it is the new year and mandy has made a resolution to lose weight this year . she plans to exercise and do yoga . for exercise she plans to workout at the gym and ride her bicycle in the ratio of 2 : 3 everyday . she will also do yoga in the ratio , yoga : exercise = 2 : 3 . if she rides her bike for 10 minutes , how much time will she spend doing yoga ? ( rounded to minutes )

Explanation: "the ratio is 2 : 3 = gym : ride , so ( 10 ) ( 3 / 2 ) = 15 minutes at the gym , and 15 + 10 = 25 minutes exercise , so ( 2 / 3 ) ( 25 ) = 17 minutes yoga . answer : c"

divide(multiply(10, divide(3, add(2, 3))), multiply(divide(3, add(2, 3)), divide(3, add(2, 3))))

<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">10 * (3/5)</gadget>
<output>6</output>
<gadget id="calculator">(3/5) * (3/5)</gadget>
<output>9/25 = around 0.36</output>
<gadget id="calculator">6 / (9/25)</gadget>
<output>50/3 = around 16.666667</output>
<result>50/3 = around 16.666667</result>


the length of the bridge , which a train 180 metres long and travelling at 45 km / hr can cross in 30 seconds , is ?

Explanation: "speed = [ 45 x 5 / 18 ] m / sec = [ 25 / 2 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 180 + x ) / 30 = 25 / 2 = > 2 ( 180 + x ) = 750 = > x = 195 m . answer : c"

subtract(multiply(divide(multiply(45, speed(const_1000, const_1)), speed(const_3600, const_1)), 30), 180)

<gadget id="calculator">1_000 / 1</gadget>
<output>1_000</output>
<gadget id="calculator">45 * 1_000</gadget>
<output>45_000</output>
<gadget id="calculator">3_600 / 1</gadget>
<output>3_600</output>
<gadget id="calculator">45_000 / 3_600</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">(25/2) * 30</gadget>
<output>375</output>
<gadget id="calculator">375 - 180</gadget>
<output>195</output>
<result>195</result>


the difference of 2 digit number & the number obtained by interchanging the digits is 36 . what is the difference the sum and the number if the ratio between the digits of the number is 1 : 2 ?

Explanation: let the number be xy . given xy – yx = 36 . this means the number is greater is than the number got on reversing the digits . this shows that the ten ’ s digit x > unit digit y . also given ratio between digits is 1 : 2 = > x = 2 y ( 10 x + y ) – ( 10 y + x ) = 36 = > x – y = 4 = > 2 y – y = 4 . hence , ( x + y ) – ( x – y ) = 3 y – y = 2 y = 8 b

multiply(divide(36, subtract(multiply(subtract(const_10, const_1), multiply(2, const_1)), subtract(const_10, const_1))), const_2)

<gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">2 * 1</gadget>
<output>2</output>
<gadget id="calculator">9 * 2</gadget>
<output>18</output>
<gadget id="calculator">18 - 9</gadget>
<output>9</output>
<gadget id="calculator">36 / 9</gadget>
<output>4</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<result>8</result>


at the faculty of aerospace engineering , 312 students study random - processing methods , 232 students study scramjet rocket engines and 112 students study them both . if every student in the faculty has to study one of the two subjects , how many students are there in the faculty of aerospace engineering ?

Explanation: "students studying random - processing methods = 312 students studying scramjet rocket engines = 232 students studying them both = 112 therefore ; students studying only random processing methods = 312 - 112 = 200 students studying only scramjet rocket engines = 232 - 112 = 120 students studying both = 112 students studying none = 0 ( as mentioned in question that every student in the faculty has to study one of the two subjects ) total students in faculty of aerospace engineering = students of only random processing methods + students of only scramjet rocket engines + both + none total number of students = 200 + 120 + 112 + 0 = 432 . . . . answer d"

add(subtract(312, divide(112, const_2)), subtract(232, divide(112, const_2)))

<gadget id="calculator">112 / 2</gadget>
<output>56</output>
<gadget id="calculator">312 - 56</gadget>
<output>256</output>
<gadget id="calculator">232 - 56</gadget>
<output>176</output>
<gadget id="calculator">256 + 176</gadget>
<output>432</output>
<result>432</result>


if n = 2 ^ 0.20 and n ^ b = 16 , b must equal

Explanation: "20 / 100 = 1 / 5 n = 2 ^ 1 / 5 n ^ b = 2 ^ 4 ( 2 ^ 1 / 5 ) ^ b = 2 ^ 4 b = 20 answer : c"

<gadget id="calculator">log(16)</gadget>
<output>log(16) = around 2.772589</output>
<gadget id="calculator">2 ** 0.2</gadget>
<output>1.148698</output>
<gadget id="calculator">log(1.148698)</gadget>
<output>0.138629</output>
<gadget id="calculator">log(16) / 0.138629</gadget>
<output>7.21349789726536*log(16) = around 20.000063</output>
<result>7.21349789726536*log(16) = around 20.000063</result>


a man buys an item at rs . 800 and sells it at the loss of 20 percent . then what is the selling price of that item

