having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.88 at the candy store . what is john ’ s weekly allowance ?

Explanation: "x = 3 x / 5 + 1 / 3 * 2 x / 5 + 88 4 x / 15 = 88 x = 330 = $ 3.30 the answer is c ."

divide(0.88, subtract(const_1, add(divide(3, 5), multiply(divide(const_1, 3), subtract(const_1, divide(3, 5))))))

<gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 - (3/5)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(1/3) * (2/5)</gadget>
<output>2/15 = around 0.133333</output>
<gadget id="calculator">(3/5) + (2/15)</gadget>
<output>11/15 = around 0.733333</output>
<gadget id="calculator">1 - (11/15)</gadget>
<output>4/15 = around 0.266667</output>
<gadget id="calculator">0.88 / (4/15)</gadget>
<output>3.3</output>
<result>3.3</result>


exactly 3 / 7 of the people in the room are under the age of 21 , and exactly 5 / 10 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ?

Explanation: "the total number of the people in the room must be a multiple of both 7 and 10 ( in order 3 / 7 and 5 / 10 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 7 and 10 , which is 70 . since , the total number of the people in the room is greater than 50 and less than 100 , then there are 70 people in the room . therefore there are 3 / 7 * 70 = 30 people in the room under the age of 21 . answer : d ."

<gadget id="calculator">7 * 10</gadget>
<output>70</output>
<gadget id="calculator">70 * 3</gadget>
<output>210</output>
<gadget id="calculator">210 / 7</gadget>
<output>30</output>
<result>30</result>


a 5 - digit number is formed by the digits 2 , 45 , 68 ( each digit used exactly once ) . what is the probability that the number formed is divisible by 4 ?

Explanation: a no . is divisible by 4 if last two digit is divisible by 4 so numbers ending with 2428 , 4852 , 5664 , 6884 are divisible by 4 last two places are fixed by 2428 , 4852 , 5664 , 6884 so remaining 3 places can be filled in 3 ! ways for each total = 8 * 3 ! = 48 = n ( e ) n ( s ) = 5 c 4 = 120 p = 48 / 120 = 2 / 5 answer : a

<gadget id="calculator">factorial(4)</gadget>
<output>24</output>
<gadget id="calculator">24 * 2</gadget>
<output>48</output>
<gadget id="calculator">factorial(5)</gadget>
<output>120</output>
<gadget id="calculator">48 / 120</gadget>
<output>2/5 = around 0.4</output>
<result>2/5 = around 0.4</result>


if x is 20 percent more than y and y is 60 percent less than z , then x is what percent of z ?

Explanation: "z = 100 ; y = 40 so x = 48 x as % of z = 48 / 100 * 100 = > 48 % answer will be ( b )"

multiply(add(const_1, divide(20, const_100)), subtract(const_100, 60))

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 + (1/5)</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">100 - 60</gadget>
<output>40</output>
<gadget id="calculator">(6/5) * 40</gadget>
<output>48</output>
<result>48</result>


from mumbai railway station , two trains a and b start simultaneously from stations 400 miles apart , and travel the same route toward each other on adjacent parallel tracks . if train a and train b travel at a constant rate of 40 miles per hour and 40 miles per hour , respectively , how many miles will train a have traveled when the trains pass each other , to the nearest mile ?

Explanation: since we know the distance ( 400 ) and the combined rate ( 80 ) , we plug it into the formula : distance = rate * time 400 = 80 * time we can solve for the time they will meet cause we added the rate of train a and train b together . so the time will be 400 / 80 from dividing 80 on both sides to isolate time in the equation above . time will be 20 hours so now you can plug that in for train a ’ s distance . distance = rate * time distance = 40 * 20 distance = 180 according to answer choice e .

multiply(divide(400, add(add(40, multiply(const_2, add(const_4, const_1))), 40)), 40)

<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">2 * 5</gadget>
<output>10</output>
<gadget id="calculator">40 + 10</gadget>
<output>50</output>
<gadget id="calculator">50 + 40</gadget>
<output>90</output>
<gadget id="calculator">400 / 90</gadget>
<output>40/9 = around 4.444444</output>
<gadget id="calculator">(40/9) * 40</gadget>
<output>1_600/9 = around 177.777778</output>
<result>1_600/9 = around 177.777778</result>


there is a church tower 150 feet tall and another catholic tower at a distance of 350 feet from it which is 200 feet tall . there is one each bird sitting on top of both the towers . they fly at a constant speed and time to reach a grain in b / w the towers at the same time . at what distance from the church is the grain ?

Explanation: if x ft is the distance of grain from 200 ft tall tower , then 150 ^ 2 + ( 350 - x ) ^ 2 = 200 ^ 2 + x ^ 2 then x = 150 meters answer : c

divide(subtract(add(power(150, const_2), power(350, const_2)), power(200, const_2)), multiply(const_2, 350))

<gadget id="calculator">150 ** 2</gadget>
<output>22_500</output>
<gadget id="calculator">350 ** 2</gadget>
<output>122_500</output>
<gadget id="calculator">22_500 + 122_500</gadget>
<output>145_000</output>
<gadget id="calculator">200 ** 2</gadget>
<output>40_000</output>
<gadget id="calculator">145_000 - 40_000</gadget>
<output>105_000</output>
<gadget id="calculator">2 * 350</gadget>
<output>700</output>
<gadget id="calculator">105_000 / 700</gadget>
<output>150</output>
<result>150</result>


for 1 rs 4 p interest wat will be for 5000 rs ?

Explanation: for 1 rs , 4 p interest for 5000 rs , x x = 5000 / 1 * 4 p = = > 20000 paise to express in rs , 20000 / 100 = 200 rs answer : c

<gadget id="calculator">4 / 100</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">5_000 * (1/25)</gadget>
<output>200</output>
<result>200</result>


a train running at the speed of 60 km / hr crosses a pole in 15 seconds . find the length of the train .

Explanation: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 15 = 250 meter answer : e"

multiply(divide(multiply(60, const_1000), const_3600), 15)

<gadget id="calculator">60 * 1_000</gadget>
<output>60_000</output>
<gadget id="calculator">60_000 / 3_600</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">(50/3) * 15</gadget>
<output>250</output>
<result>250</result>


a sum was put at simple interest at a certain rate for 10 years . had it been put at 5 % higher rate , it would have fetched rs . 600 more . what was the sum ?