Explanation: "explanation : here always remember , when ever x % loss , it means s . p . = ( 100 - x ) % of c . p when ever x % profit , it means s . p . = ( 100 + x ) % of c . p so here will be ( 100 - x ) % of c . p . = 80 % of 800 = 80 / 100 * 800 = 640 option a"

multiply(800, subtract(const_1, divide(20, const_100)))

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">800 * (4/5)</gadget>
<output>640</output>
<result>640</result>


find the expenditure on digging a well 14 m deep and of 3 m diameter at rs . 14 per cubic meter ?

Explanation: "22 / 7 * 14 * 3 / 2 * 3 / 2 = 99 m 2 99 * 14 = 1386 answer : a"

multiply(volume_cylinder(divide(3, const_2), 14), 14)

<gadget id="calculator">3 / 2</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">pi * ((3/2) ** 2) * 14</gadget>
<output>63*pi/2 = around 98.960169</output>
<gadget id="calculator">(63*pi/2) * 14</gadget>
<output>441*pi = around 1_385.44236</output>
<result>441*pi = around 1_385.44236</result>


rani bought more apples than oranges . she sells apples at ₹ 23 apiece and makes 15 % profit . she sells oranges at ₹ 10 apiece and makes 25 % profit . if she gets ₹ 653 after selling all the apples and oranges , find her profit percentage z .

Explanation: "given : selling price of an apple = 23 - - > cost price = 23 / 1.15 = 20 selling price of an orange = 10 - - > cost price = 10 / 1.25 = 8 a > o 23 * ( a ) + 10 * ( o ) = 653 653 - 23 * ( a ) has to be divisible by 10 - - > units digit has to be 0 values of a can be 1 , 11 , 21 , 31 , . . . . - - > 1 can not be the value between 11 and 21 , if a = 11 , o = 30 - - > not possible if a = 21 , o = 17 - - > possible cost price = 20 * 21 + 8 * 17 = 420 + 136 = 556 profit = 653 - 556 = 97 profit % z = ( 97 / 556 ) * 100 = 17.4 % answer : b"

multiply(divide(subtract(653, add(multiply(multiply(const_2, 10), add(multiply(const_2, 10), const_1)), multiply(divide(10, add(divide(25, const_100), const_1)), add(15, const_2)))), add(multiply(multiply(const_2, 10), add(multiply(const_2, 10), const_1)), multiply(divide(10, add(divide(25, const_100), const_1)), add(15, const_2)))), const_100)

<gadget id="calculator">2 * 10</gadget>
<output>20</output>
<gadget id="calculator">20 + 1</gadget>
<output>21</output>
<gadget id="calculator">20 * 21</gadget>
<output>420</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) + 1</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">10 / (5/4)</gadget>
<output>8</output>
<gadget id="calculator">15 + 2</gadget>
<output>17</output>
<gadget id="calculator">8 * 17</gadget>
<output>136</output>
<gadget id="calculator">420 + 136</gadget>
<output>556</output>
<gadget id="calculator">653 - 556</gadget>
<output>97</output>
<gadget id="calculator">97 / 556</gadget>
<output>97/556 = around 0.17446</output>
<gadget id="calculator">(97/556) * 100</gadget>
<output>2_425/139 = around 17.446043</output>
<result>2_425/139 = around 17.446043</result>


if 8 men or 12 women can do a piece of work in 25 days , in how many days can the same work be done by 6 men and 11 women ?

Explanation: "8 men = 12 women ( i . e 2 men = 3 women ) 12 women 1 day work = 1 / 25 soln : 6 men ( 9 women ) + 11 women = 20 women = ? 1 women 1 day work = 12 * 25 = 1 / 300 so , 20 women work = 20 / 300 = 1 / 15 ans : 15 days answer : d"

inverse(add(divide(6, multiply(8, 25)), divide(11, multiply(12, 25))))

<gadget id="calculator">8 * 25</gadget>
<output>200</output>
<gadget id="calculator">6 / 200</gadget>
<output>3/100 = around 0.03</output>
<gadget id="calculator">12 * 25</gadget>
<output>300</output>
<gadget id="calculator">11 / 300</gadget>
<output>11/300 = around 0.036667</output>
<gadget id="calculator">(3/100) + (11/300)</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">1 / (1/15)</gadget>
<output>15</output>
<result>15</result>


a train 140 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train . find the speed of the train .

Explanation: "explanation : let the speed of the train be x kmph . speed of the train relative to man = ( x + 5 ) kmph = ( x + 5 ) × 5 / 18 m / sec . therefore 140 / ( ( x + 5 ) × 5 / 18 ) = 6 < = > 30 ( x + 5 ) = 2520 < = > x = 79 speed of the train is 79 kmph . answer : option e"

subtract(divide(140, multiply(6, const_0_2778)), 5)

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">6 * (5/18)</gadget>
<output>5/3 = around 1.666667</output>
<gadget id="calculator">140 / (5/3)</gadget>
<output>84</output>
<gadget id="calculator">84 - 5</gadget>
<output>79</output>
<result>79</result>


find the average of all the number between 6 and 34 which are divisible by 5 .

Explanation: "solution average = ( 10 + 15 + 20 + 25 + 30 / 5 ) = 100 / 2 = 20 answer b"

divide(add(add(6, const_4), subtract(34, const_4)), const_2)

<gadget id="calculator">6 + 4</gadget>
<output>10</output>
<gadget id="calculator">34 - 4</gadget>
<output>30</output>
<gadget id="calculator">10 + 30</gadget>
<output>40</output>
<gadget id="calculator">40 / 2</gadget>
<output>20</output>
<result>20</result>


if the wheel is 14 cm then the number of revolutions to cover a distance of 880 cm is ?

Explanation: "2 * 22 / 7 * 14 * x = 880 = > x = 10 answer : b"

divide(880, multiply(multiply(const_2, divide(add(add(multiply(const_3, const_100), multiply(const_1, const_10)), const_4), const_100)), 14))

<gadget id="calculator">3 * 100</gadget>
<output>300</output>
<gadget id="calculator">1 * 10</gadget>
<output>10</output>
<gadget id="calculator">300 + 10</gadget>
<output>310</output>
<gadget id="calculator">310 + 4</gadget>
<output>314</output>
<gadget id="calculator">314 / 100</gadget>
<output>157/50 = around 3.14</output>
<gadget id="calculator">2 * (157/50)</gadget>
<output>157/25 = around 6.28</output>
<gadget id="calculator">(157/25) * 14</gadget>
<output>2_198/25 = around 87.92</output>
<gadget id="calculator">880 / (2_198/25)</gadget>
<output>11_000/1_099 = around 10.009099</output>
<result>11_000/1_099 = around 10.009099</result>


a and b can do a piece of work in 7 days , b and c in 8 days , c and a in 9 days . how long will c take to do it ?

Explanation: "2 c = 1 / 8 + 1 / 9 – 1 / 7 = 47 / 504 c = 47 / 1008 = > 1008 / 47 = 21.4 days the answer is c ."

divide(multiply(7, const_3), subtract(divide(add(divide(multiply(7, const_3), 9), add(divide(multiply(7, const_3), 7), divide(multiply(7, const_3), 8))), const_2), divide(multiply(7, const_3), 7)))

<gadget id="calculator">7 * 3</gadget>
<output>21</output>
<gadget id="calculator">21 / 9</gadget>
<output>7/3 = around 2.333333</output>
<gadget id="calculator">21 / 7</gadget>
<output>3</output>
<gadget id="calculator">21 / 8</gadget>
<output>21/8 = around 2.625</output>
<gadget id="calculator">3 + (21/8)</gadget>
<output>45/8 = around 5.625</output>
<gadget id="calculator">(7/3) + (45/8)</gadget>
<output>191/24 = around 7.958333</output>
<gadget id="calculator">(191/24) / 2</gadget>
<output>191/48 = around 3.979167</output>
<gadget id="calculator">(191/48) - 3</gadget>
<output>47/48 = around 0.979167</output>
<gadget id="calculator">21 / (47/48)</gadget>
<output>1_008/47 = around 21.446809</output>
<result>1_008/47 = around 21.446809</result>


oil cans x and y are right circular cylinders and the height and radius of y are each 5 times those of x . if the oil in can x filled to capacity sells for $ 1 , how much does the oil in y sell for if y is only 1 / 5 th filled ?

Explanation: "formula for vol of a cyl is pi * r ^ 2 * h so vy = 125 * vy y when half filled will cost 25 times x so ans is a"

<gadget id="calculator">5 ** 1</gadget>
<output>5</output>
<gadget id="calculator">5 * 5</gadget>
<output>25</output>
<result>25</result>


car x began traveling at an average speed of 35 miles per hour . after 36 minutes , car y began traveling at an average speed of 38 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ?

Explanation: "in 36 minutes , car x travels 21 miles . car y gains 3 miles each hour , so it takes 7 hours to catch car x . in 7 hours , car x travels 245 miles . the answer is e ."

multiply(35, divide(multiply(divide(36, const_60), 35), subtract(38, 35)))

<gadget id="calculator">36 / 60</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(3/5) * 35</gadget>
<output>21</output>
<gadget id="calculator">38 - 35</gadget>
<output>3</output>
<gadget id="calculator">21 / 3</gadget>
<output>7</output>
<gadget id="calculator">35 * 7</gadget>
<output>245</output>
<result>245</result>


cindy has her eye on a sundress but thinks it is too expensive . it goes on sale for 15 % less than the original price . before cindy can buy the dress , however , the store raises the new price by 25 % . if the dress cost $ 51 after it went on sale for 15 % off , what is the difference between the original price and the final price ?