Explanation: "explanation : at 5 % more rate , the increase in s . i for 10 years = rs . 600 ( given ) so , at 5 % more rate , the increase in si for 1 year = 600 / 10 = rs . 60 / - i . e . rs . 60 is 5 % of the invested sum so , 1 % of the invested sum = 60 / 5 therefore , the invested sum = 60 × 100 / 5 = rs . 1200 answer : a"

divide(600, multiply(divide(5, const_100), 10))

<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/20) * 10</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">600 / (1/2)</gadget>
<output>1_200</output>
<result>1_200</result>


a shop owner sells 60 mtr of cloth and gains sp of 10 mtrs . find the gain % ?

Explanation: "here , selling price of 10 m cloth is obtained as profit . profit of 10 m cloth = ( s . p . of 60 m cloth ) – ( c . p . of 60 m cloth ) selling price of 50 m cloth = selling price of 60 m of cloth let cost of each metre be rs . 100 . therefore , cost price of 50 m cloth = rs . 5000 and s . p . of 50 m cloth = rs . rs . 6000 profit % = 10 / 50 × 100 = 20 % 20 profit of 20 % was made by the merchant . a"

multiply(divide(10, subtract(60, 10)), const_100)

<gadget id="calculator">60 - 10</gadget>
<output>50</output>
<gadget id="calculator">10 / 50</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 100</gadget>
<output>20</output>
<result>20</result>


in a certain pet shop , the ratio of dogs to cats to bunnies in stock is 4 : 7 : 9 . if the shop carries 364 dogs and bunnies total in stock , how many dogs are there ?

Explanation: "let us assume the number of dogs , cats and bunnies to be 4 x , 7 x and 9 x total dogs and bunnies = 13 x . and we are given that 13 x = 364 . hence x = 28 . dogs = 4 x = 4 * 28 = 112 ( option d )"

<gadget id="calculator">4 + 9</gadget>
<output>13</output>
<gadget id="calculator">364 / 13</gadget>
<output>28</output>
<gadget id="calculator">28 * 4</gadget>
<output>112</output>
<result>112</result>


albert invested rs . 6500 in a scheme for 2 years at compound interest rate 6.5 % p . a . how much amount will albert get on maturity of the fixed deposit ?

Explanation: amount = [ 6500 * ( 1 + 6.5 / 100 ) 2 ] = 6500 * 106.5 / 100 * 106.5 / 100 = rs . 7372.46 answer : e

multiply(6500, power(add(const_1, divide(6.5, const_100)), 2))

<gadget id="calculator">6.5 / 100</gadget>
<output>0.065</output>
<gadget id="calculator">1 + 0.065</gadget>
<output>1.065</output>
<gadget id="calculator">1.065 ** 2</gadget>
<output>1.134225</output>
<gadget id="calculator">6_500 * 1.134225</gadget>
<output>7_372.4625</output>
<result>7_372.4625</result>


keats library purchases a number of new books , all in the category of biography , and the library does not acquire any other books . with the addition of the new biographies , the biography collection of the library amounts to 30 % of the total number of books in the library . if prior to the purchase , only 20 % of the books in keats library were biographies , by what percent has the number of biographies in the library increased ?

Explanation: "let x be the number of new biographies added to the library . let b be the original number of biographies , so the original number of books was 5 b . 0.3 ( 5 b + x ) = b + x 0.5 b = 0.7 x x = 0.71 b the answer is c ."

multiply(divide(divide(subtract(multiply(30, const_100), multiply(20, const_100)), subtract(const_100, 30)), 20), const_100)

<gadget id="calculator">30 * 100</gadget>
<output>3_000</output>
<gadget id="calculator">20 * 100</gadget>
<output>2_000</output>
<gadget id="calculator">3_000 - 2_000</gadget>
<output>1_000</output>
<gadget id="calculator">100 - 30</gadget>
<output>70</output>
<gadget id="calculator">1_000 / 70</gadget>
<output>100/7 = around 14.285714</output>
<gadget id="calculator">(100/7) / 20</gadget>
<output>5/7 = around 0.714286</output>
<gadget id="calculator">(5/7) * 100</gadget>
<output>500/7 = around 71.428571</output>
<result>500/7 = around 71.428571</result>


if the average ( arithmetic mean ) of the 4 numbers 3 , 16 , 33 , and ( n + 1 ) is 20 , then n =

Explanation: 3 + 16 + 33 + n + 1 = 20 x 4 = 80 = > n + 53 = 80 = > n = 27 answer d

subtract(multiply(20, 4), add(add(add(3, 16), 33), 1))

<gadget id="calculator">20 * 4</gadget>
<output>80</output>
<gadget id="calculator">3 + 16</gadget>
<output>19</output>
<gadget id="calculator">19 + 33</gadget>
<output>52</output>
<gadget id="calculator">52 + 1</gadget>
<output>53</output>
<gadget id="calculator">80 - 53</gadget>
<output>27</output>
<result>27</result>


the mean of 50 observations is 200 . but later he found that there is decrements of 6 from each observations . what is the the updated mean is ?

Explanation: 194 answer is e

<gadget id="calculator">200 - 6</gadget>
<output>194</output>
<result>194</result>


the ` ` racing magic ' ' takes 120 seconds to circle the racing track once . the ` ` charging bull ' ' makes 40 rounds of the track in an hour . if they left the starting point together , how many minutes will it take for them to meet at the starting point for the second time ?

Explanation: time taken by racing magic to make one circle = 120 seconds = 2 mins time taken by ` ` charging bull ' ' to make one circle = 60 mins / 40 = 1.5 mins = 90 seconds lcm of 90 and 120 seconds = 360 seconds = 6 mins time taken for them to meet at the starting point for the second time = 6 mins * 2 = 12 mins answer d

add(add(const_2, const_4), add(const_2, const_4))

<gadget id="calculator">2 + 4</gadget>
<output>6</output>
<gadget id="calculator">6 + 6</gadget>
<output>12</output>
<result>12</result>


find the constant k so that : - x 2 - ( k + 10 ) x - 8 = - ( x - 2 ) ( x - 4 )

Explanation: "- x 2 - ( k + 10 ) x - 8 = - ( x - 2 ) ( x - 4 ) : given - x 2 - ( k + 10 ) x - 8 = - x 2 + 6 x - 8 - ( k + 10 ) = 6 : two polynomials are equal if their corresponding coefficients are equal . k = - 16 : solve the above for k correct answer c"

<gadget id="calculator">4 + 2</gadget>
<output>6</output>
<gadget id="calculator">10 + 6</gadget>
<output>16</output>
<result>16</result>


Explanation: "explanation : ( a + b ) 2 + ( a â ˆ ’ b ) 2 = 2 ( a 2 + b 2 ) ( reference : basic algebraic formulas ) 1022 + 982 = ( 100 + 2 ) 2 + ( 100 â ˆ ’ 2 ) 2 = 2 ( 1002 + 22 ) = 2 ( 10000 + 4 ) = 20008 . answer : option e"

add(subtract(power(102, const_2), 102), subtract(power(98, const_2), 98))

<gadget id="calculator">102 ** 2</gadget>
<output>10_404</output>
<gadget id="calculator">10_404 - 102</gadget>
<output>10_302</output>
<gadget id="calculator">98 ** 2</gadget>
<output>9_604</output>
<gadget id="calculator">9_604 - 98</gadget>
<output>9_506</output>
<gadget id="calculator">10_302 + 9_506</gadget>
<output>19_808</output>
<result>19_808</result>


two trains 140 m and 190 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?

Explanation: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 140 + 190 = 330 m . required time = 330 * 9 / 250 = 11.88 sec . answer : a :"

<gadget id="calculator">140 + 190</gadget>
<output>330</output>
<gadget id="calculator">60 + 40</gadget>
<output>100</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">100 * (5/18)</gadget>
<output>250/9 = around 27.777778</output>
<gadget id="calculator">330 / (250/9)</gadget>
<output>297/25 = around 11.88</output>
<result>297/25 = around 11.88</result>


mary works in a restaurant a maximum of 70 hours . for the first 20 hours , she is paid $ 8 per hour . for each overtime hour , she is paid at a rate which is 25 % higher than her regular rate . how much mary can earn in a week ?

Explanation: "mary receives $ 8 ( 20 ) = $ 160 for the first 20 hours . for the 50 overtime hours , she receives $ 8 ( 0.25 ) + $ 8 = $ 10 per hour , that is $ 50 ( 20 ) = $ 500 . the total amount is $ 160 + $ 500 = $ 660 answer c 660 ."

add(multiply(70, 8), multiply(subtract(70, 20), multiply(8, divide(25, const_100))))

<gadget id="calculator">70 * 8</gadget>
<output>560</output>
<gadget id="calculator">70 - 20</gadget>
<output>50</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">8 * (1/4)</gadget>
<output>2</output>
<gadget id="calculator">50 * 2</gadget>
<output>100</output>
<gadget id="calculator">560 + 100</gadget>
<output>660</output>
<result>660</result>


the area of a circular field is 17.56 hectares . find the cost of fencing it at the rate of rs . 4 per metre approximately

Explanation: "explanation : area = ( 17.56 x 10000 ) m 2 = 175600 m 2 . π r 2 = 175600 ⇔ ( r ) 2 = ( 175600 x ( 7 / 22 ) ) ⇔ r = 236.37 m . circumference = 2 π r = ( 2 x ( 22 / 7 ) x 236.37 ) m = 1485.78 m . cost of fencing = rs . ( 1485.78 x 4 ) = rs . 5943 . answer : option c"

multiply(circumface(multiply(sqrt(divide(17.56, const_pi)), const_100)), 4)


30 pens and 75 pencils were purchased for 750 . if the average price of a pencil was 2.00 , find the average price of a pen .

Explanation: "since average price of a pencil = 2 ∴ price of 75 pencils = 150 ∴ price of 30 pens = ( 750 – 150 ) = 600 ∴ average price of a pen = 600 ⁄ 60 = 20 answer a"

divide(subtract(750, multiply(75, 2.00)), 30)

<gadget id="calculator">75 * 2</gadget>
<output>150</output>
<gadget id="calculator">750 - 150</gadget>
<output>600</output>
<gadget id="calculator">600 / 30</gadget>
<output>20</output>
<result>20</result>


the h . c . f of two numbers is 23 and the other two factors of their l . c . m are 16 and 17 . the larger of the two numbers is :

Explanation: "clearly , the numbers are ( 23 * 16 ) and ( 23 * 17 ) . larger number = ( 23 * 17 ) = 391 . answer : e"

<gadget id="calculator">23 * 17</gadget>
<output>391</output>
<result>391</result>


to fill a tank , 25 buckets of water is required . how many buckets of water will be required to fill the same tank if the capacity of bucket is reduced to two - fifth of its present ?

Explanation: explanation : let the capacity of 1 bucket = x . then , capacity of tank = 25 x . new capacity of bucket = 2 / 5 x . required no of buckets = 25 x / ( 2 x / 5 ) = 62.5 answer is b

divide(multiply(25, add(const_4, const_1)), const_2)

<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">25 * 5</gadget>
<output>125</output>
<gadget id="calculator">125 / 2</gadget>
<output>125/2 = around 62.5</output>
<result>125/2 = around 62.5</result>


the visitors of a modern art museum who watched a certain picasso painting were asked to fill in a short questionnaire indicating whether they had enjoyed looking at the picture and whether they felt they had understood it . according to the results of the survey , all 110 visitors who did not enjoy the painting also did not feel they had understood the painting , and the number of visitors who enjoyed the painting was equal to the number of visitors who felt they had understood the painting . if 3 / 4 of the visitors who answered the questionnaire both enjoyed the painting and felt they had understood the painting , then how many visitors answered the questionnaire ?

Explanation: "if we exclude those cases and take the question at face value , then it seems straightforward . group # 1 = ( did n ' t like , did n ' t understand ) = 110 group # 2 = ( like understood ) = 3 / 4 ( 1 / 4 ) n = 110 n = 440 answer = ( e )"

divide(110, subtract(const_1, divide(3, 4)))

<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">1 - (3/4)</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">110 / (1/4)</gadget>
<output>440</output>
<result>440</result>


a rectangular lawn of length 200 m by 120 m has two roads running along its center , one along the length and the other along the width . if the width of the roads is 5 m what is the area r covered by the two roads ?

Explanation: "area covered by road along the length = 5 * 200 = 1000 square meter area covered by road along the width = 5 * 120 = 600 square meter common area in both roads ( where the roads intersect ) = square with side 5 meter = 5 * 5 = 25 total area of the roads r = 1000 + 600 - 25 = 1575 answer : option c"

add(rectangle_area(200, 5), rectangle_area(120, 5))

<gadget id="calculator">200 * 5</gadget>
<output>1_000</output>
<gadget id="calculator">120 * 5</gadget>
<output>600</output>
<gadget id="calculator">1_000 + 600</gadget>
<output>1_600</output>
<result>1_600</result>


a and b can together finish a work in 40 days . they worked together for 10 days and then b left . after another 21 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 21 days whole work will be done by a in 21 * 4 / 3 = 28 days answer is e"

divide(multiply(21, 40), subtract(40, 10))

<gadget id="calculator">21 * 40</gadget>
<output>840</output>
<gadget id="calculator">40 - 10</gadget>
<output>30</output>
<gadget id="calculator">840 / 30</gadget>
<output>28</output>
<result>28</result>


what will be the cost of building to paint which area equal to 196 sq ft , if the price per foot of building is rs . 15 ?