Explanation: "0.85 * { original price } = $ 51 - - > { original price } = $ 60 . { final price } = $ 51 * 1.25 = $ 63.75 . the difference = $ 63.75 - 60 $ = $ 3.75 . answer : c ."

subtract(multiply(51, divide(add(const_100, 25), const_100)), divide(51, divide(subtract(const_100, 15), const_100)))

<gadget id="calculator">100 + 25</gadget>
<output>125</output>
<gadget id="calculator">125 / 100</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">51 * (5/4)</gadget>
<output>255/4 = around 63.75</output>
<gadget id="calculator">100 - 15</gadget>
<output>85</output>
<gadget id="calculator">85 / 100</gadget>
<output>17/20 = around 0.85</output>
<gadget id="calculator">51 / (17/20)</gadget>
<output>60</output>
<gadget id="calculator">(255/4) - 60</gadget>
<output>15/4 = around 3.75</output>
<result>15/4 = around 3.75</result>


2 trains starting at the same time from 2 stations 200 km apart and going in opposite direction cross each other at a distance of 110 km from one of the stations . what is the ratio of their speeds ?

Explanation: in same time , they cover 110 km & 90 km respectively so ratio of their speed = 110 : 90 = 11 : 9 answer : a

<gadget id="calculator">200 - 110</gadget>
<output>90</output>
<gadget id="calculator">90 / 110</gadget>
<output>9/11 = around 0.818182</output>
<gadget id="calculator">1 / (9/11)</gadget>
<output>11/9 = around 1.222222</output>
<result>11/9 = around 1.222222</result>


a grocer has a sale of rs . 4435 , rs . 4927 , rs . 4855 , rs . 5230 and rs . 4562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 4500 ?

Explanation: "total sale for 5 months = rs . ( 4435 + 4927 + 4855 + 5230 + 4562 ) = rs . 24009 . required sale = rs . [ ( 4500 x 6 ) - 24009 ] = rs . ( 27000 - 24009 ) = rs . 2991 answer : option b"

<gadget id="calculator">5 + 1</gadget>
<output>6</output>
<gadget id="calculator">6 * 4_500</gadget>
<output>27_000</output>
<gadget id="calculator">4_435 + 4_927</gadget>
<output>9_362</output>
<gadget id="calculator">9_362 + 4_855</gadget>
<output>14_217</output>
<gadget id="calculator">14_217 + 5_230</gadget>
<output>19_447</output>
<gadget id="calculator">19_447 + 4_562</gadget>
<output>24_009</output>
<gadget id="calculator">27_000 - 24_009</gadget>
<output>2_991</output>
<result>2_991</result>


what is the sum of all 3 digit integers formed using the digits 34 and 5 ( repetition is allowed )

Explanation: n = 3 * 3 * 3 = 27 = ( 555 + 333 ) / 2 = 444 sum = number of integers x average value n * = 27 * 444 = 11988 answer = d

multiply(multiply(add(add(const_100, const_10), const_1), add(add(3, 5), const_4)), power(const_3, const_2))

<gadget id="calculator">100 + 10</gadget>
<output>110</output>
<gadget id="calculator">110 + 1</gadget>
<output>111</output>
<gadget id="calculator">3 + 5</gadget>
<output>8</output>
<gadget id="calculator">8 + 4</gadget>
<output>12</output>
<gadget id="calculator">111 * 12</gadget>
<output>1_332</output>
<gadget id="calculator">3 ** 2</gadget>
<output>9</output>
<gadget id="calculator">1_332 * 9</gadget>
<output>11_988</output>
<result>11_988</result>


two men are going along a track rail in the opposite direction . one goods train crossed the first person in 20 sec . after 10 min the train crossed the other person who is coming in opposite direction in 18 sec . after the train has passed , when the two persons will meet ?

Explanation: explanation : let us consider that speed of train , first man and second man are respectively t , f and s . according to first given condition goods train crossed the first person moving in same direction in 20 sec . so length of the will be 20 ( t - f ) similarly train crossed the second man in 18 sec . so length of the train will be 18 ( t + s ) on comparing these two equations , we get 20 ( t - f ) = 18 ( t + s ) = > 2 t = 20 f + 18 s = > t = 10 f + 9 s now it is given that after 10 min the train crossed the other person who is coming in opposite direction . so , if we consider this way of train as l then the next equation will be l = 600 t ( here 600 is used for 10 minutes ) finally as asked in the question the time required to meet the two man after the train has passed will be given by time = ( l - 600 f ) / ( f + s ) { here 600 f is used for the distance traveled by first man in 10 minutes } = > = ( 600 t - 600 f ) / ( f + s ) = > = [ 600 ( 10 f + 9 s ) - 600 f ] / ( f + s ) = > = 600 ( 10 f + 9 s - f ) / ( f + s ) = 600 * 9 ( f + s ) / ( f + s ) = > = 600 * 9 seconds = > = 600 * 9 / 60 min = > = 90 minutes hence ( b ) is the correct answer . answer : b

divide(multiply(multiply(const_60, 10), divide(18, const_2)), const_60)

<gadget id="calculator">60 * 10</gadget>
<output>600</output>
<gadget id="calculator">18 / 2</gadget>
<output>9</output>
<gadget id="calculator">600 * 9</gadget>
<output>5_400</output>
<gadget id="calculator">5_400 / 60</gadget>
<output>90</output>
<result>90</result>


there are 6 people in the elevator . their average weight is 150 lbs . another person enters the elevator , and increases the average weight to 151 lbs . what is the weight of the 7 th person .

Explanation: "solution average of 7 people after the last one enters = 151 . â ˆ ´ required weight = ( 7 x 151 ) - ( 6 x 150 ) = 1057 - 900 = 157 . answer a"

subtract(multiply(151, 7), multiply(6, 150))

<gadget id="calculator">151 * 7</gadget>
<output>1_057</output>
<gadget id="calculator">6 * 150</gadget>
<output>900</output>
<gadget id="calculator">1_057 - 900</gadget>
<output>157</output>
<result>157</result>


average of money that group of 4 friends pay for rent each month is $ 800 . after one persons rent is increased by 20 % the new mean is $ 860 . what was original rent of friend whose rent is increased ?

Explanation: "0.2 x = 4 ( 860 - 800 ) 0.2 x = 240 x = 1200 answer e"

divide(multiply(subtract(860, 800), 4), divide(20, const_100))

<gadget id="calculator">860 - 800</gadget>
<output>60</output>
<gadget id="calculator">60 * 4</gadget>
<output>240</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">240 / (1/5)</gadget>
<output>1_200</output>
<result>1_200</result>


if 11.25 m of a uniform steel rod weighs 42.75 kg . what will be the weight of 10 m of the same rod ?

Explanation: "explanation : let the required weight be x kg . then , less length , less weight ( direct proportion ) = > 11.25 : 10 : : 42.75 : x = > 11.25 x x = 10 x 42.75 = > x = ( 10 x 42.75 ) / 11.25 = > x = 38 answer : a"

<gadget id="calculator">10 * 42.75</gadget>
<output>427.5</output>
<gadget id="calculator">427.5 / 11.25</gadget>
<output>38</output>
<result>38</result>


8 men can dig a pit in 20 days . if a man works half as much again a s a boy , then 4 men and 9 boys can dig a similar pit in :

Explanation: explanation : 1 work done = 8 × 20 1 man = 3 / 2 boys 1 boy = 2 / 3 men then , 9 boys = 9 × 2 / 3 men = 6 men then , 4 men + 9 boys = 10 men then , 8 × 20 = 10 × ? days ? days = 8 × 20 / 10 = 16 days . answer : option d

divide(multiply(multiply(8, divide(const_3, const_2)), 20), add(multiply(4, divide(const_3, const_2)), 9))

<gadget id="calculator">3 / 2</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">8 * (3/2)</gadget>
<output>12</output>
<gadget id="calculator">12 * 20</gadget>
<output>240</output>
<gadget id="calculator">4 * (3/2)</gadget>
<output>6</output>
<gadget id="calculator">6 + 9</gadget>
<output>15</output>
<gadget id="calculator">240 / 15</gadget>
<output>16</output>
<result>16</result>


john makes $ 40 a week from his job . he earns a raise and now makes $ 70 a week . what is the % increase ?

Explanation: "increase = ( 30 / 40 ) * 100 = ( 3 / 4 ) * 100 = 75 % . e"

multiply(divide(subtract(70, 40), 40), const_100)

<gadget id="calculator">70 - 40</gadget>
<output>30</output>
<gadget id="calculator">30 / 40</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(3/4) * 100</gadget>
<output>75</output>
<result>75</result>


a train is 410 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length

Explanation: "explanation : speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 410 + 140 = 550 meter time = distance / speed = 550 ∗ 2 / 25 = 44 seconds option b"

divide(add(410, 140), divide(multiply(45, const_1000), const_3600))

<gadget id="calculator">410 + 140</gadget>
<output>550</output>
<gadget id="calculator">45 * 1_000</gadget>
<output>45_000</output>
<gadget id="calculator">45_000 / 3_600</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">550 / (25/2)</gadget>
<output>44</output>
<result>44</result>


the average ( arithmetic mean ) of 4 positive integers is 50 . if the average of 2 of these integers is 40 , what is the greatest possible value that one of the other 2 integers can have ?