Explanation: let the side of the square plot be a ft . a 2 = 196 = > a = 14 length of the fence = perimeter of the plot = 4 a = 56 ft . cost of building the fence = 56 * 15 = rs . 840 . answer : e

<gadget id="calculator">196 ** (1/2)</gadget>
<output>14</output>
<gadget id="calculator">4 * 14</gadget>
<output>56</output>
<gadget id="calculator">56 * 15</gadget>
<output>840</output>
<result>840</result>


exactly 3 sides of a certain 10 - sided die are red . what is the probability that kumar rolls the die 3 times and the die lands with a red side up for the first time on the third roll ?

Explanation: total no . of sides = 10 sides that are red = 3 probability that the die lands with red side up = 3 / 10 therefore , probability that the die does not land with red side up = 1 - 3 / 10 = 7 / 10 probability that kumar rolls the die 3 times and the die lands with a red side up for the first time on the third roll = ( 1 st roll - non red face ) x ( 2 nd roll - non red face ) x ( 3 rd roll - red face ) = ( 7 / 10 ) x ( 7 / 10 ) x ( 3 / 10 ) = 128 / 1000 = 0.147 d

multiply(power(divide(subtract(10, 3), 10), const_2), divide(3, 10))

<gadget id="calculator">10 - 3</gadget>
<output>7</output>
<gadget id="calculator">7 / 10</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">(7/10) ** 2</gadget>
<output>49/100 = around 0.49</output>
<gadget id="calculator">3 / 10</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(49/100) * (3/10)</gadget>
<output>147/1_000 = around 0.147</output>
<result>147/1_000 = around 0.147</result>


the average runs scored by a batsman in 25 matches is 45 . in the next 7 matches the batsman scored an average of 15 runs . find his average in all the 32 matches ?

Explanation: total score of the batsman in 25 matches = 1125 . total score of the batsman in the next 7 matches = 105 . total score of the batsman in the 32 matches = 1230 . average score of the batsman = 1230 / 32 = 38.44 . answer : b

divide(add(multiply(45, 25), multiply(15, 7)), add(25, 7))

<gadget id="calculator">45 * 25</gadget>
<output>1_125</output>
<gadget id="calculator">15 * 7</gadget>
<output>105</output>
<gadget id="calculator">1_125 + 105</gadget>
<output>1_230</output>
<gadget id="calculator">25 + 7</gadget>
<output>32</output>
<gadget id="calculator">1_230 / 32</gadget>
<output>615/16 = around 38.4375</output>
<result>615/16 = around 38.4375</result>


carl is facing very difficult financial times and can only pay the interest on a $ 10,000 loan he has taken . the bank charges him a quarterly compound rate of 4 % . what is the approximate interest he pays annually ?

Explanation: "an easy way too attempt this is by approximation : for the first quarter , he pays 4 % of 10,000 which is $ 400 . so for the four quarters in the year , he will approximately play 400 * 4 = 1600 over the entire year . because of compound interest it will be more than 1600 . approx . option a is correct . answer : a"

subtract(multiply(multiply(const_100, const_100), power(add(const_1, divide(4, const_100)), const_4)), multiply(const_100, const_100))


jack and jill work at a hospital with 7 other workers . for an internal review , 2 of the 9 workers will be randomly chosen to be interviewed . what is the probability that jack and jill will both be chosen ?

Explanation: "1 / 9 c 2 = 1 / 36 . answer : e ."

<gadget id="calculator">factorial(9)</gadget>
<output>362_880</output>
<gadget id="calculator">factorial(2)</gadget>
<output>2</output>
<gadget id="calculator">factorial(7)</gadget>
<output>5_040</output>
<gadget id="calculator">2 * 5_040</gadget>
<output>10_080</output>
<gadget id="calculator">362_880 / 10_080</gadget>
<output>36</output>
<gadget id="calculator">1 / 36</gadget>
<output>1/36 = around 0.027778</output>
<result>1/36 = around 0.027778</result>


a student has to obtain 50 % of the total marks to pass . he got 200 marks and failed by 20 marks . the maximum marks are ?

Explanation: "let the maximum marks be x then , 50 % of x = 200 + 20 50 x / 100 = 220 50 x = 220 * 100 = 22000 x = 440 answer is e"

divide(add(200, 20), divide(50, const_100))

<gadget id="calculator">200 + 20</gadget>
<output>220</output>
<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">220 / (1/2)</gadget>
<output>440</output>
<result>440</result>


the cost of 3 pens and 5 pencils is rs . 150 . also the cost of one pen and one pencil is in the ratio of 5 : 1 respectively . what is the cost of one dozen pens ?

Explanation: "explanation : let the cost of one pen is ‘ 5 x ’ and pencil is ‘ x ’ 3 x 5 x + 5 x = rs . 150 15 x + 5 x = rs . 150 x = 150 / 20 = 7.50 : . cost of 1 pen = 5 x = 5 x 7.50 = 37.50 : . cost of 12 pens , i . e . ( one dozen ) = 37.50 x 12 = rs . 450 answer : option d"

multiply(multiply(3, const_4), divide(150, add(3, 1)))

<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">3 + 1</gadget>
<output>4</output>
<gadget id="calculator">150 / 4</gadget>
<output>75/2 = around 37.5</output>
<gadget id="calculator">12 * (75/2)</gadget>
<output>450</output>
<result>450</result>


the tax on a commodity is diminished by 20 % but its consumption is increased by 10 % . find the decrease percent in the revenue derived from it ?

Explanation: "answer : option d 100 * 100 = 10000 80 * 110 = 8800 10000 - - - - - - - 1200 100 - - - - - - - ? = 12 %"

subtract(const_100, divide(multiply(add(const_100, 10), subtract(const_100, 20)), const_100))

<gadget id="calculator">100 + 10</gadget>
<output>110</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">110 * 80</gadget>
<output>8_800</output>
<gadget id="calculator">8_800 / 100</gadget>
<output>88</output>
<gadget id="calculator">100 - 88</gadget>
<output>12</output>
<result>12</result>


a store sells chairs and tables . if the price of 2 chairs and 1 table is 60 % of the price of 1 chair and 2 tables , and the price of 1 table and 1 chair is $ 72 , what is the price , in dollars , of 1 table ? ( assume that every chair has the same price and every table has the same price . )

Explanation: "let c = chair ; t = table 2 c + 1 t = 0.6 ( 1 c + 2 t ) or c ( 2 - 0.6 ) = 1.2 t - 1 t or 1.4 c = 0.2 t therefore c = 0.2 / 1.4 t = 1 / 7 t ic + 1 t = 72 or 1 / 7 t + 1 t = 60 therefore t = 72 * 7 / 8 = 63 c"

divide(subtract(multiply(72, 2), multiply(72, divide(60, const_100))), add(divide(60, const_100), 1))

<gadget id="calculator">72 * 2</gadget>
<output>144</output>
<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">72 * (3/5)</gadget>
<output>216/5 = around 43.2</output>
<gadget id="calculator">144 - (216/5)</gadget>
<output>504/5 = around 100.8</output>
<gadget id="calculator">(3/5) + 1</gadget>
<output>8/5 = around 1.6</output>
<gadget id="calculator">(504/5) / (8/5)</gadget>
<output>63</output>
<result>63</result>


a small pool filled only with water will require an additional 300 gallons of water in order to be filled to 80 % of its capacity . if pumping in these additional 300 gallons of water will increase the amount of water in the pool by 25 % , what is the total capacity of the pool in gallons ?