Explanation: "a + b + c + d = 200 a + b = 80 c + d = 120 greatest possible = 119 ( just less than 1 ) answer = c"

subtract(multiply(50, 4), multiply(40, 2))

<gadget id="calculator">50 * 4</gadget>
<output>200</output>
<gadget id="calculator">40 * 2</gadget>
<output>80</output>
<gadget id="calculator">200 - 80</gadget>
<output>120</output>
<result>120</result>


an uneducated retailer marks all his goods at 50 % above the cost price and thinking that he will still make 25 % profit , offers a discount of 25 % on the marked price . what is his actual profit on the sales ?

Explanation: "sol . let c . p . = rs . 100 . then , marked price = rs . 150 . s . p . = 75 % of rs . 150 = rs . 112.50 . ∴ gain % = 12.50 % . answer a"

multiply(subtract(subtract(add(const_1, divide(50, const_100)), multiply(add(const_1, divide(50, const_100)), divide(25, const_100))), const_1), const_100)

<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 + (1/2)</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(3/2) * (1/4)</gadget>
<output>3/8 = around 0.375</output>
<gadget id="calculator">(3/2) - (3/8)</gadget>
<output>9/8 = around 1.125</output>
<gadget id="calculator">(9/8) - 1</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">(1/8) * 100</gadget>
<output>25/2 = around 12.5</output>
<result>25/2 = around 12.5</result>


the mass of 1 cubic meter of a substance is 300 kg under certain conditions . what is the volume in cubic centimeters of 1 gram of this substance under these conditions ? ( 1 kg = 1,000 grams and 1 cubic meter = 1 , 000,000 cubic centimeters )

Explanation: "300 kg - 1 cubic meter ; 300,000 g - 1 cubic meter ; 300,000 g - 1 , 000,000 cubic centimeters ; 1 g - 1 , 000,000 / 300,000 = 10 / 3 = 3.33 cubic centimeters . answer : a ."

<gadget id="calculator">1_000 * 1_000</gadget>
<output>1_000_000</output>
<gadget id="calculator">300 * 1_000</gadget>
<output>300_000</output>
<gadget id="calculator">1_000_000 / 300_000</gadget>
<output>10/3 = around 3.333333</output>
<result>10/3 = around 3.333333</result>


a dishonest person wants to make a profit on the selling of milk . he would like to mix water ( costing nothing ) with milk costing 33 $ per litre so as to make a profit of 50 % on cost when he sells the resulting milk and water mixture for 36 $ . in what ratio should he mix the water and milk ?

Explanation: "first of all , let ' s consider 1 liter of the stuff he is going to sell - - - naive customers think it ' s pure milk , but we know it ' s some milk - water mixture . he is going to sell this liter of milk - water for $ 36 . this $ 36 should be a 50 % increase over cost . here , we need to think about percentage increases as multipliers . using multipliers ( cost ) * 1.50 = $ 36 cost = 36 / 1.5 = 360 / 12 = $ 24 if he wants a 20 % increase over cost on the sale of one liter of his milk - water , the cost has to be $ 24 . well , a liter of milk costs $ 33 , so if he is going to use just $ 30 of milk in his mixture , that ' s 24 / 33 = 8 / 11 of a liter . if milk is 8 / 11 of the liter , then water is 3 / 11 of the liter , and the ratio of water to milk is 3 : 8 . answer choice ( c )"

divide(subtract(33, divide(36, divide(add(const_100, 50), const_100))), divide(36, divide(add(const_100, 50), const_100)))

<gadget id="calculator">100 + 50</gadget>
<output>150</output>
<gadget id="calculator">150 / 100</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">36 / (3/2)</gadget>
<output>24</output>
<gadget id="calculator">33 - 24</gadget>
<output>9</output>
<gadget id="calculator">9 / 24</gadget>
<output>3/8 = around 0.375</output>
<result>3/8 = around 0.375</result>


a train 520 m long can cross an electric pole in 20 sec and then find the speed of the train ?

Explanation: "length = speed * time speed = l / t s = 520 / 20 s = 26 m / sec speed = 26 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 94 kmph answer : b"

divide(divide(520, const_1000), divide(20, const_3600))

<gadget id="calculator">520 / 1_000</gadget>
<output>13/25 = around 0.52</output>
<gadget id="calculator">20 / 3_600</gadget>
<output>1/180 = around 0.005556</output>
<gadget id="calculator">(13/25) / (1/180)</gadget>
<output>468/5 = around 93.6</output>
<result>468/5 = around 93.6</result>


in a throw of dice what is the probability of ge æ « ng number greater than 4

Explanation: "explanation : number greater than 4 is 5 & 6 , so only 2 number total cases of dice = [ 1,2 , 3,4 , 5,6 ] so probability = 2 / 6 = 1 / 3 answer : b"

<gadget id="calculator">6 - 4</gadget>
<output>2</output>
<gadget id="calculator">2 / 6</gadget>
<output>1/3 = around 0.333333</output>
<result>1/3 = around 0.333333</result>


in a particular state , 60 % of the counties received some rain on monday , and 65 % of the counties received some rain on tuesday . no rain fell either day in 25 % of the counties in the state . what percent of the counties received some rain on monday and tuesday ?