Explanation: "300 gallons of water increases capacity by 25 % that means 25 % is 300 gallons , so 100 % would be = 300 * 100 / 25 = 1200 gallons now 1200 + 300 gallons is 80 % capacity of tank . so 100 % capacity would be = 1500 * 100 / 80 = 1875 a is the answer"

divide(add(divide(multiply(300, const_100), 25), 300), divide(80, const_100))

<gadget id="calculator">300 * 100</gadget>
<output>30_000</output>
<gadget id="calculator">30_000 / 25</gadget>
<output>1_200</output>
<gadget id="calculator">1_200 + 300</gadget>
<output>1_500</output>
<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">1_500 / (4/5)</gadget>
<output>1_875</output>
<result>1_875</result>


at 3 : 40 , the hour hand and the minute hand of a clock form an angle of

Explanation: "angle between hands of a clock when the minute hand is behind the hour hand , the angle between the two hands at m minutes past h ' o clock = 30 ( h − m / 5 ) + m / 2 degree when the minute hand is ahead of the hour hand , the angle between the two hands at m minutes past h ' o clock = 30 ( m / 5 − h ) − m / 2 degree here h = 3 , m = 40 and minute hand is ahead of the hour hand . hence the angle = 30 ( m / 5 − h ) − m / 2 = 30 ( 40 / 5 − 3 ) − 40 / 2 = 30 ( 8 − 3 ) − 20 = 30 × 5 − 20 = 130 ° answer is c ."

subtract(multiply(multiply(multiply(const_60, 3), const_2), divide(40, const_60)), multiply(divide(divide(multiply(multiply(const_60, 3), const_2), 3), const_4), add(divide(40, const_60), 3)))

<gadget id="calculator">60 * 3</gadget>
<output>180</output>
<gadget id="calculator">180 * 2</gadget>
<output>360</output>
<gadget id="calculator">40 / 60</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">360 * (2/3)</gadget>
<output>240</output>
<gadget id="calculator">360 / 3</gadget>
<output>120</output>
<gadget id="calculator">120 / 4</gadget>
<output>30</output>
<gadget id="calculator">(2/3) + 3</gadget>
<output>11/3 = around 3.666667</output>
<gadget id="calculator">30 * (11/3)</gadget>
<output>110</output>
<gadget id="calculator">240 - 110</gadget>
<output>130</output>
<result>130</result>


heinz produces tomato puree by boiling tomato juice . the tomato puree has only 20 % water while the tomato juice has 90 % water . how many liters of tomato puree will be obtained from 20 litres of tomato juice ?

Explanation: "answer : explanation : in each of the solutions , there is a pure tomato component and some water . so while boiling , water evaporates but tomato not . so we equate tomato part in the both equations . ⇒ ⇒ 10 % ( 20 ) = 80 % ( x ) ⇒ ⇒ x = 2.5 liters . answer : b"

divide(multiply(divide(subtract(const_100, 90), const_100), 20), divide(subtract(const_100, 20), const_100))

<gadget id="calculator">100 - 90</gadget>
<output>10</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) * 20</gadget>
<output>2</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">2 / (4/5)</gadget>
<output>5/2 = around 2.5</output>
<result>5/2 = around 2.5</result>


if 2 ^ 5 , 3 ^ 3 , and 14 ^ 2 are all factors of the product of 936 and w where w is a positive integer , what is the smallest possible value of w ?

Explanation: here 156 has three two ' s two three ' s and one 14 rest of them must be in w so w = 14 * 3 * 4 = 168 smash e

multiply(multiply(multiply(power(2, 2), 3), divide(14, 2)), 2)

<gadget id="calculator">2 ** 2</gadget>
<output>4</output>
<gadget id="calculator">4 * 3</gadget>
<output>12</output>
<gadget id="calculator">14 / 2</gadget>
<output>7</output>
<gadget id="calculator">12 * 7</gadget>
<output>84</output>
<gadget id="calculator">84 * 2</gadget>
<output>168</output>
<result>168</result>


a and b can finish a work in 10 days while b and c can do it in 18 days . a started the work , worked for 5 days , then b worked for 10 days and the remaining work was finished by c in 15 days . in how many days could c alone have finished the whole work ?

Explanation: let c completes the work in x days . work done by ( a + b ) in 1 day = 1 ⁄ 10 work done by ( b + c ) in 1 day = 1 ⁄ 18 a ’ s 5 days ’ work + b ’ s 10 days ’ work + c ’ s 15 days ’ work = 1 or ( a + b ) ’ s 5 days ’ work + ( b + c ) ’ s 5 days ’ work + c ’ s 10 days ’ work = 1 or 5 ⁄ 10 + 5 ⁄ 18 + 10 ⁄ x = 1 or x = 45 days answer c

divide(10, subtract(const_1, add(divide(5, 10), divide(5, 18))))

<gadget id="calculator">5 / 10</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">5 / 18</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">(1/2) + (5/18)</gadget>
<output>7/9 = around 0.777778</output>
<gadget id="calculator">1 - (7/9)</gadget>
<output>2/9 = around 0.222222</output>
<gadget id="calculator">10 / (2/9)</gadget>
<output>45</output>
<result>45</result>


a boat running upstream takes 8 hours 48 minutes to cover a certain distance , while it take 4 hours to cover the same distance running downstream . what is the ratio between the speed of the boat and speed of the water current respectively ?