Explanation: "60 + 65 + 25 = 150 % the number is 50 % above 100 % because 50 % of the counties were counted twice . the answer is c ."

subtract(add(60, 65), subtract(const_100, 25))

<gadget id="calculator">60 + 65</gadget>
<output>125</output>
<gadget id="calculator">100 - 25</gadget>
<output>75</output>
<gadget id="calculator">125 - 75</gadget>
<output>50</output>
<result>50</result>


two boys starts from the same place walking at the rate of 5 kmph and 5.5 kmph respectively in the same direction . what time will they take to be 8.5 km apart ?

Explanation: "relative speed = 5.5 - 5 = 0.5 kmph ( because they walk in the same direction ) distance = 8.5 km time = distance / speed = 8.5 / 0.5 = 17 hr answer is a"

<gadget id="calculator">5.5 - 5</gadget>
<output>0.5</output>
<gadget id="calculator">8.5 / 0.5</gadget>
<output>17</output>
<result>17</result>


two dogsled teams raced across a 300 mile course in wyoming . team a finished the course in 3 fewer hours than team q . if team a ' s average speed was 5 mph greater than team q ' s , what was team q ' s average mph ?

Explanation: "this is a very specific format that has appeared in a handful of real gmat questions , and you may wish to learn to recognize it : here we have a * fixed * distance , and we are given the difference between the times and speeds of two things that have traveled that distance . this is one of the very small number of question formats where backsolving is typically easier than solving directly , since the direct approach normally produces a quadratic equation . say team q ' s speed was s . then team q ' s time is 300 / s . team a ' s speed was then s + 5 , and team a ' s time was then 300 / ( s + 5 ) . we need to find an answer choice for s so that the time of team a is 3 less than the time of team q . that is , we need an answer choice so that 300 / ( s + 5 ) = ( 300 / s ) - 3 . you can now immediately use number properties to zero in on promising answer choices : the times in these questions will always work out to be integers , and we need to divide 300 by s , and by s + 5 . so we want an answer choice s which is a factor of 300 , and for which s + 5 is also a factor of 300 . so you can rule out answers a and c immediately , since s + 5 wo n ' t be a divisor of 300 in those cases ( sometimes using number properties you get to the correct answer without doing any other work , but unfortunately that ' s not the case here ) . testing the other answer choices , if you try answer d , you find the time for team q is 15 hours , and for team a is 12 hours , and since these differ by 3 , as desired , d is correct ."

<gadget id="calculator">300 / 5</gadget>
<output>60</output>
<gadget id="calculator">60 / 3</gadget>
<output>20</output>
<result>20</result>


the average salary of the employees in a office is rs . 120 / month . the avg salary of officers is rs . 460 and of non officers is rs 110 . if the no . of officers is 15 , then find the no of nonofficers in the office .

Explanation: "let no . of non - officers be x 15 * 460 + x * 110 = ( x + 15 ) 120 x = 510 e"

divide(subtract(multiply(15, 460), multiply(15, 120)), subtract(120, 110))

<gadget id="calculator">15 * 460</gadget>
<output>6_900</output>
<gadget id="calculator">15 * 120</gadget>
<output>1_800</output>
<gadget id="calculator">6_900 - 1_800</gadget>
<output>5_100</output>
<gadget id="calculator">120 - 110</gadget>
<output>10</output>
<gadget id="calculator">5_100 / 10</gadget>
<output>510</output>
<result>510</result>


the h . c . f . of two numbers is 10 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is :

Explanation: "clearly , the numbers are ( 10 x 13 ) and ( 10 x 14 ) . larger number = ( 10 x 14 ) = 140 . answer : option d"

<gadget id="calculator">10 * 14</gadget>
<output>140</output>
<result>140</result>


a and b began business with rs . 3000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000 more . at the end of the year , their profits amounted to rs . 672 find the share of a .