Explanation: "sol . let the man rate upstream be x kmph and that downstream be y kmph . then , distance coverd upstream in 8 hrs 48 min . = distance coverd downstream in 4 hrs . ⇒ [ x 8 4 / 5 ] = ( y * 4 ) ⇒ 44 / 5 x = 4 y ⇒ y = 11 / 5 x . ∴ required ratio = [ y + x / 2 ] : [ 6 x / 5 * 1 / 2 ] : [ 6 x / 5 * 1 / 2 ] = 8 / 5 : 3 / 5 = 8 : 3 . answer d"

divide(divide(add(divide(add(divide(48, const_60), 8), 4), const_1), const_2), divide(subtract(divide(add(divide(48, const_60), 8), 4), const_1), const_2))

<gadget id="calculator">48 / 60</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(4/5) + 8</gadget>
<output>44/5 = around 8.8</output>
<gadget id="calculator">(44/5) / 4</gadget>
<output>11/5 = around 2.2</output>
<gadget id="calculator">(11/5) + 1</gadget>
<output>16/5 = around 3.2</output>
<gadget id="calculator">(16/5) / 2</gadget>
<output>8/5 = around 1.6</output>
<gadget id="calculator">(11/5) - 1</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">(6/5) / 2</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(8/5) / (3/5)</gadget>
<output>8/3 = around 2.666667</output>
<result>8/3 = around 2.666667</result>


if 2 ^ x + 2 ^ y = 10 ^ 0 + 90 ^ 0 , where x and y are non negative integers , what is the greatest possible value of | x â € “ y | ?

Explanation: | x â € “ y | for x and y 2 ^ x + 2 ^ y = 10 ^ 0 + 90 ^ 0 a . x = y x = y = 0 1 + 1 = 1 + 1 right b . 1 x = 2 , y = 1 4 + 2 = 1 + 1 wrong c . 2 x = 3 , y = 1 8 + 2 = 1 + 1 wrong d . 3 x = 4 , y = 1 16 + 2 = 1 + 1 wrong e . 4 x = 5 , y = 1 32 + 2 = 1 + 1 wrong my answer is a .

<gadget id="calculator">2 - 2</gadget>
<output>0</output>
<result>0</result>


a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 1032 in total compensation , how many total hours did he work that week ?

Explanation: for 40 hrs = 40 * 16 = 640 excess = 1032 - 640 = 392 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 392 / 28 = 98 / 7 = 14 total hrs = 40 + 14 = 54 answer e 52

add(40, divide(subtract(1032, multiply(16, 40)), divide(multiply(16, add(const_100, 75)), const_100)))

<gadget id="calculator">16 * 40</gadget>
<output>640</output>
<gadget id="calculator">1_032 - 640</gadget>
<output>392</output>
<gadget id="calculator">100 + 75</gadget>
<output>175</output>
<gadget id="calculator">16 * 175</gadget>
<output>2_800</output>
<gadget id="calculator">2_800 / 100</gadget>
<output>28</output>
<gadget id="calculator">392 / 28</gadget>
<output>14</output>
<gadget id="calculator">40 + 14</gadget>
<output>54</output>
<result>54</result>


find the length of the wire required to go 15 times round a square field containing 69696 m 2 ?

Explanation: "a 2 = 69696 = > a = 264 4 a = 1056 1056 * 15 = 15840 answer : a"

<gadget id="calculator">69_696 ** (1/2)</gadget>
<output>264</output>
<gadget id="calculator">4 * 264</gadget>
<output>1_056</output>
<gadget id="calculator">1_056 * 15</gadget>
<output>15_840</output>
<result>15_840</result>


p , q and r have rs . 7000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?

Explanation: "let the amount with r be rs . r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 7000 - r ) = > 3 r = 14000 - 2 r = > 5 r = 14000 = > r = 2800 . answer : d"

multiply(divide(7000, add(const_1, divide(const_2, const_3))), divide(const_2, const_3))

<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">1 + (2/3)</gadget>
<output>5/3 = around 1.666667</output>
<gadget id="calculator">7_000 / (5/3)</gadget>
<output>4_200</output>
<gadget id="calculator">4_200 * (2/3)</gadget>
<output>2_800</output>
<result>2_800</result>


in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the run rate in the remaining 40 overs to reach a target of 282 runs ?

Explanation: "total runs in the first 10 overs = 10 × 3.2 = 32 run rate required in the remaining 40 overs = 282 − 32 / 40 = 250 / 40 = 6.25 runs per over . answer a"

divide(subtract(282, multiply(10, 3.2)), 40)

<gadget id="calculator">10 * 3.2</gadget>
<output>32</output>
<gadget id="calculator">282 - 32</gadget>
<output>250</output>
<gadget id="calculator">250 / 40</gadget>
<output>25/4 = around 6.25</output>
<result>25/4 = around 6.25</result>


a and b together can complete a piece of work in 10 days . if a alone can complete the same work in 15 days , in how many days , in how many days can b alone complete that work ?

Explanation: ( a + b ) ' s 1 day ' s work = 1 / 10 a ' s 1 day ' s work = 1 / 15 b ' s 1 days ' s work = ( 1 / 10 ) - ( 1 / 15 ) = 1 / 30 hence , b alone can complete the work in 30 days . answer is b

divide(const_1, subtract(divide(const_1, 10), divide(const_1, 15)))

<gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">(1/10) - (1/15)</gadget>
<output>1/30 = around 0.033333</output>
<gadget id="calculator">1 / (1/30)</gadget>
<output>30</output>
<result>30</result>


a garrison of 2000 men has provisions for 54 days . at the end of 18 days , a reinforcement arrives , and it is now found that the provisions will last only for 20 days more . what is the reinforcement ?

Explanation: "2000 - - - - 54 2000 - - - - 36 x - - - - - 20 x * 20 = 2000 * 36 x = 3600 2000 - - - - - - - 1600 answer : b"

subtract(divide(subtract(multiply(2000, 54), multiply(2000, 18)), 20), 2000)

<gadget id="calculator">2_000 * 54</gadget>
<output>108_000</output>
<gadget id="calculator">2_000 * 18</gadget>
<output>36_000</output>
<gadget id="calculator">108_000 - 36_000</gadget>
<output>72_000</output>
<gadget id="calculator">72_000 / 20</gadget>
<output>3_600</output>
<gadget id="calculator">3_600 - 2_000</gadget>
<output>1_600</output>
<result>1_600</result>


the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 75 kg . what might be the weight of the new person ?

Explanation: "a 95 kg total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 75 + 20 ) kg = 95 kg ."

<gadget id="calculator">8 * 2.5</gadget>
<output>20</output>
<gadget id="calculator">20 + 75</gadget>
<output>95</output>
<result>95</result>


when a merchant imported a certain item , she paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1,000 . if the amount of the import tax that the merchant paid was $ 109.20 , what was the total value of the item ?

Explanation: "let x be the value of the item . 0.07 * ( x - 1000 ) = 109.20 x = 2560 the answer is e ."

<gadget id="calculator">7 / 100</gadget>
<output>7/100 = around 0.07</output>
<gadget id="calculator">109.2 / (7/100)</gadget>
<output>1_560</output>
<gadget id="calculator">1_000 + 1_560</gadget>
<output>2_560</output>
<result>2_560</result>


a can finish a piece of work in 4 days . b can do it in 10 days . they work together for two days and then a goes away . in how many days will b finish the work ?

Explanation: 2 / 4 + ( 2 + x ) / 10 = 1 = > x = 3 days answer : a

divide(subtract(const_1, add(multiply(divide(const_1, 4), const_2), multiply(divide(const_1, 10), const_2))), divide(const_1, 10))

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) * 2</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/2) + (1/5)</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">1 - (7/10)</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(3/10) / (1/10)</gadget>
<output>3</output>
<result>3</result>


if the sides of a triangle are 26 cm , 24 cm and 15 cm , what is its area ?

Explanation: "the triangle with sides 26 cm , 24 cm and 15 cm is right angled , where the hypotenuse is 26 cm . area of the triangle = 1 / 2 * 24 * 15 = 180 cm 2 answer : c"

<gadget id="calculator">24 * 15</gadget>
<output>360</output>
<gadget id="calculator">360 / 2</gadget>
<output>180</output>
<result>180</result>


two trains , a and b , started simultaneously from opposite ends of a 125 - mile route and traveled toward each other on parallel tracks . train a , traveling at a constant rate , completed the 125 - mile trip in 12 hours ; train b , traveling at a constant rate , completed the 125 - mile trip in 8 hours . how many miles had train a traveled when it met train b ?

Explanation: as the ratio of the rates of a and b is 8 to 12 then the distance covered at the time of the meeting ( so after traveling the same time interval ) would also be in that ratio , which means that a would cover 8 / ( 8 + 12 ) = 8 / 20 of 125 miles : 125 * 8 / 20 = 50 miles . answer : e .

<gadget id="calculator">12 + 8</gadget>
<output>20</output>
<gadget id="calculator">8 / 20</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) * 125</gadget>
<output>50</output>
<result>50</result>


if the simple interest on a certain amount in at 4 % rate 5 years amounted to rs . 2400 less than the principal . what was the principal ?

Explanation: "p - 2400 = ( p * 5 * 4 ) / 100 p = 3000 answer : d"

divide(2400, subtract(const_1, divide(multiply(4, 5), const_100)))

<gadget id="calculator">4 * 5</gadget>
<output>20</output>
<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">2_400 / (4/5)</gadget>
<output>3_000</output>
<result>3_000</result>


out of 250 students of a college , 160 play football , 90 play cricket and 50 neither play football nor cricket . how many students play both football and cricket ?

Explanation: explanation : solution : n ( a ) = 160 , n ( b ) = 90 , n ( a u b ) = 250 - 50 = 200 . required number = > n ( a ^ b ) = n ( a ) + n ( b ) - n ( a u b ) = 160 + 90 - 200 = 250 - 200 = 50 . answer : c

<gadget id="calculator">160 + 90</gadget>
<output>250</output>
<gadget id="calculator">50 + 250</gadget>
<output>300</output>
<gadget id="calculator">300 - 250</gadget>
<output>50</output>
<result>50</result>


what is the area a of the square with the following coordinates : ( x , y ) , ( 20 , 20 ) , ( 20 , 5 ) , ( x , 5 ) ?

Explanation: length of one side = 15 ( 20 - 5 ) since , its a square , the area will be a = 15 ^ 2 = 225 d is the answer

it can not be determined from the information given

<gadget id="calculator">20 - 5</gadget>
<output>15</output>
<gadget id="calculator">15 ** 2</gadget>
<output>225</output>
<result>225</result>


a van takes 5 hours to cover a distance of 495 km . what speed in kph should the van maintain to cover the same distance in 3 / 2 of the previous time ?

Explanation: "( 3 / 2 ) * 5 = 7.5 hours 495 / 7.5 = 66 kph the answer is c ."

<gadget id="calculator">3 / 2</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(3/2) * 5</gadget>
<output>15/2 = around 7.5</output>
<gadget id="calculator">495 / (15/2)</gadget>
<output>66</output>
<result>66</result>


find the compound interest on $ 1000 in 2 years at 4 % per annum , the interest being compounded half - yearly ?

Explanation: "principle = $ 10000 rate = 2 % half yearly = 4 half years amount = 1000 * ( 1 + 2 / 100 ) ^ 4 = 1000 * 51 / 50 * 51 / 50 * 51 / 50 * 51 / 50 = $ 1082.43 c . i . = 1082.43 - 1000 = $ 82.43 answer is b"

subtract(multiply(power(add(divide(divide(4, const_100), 2), const_1), 4), 1000), 1000)


a train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 15 seconds . what is the length of the platform in meters ?

Explanation: speed of the train in metres / sec = 72000 / 3600 = 20 distance travelled by train to cross the platform = 30 * 20 = 600 = length of train + length of platform distance travelled by train to cross the man = 15 * 20 = 300 = length of train length of platform = 600 - 300 = 300 answer : c

subtract(multiply(divide(multiply(72, const_1000), const_3600), 30), multiply(divide(multiply(72, const_1000), const_3600), 15))

<gadget id="calculator">72 * 1_000</gadget>
<output>72_000</output>
<gadget id="calculator">72_000 / 3_600</gadget>
<output>20</output>
<gadget id="calculator">20 * 30</gadget>
<output>600</output>
<gadget id="calculator">20 * 15</gadget>
<output>300</output>
<gadget id="calculator">600 - 300</gadget>
<output>300</output>
<result>300</result>


brenda and sally run in opposite direction on a circular track , starting at diametrically opposite points . they first meet after brenda has run 50 meters . they next meet after sally has run 150 meters past their first meeting point . each girl runs at a constant speed . what is the length of the track in meters ?

Explanation: "nice problem . + 1 . first timetogetherthey run half of the circumference . second timetogetherthey run full circumference . first time brenda runs 50 meters , thus second time she runs 2 * 50 = 100 meters . since second time ( when they run full circumference ) brenda runs 200 meters and sally runs 150 meters , thus the circumference is 100 + 150 = 250 meters . answer : a ."

<gadget id="calculator">2 * 50</gadget>
<output>100</output>
<gadget id="calculator">100 + 150</gadget>
<output>250</output>
<result>250</result>


a man buys a cycle for rs . 1900 and sells it at a loss of 18 % . what is the selling price of the cycle ?