Explanation: "explanation : ( 3 * 8 + 2 * 4 ) : ( 4 * 8 + 5 * 4 ) 8 : 13 8 / 21 * 672 = 256 answer : a"

multiply(divide(672, add(add(multiply(3000, 8), multiply(subtract(3000, 1000), subtract(const_12, 8))), add(multiply(4000, 8), multiply(add(4000, 1000), subtract(const_12, 8))))), add(multiply(3000, 8), multiply(subtract(3000, 1000), subtract(const_12, 8))))

<gadget id="calculator">3_000 * 8</gadget>
<output>24_000</output>
<gadget id="calculator">3_000 - 1_000</gadget>
<output>2_000</output>
<gadget id="calculator">12 - 8</gadget>
<output>4</output>
<gadget id="calculator">2_000 * 4</gadget>
<output>8_000</output>
<gadget id="calculator">24_000 + 8_000</gadget>
<output>32_000</output>
<gadget id="calculator">4_000 * 8</gadget>
<output>32_000</output>
<gadget id="calculator">4_000 + 1_000</gadget>
<output>5_000</output>
<gadget id="calculator">5_000 * 4</gadget>
<output>20_000</output>
<gadget id="calculator">32_000 + 20_000</gadget>
<output>52_000</output>
<gadget id="calculator">32_000 + 52_000</gadget>
<output>84_000</output>
<gadget id="calculator">672 / 84_000</gadget>
<output>1/125 = around 0.008</output>
<gadget id="calculator">(1/125) * 32_000</gadget>
<output>256</output>
<result>256</result>


a cricketer whose bowling average is 12.4 runs per wicket takes 5 wickets for 26 runs and there by decreases his average by 0.4 . the number age of the family now is ?

Explanation: let the number of wickets taken till the last match be x . then , ( 12.4 x + 26 ) / ( x + 5 ) = 12 = 12.4 x + 26 = 12 x + 60 = 0.4 x = 34 = x = 340 / 4 = 85 . answer : d

divide(subtract(multiply(5, subtract(12.4, 0.4)), 26), 0.4)

<gadget id="calculator">12.4 - 0.4</gadget>
<output>12</output>
<gadget id="calculator">5 * 12</gadget>
<output>60</output>
<gadget id="calculator">60 - 26</gadget>
<output>34</output>
<gadget id="calculator">34 / 0.4</gadget>
<output>85</output>
<result>85</result>


a began business with rs . 27000 and was joined afterwards by b with rs . 54000 . when did b join if the profits at the end of the year were divided in the ratio of 2 : 1 ?

Explanation: 27 * 12 : 54 * x = 2 : 1 x = 3 12 - 3 = 9 answer : a

subtract(multiply(const_4, const_3), divide(divide(multiply(27000, multiply(const_4, const_3)), 54000), 2))

<gadget id="calculator">4 * 3</gadget>
<output>12</output>
<gadget id="calculator">27_000 * 12</gadget>
<output>324_000</output>
<gadget id="calculator">324_000 / 54_000</gadget>
<output>6</output>
<gadget id="calculator">6 / 2</gadget>
<output>3</output>
<gadget id="calculator">12 - 3</gadget>
<output>9</output>
<result>9</result>


a , band c can do a piece of work in 11 days , 20 days and 20 days respectively , working alone . how soon can the work be done if a is assisted by band c on alternate days ?

Explanation: "( a + b ) ' s 1 day ' s work = 1 / 11 + 1 / 20 = 31 / 220 ( a + c ) ' s 1 day ' s work = 1 / 11 + 1 / 20 = 31 / 220 work done in 2 day ' s = 31 / 220 + 31 / 220 = 31 / 110 31 / 110 th work done in 2 days work done = 110 / 31 * 2 = 7 days ( approx ) answer : a"

divide(20, divide(add(add(divide(20, 11), divide(20, 20)), add(divide(20, 11), divide(20, 20))), const_2))

<gadget id="calculator">20 / 11</gadget>
<output>20/11 = around 1.818182</output>
<gadget id="calculator">20 / 20</gadget>
<output>1</output>
<gadget id="calculator">(20/11) + 1</gadget>
<output>31/11 = around 2.818182</output>
<gadget id="calculator">(31/11) + (31/11)</gadget>
<output>62/11 = around 5.636364</output>
<gadget id="calculator">(62/11) / 2</gadget>
<output>31/11 = around 2.818182</output>
<gadget id="calculator">20 / (31/11)</gadget>
<output>220/31 = around 7.096774</output>
<result>220/31 = around 7.096774</result>


out of 40 applicants to a law school , 15 majored in political science , 20 had a grade point average higher than 3.0 , and 10 did not major in political science and had a gpa equal to or lower than 3.0 . how many t applicants majored in political science and had a gpa higher than 3.0 ?

Explanation: "total applicants = 40 political science = 15 and non political science = 40 - 15 = 25 gpa > 3.0 = 20 and gpa < = 3.0 = 20 10 non political science students had gpa < = 3.0 - - > 15 non political science students had gpa > 3.0 gpa > 3.0 in political science = total - ( gpa > 3.0 in non political science ) t = 20 - 15 = 5 answer : a"

<gadget id="calculator">10 + 15</gadget>
<output>25</output>
<gadget id="calculator">40 - 25</gadget>
<output>15</output>
<gadget id="calculator">20 - 15</gadget>
<output>5</output>
<result>5</result>