Explanation: "s . p . = 82 % of rs . 1900 = rs . 82 x 1900 / 100 = rs . 1558 answer : option c"

divide(multiply(subtract(const_100, 18), 1900), const_100)

<gadget id="calculator">100 - 18</gadget>
<output>82</output>
<gadget id="calculator">82 * 1_900</gadget>
<output>155_800</output>
<gadget id="calculator">155_800 / 100</gadget>
<output>1_558</output>
<result>1_558</result>


at the end of the day , february 14 th , a florist had 120 roses left in his shop , all of which were red , white or pink in color and either long or short - stemmed . a third of the roses were short - stemmed , 20 of which were white and 10 of which were pink . the percentage of pink roses that were short - stemmed equaled the percentage of red roses that were short - stemmed . if none of the long - stemmed roses were white , what percentage of the long - stemmed roses were red ?

Explanation: "r + w + p = 120 s + l = 120 1 / 3 * 120 = 40 short - stemmed white = 20 short - stemmed pink = 10 = > short - stemmed red = 10 10 / p = 10 / r = > r = p so total long stemmed = 80 and long stemmed red + long stemmed pink = 80 so long stemmed red / long stemmed = ? total white = 20 ( as no long stemmed white ) = > r + r + 20 = 120 = > 2 r = 100 and r = 50 long stemmed r = 50 - 10 = 40 so long stemmed red / r = 40 / 80 = 50 % answer - b"

multiply(divide(divide(multiply(subtract(120, divide(120, const_3)), subtract(subtract(divide(120, const_3), 20), 10)), add(10, subtract(subtract(divide(120, const_3), 20), 10))), subtract(120, divide(120, const_3))), const_100)

<gadget id="calculator">120 / 3</gadget>
<output>40</output>
<gadget id="calculator">120 - 40</gadget>
<output>80</output>
<gadget id="calculator">40 - 20</gadget>
<output>20</output>
<gadget id="calculator">20 - 10</gadget>
<output>10</output>
<gadget id="calculator">80 * 10</gadget>
<output>800</output>
<gadget id="calculator">10 + 10</gadget>
<output>20</output>
<gadget id="calculator">800 / 20</gadget>
<output>40</output>
<gadget id="calculator">40 / 80</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * 100</gadget>
<output>50</output>
<result>50</result>


the difference between a two - digit number and the number obtained by interchanging the positions of its digits is 27 . what is the difference between the two digits of that number ?

Explanation: "sol . let the ten ’ s digit be x and unit ’ s digit be y , then , ( 10 x + y ) - ( 10 y + x ) = 27 ⇔ 9 ( x - y ) = 27 ⇔ x - y = 3 answer a"

<gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">27 / 9</gadget>
<output>3</output>
<result>3</result>


a fair price shopkeeper takes 10 % profit on his goods . he lost 60 % goods during theft . his loss percent is :

Explanation: "explanation : suppose he has 100 items . let c . p . of each item be re . 1 . total cost = rs . 100 . number of items left after theft = 40 . s . p . of each item = rs . 1.10 total sale = 1.10 * 40 = rs . 44 hence , loss % = 56 / 100 * 100 = 56 % answer : c"

subtract(const_100, subtract(add(const_100, 10), divide(multiply(add(const_100, 10), 60), const_100)))

<gadget id="calculator">100 + 10</gadget>
<output>110</output>
<gadget id="calculator">110 * 60</gadget>
<output>6_600</output>
<gadget id="calculator">6_600 / 100</gadget>
<output>66</output>
<gadget id="calculator">110 - 66</gadget>
<output>44</output>
<gadget id="calculator">100 - 44</gadget>
<output>56</output>
<result>56</result>


a corporation that had $ 115.19 billion in profits for the year paid out $ 230.10 million in employee benefits . approximately what percent of the profits were the employee benefits ? ( note : 1 billion = 10 ^ 9 )

Explanation: required answer = [ employee benefit / profit ] * 100 = [ ( 230.10 million ) / ( 115.19 billion ) ] * 100 = [ ( 230.10 * 10 ^ 6 ) / ( 115.19 * 10 ^ 9 ) ] * 100 = ( 2 / 1000 ) * 100 = 0.2 % so answer is ( e )

multiply(divide(multiply(230.1, power(10, add(const_3, const_3))), multiply(115.19, power(10, 9))), const_100)


39 men can complete a piece of work in 18 days . in how many days will 27 men complete the same work ?

Explanation: "explanation : less men , means more days { indirect proportion } let the number of days be x then , 27 : 39 : : 18 : x [ please pay attention , we have written 27 : 39 rather than 39 : 27 , in indirect proportion , if you get it then chain rule is clear to you : ) ] { \ color { blue } x = \ frac { 39 \ times 18 } { 27 } } x = 26 so 26 days will be required to get work done by 27 men . answer : c"

<gadget id="calculator">18 * 39</gadget>
<output>702</output>
<gadget id="calculator">702 / 27</gadget>
<output>26</output>
<result>26</result>


a metallic sphere of radius 24 cm is melted and drawn into a wire , whose radius of cross section is 16 cm . what is the length of the wire ?

Explanation: "volume of the wire ( in cylindrical shape ) is equal to the volume of the sphere . π ( 16 ) ^ 2 * h = ( 4 / 3 ) π ( 24 ) ^ 3 = > h = 72 cm answer : e"

divide(multiply(const_4, divide(power(24, const_3), power(16, const_2))), const_3)

<gadget id="calculator">24 ** 3</gadget>
<output>13_824</output>
<gadget id="calculator">16 ** 2</gadget>
<output>256</output>
<gadget id="calculator">13_824 / 256</gadget>
<output>54</output>
<gadget id="calculator">4 * 54</gadget>
<output>216</output>
<gadget id="calculator">216 / 3</gadget>
<output>72</output>
<result>72</result>


how many multiples of 4 are there between 32 and 252 ?

Explanation: "it should be mentioned whether 32 and 252 are inclusive . if 32 and 252 are inclusive , then the answer is ( 252 - 32 ) / 4 + 1 = 56 . if 32 and 252 are not inclusive , then the answer is ( 248 - 36 ) / 4 + 1 = 54 . since oa is c , then we have not inclusive case ."

add(divide(subtract(252, 32), 4), const_1)

<gadget id="calculator">252 - 32</gadget>
<output>220</output>
<gadget id="calculator">220 / 4</gadget>
<output>55</output>
<gadget id="calculator">55 + 1</gadget>
<output>56</output>
<result>56</result>


set # 1 = { a , b , c , d , e , f } set # 2 = { k , l , m , n , o , p } there are these two sets of letters , and you are going to pick exactly one letter from each set . what is the probability of picking at least one vowel ?

Explanation: so not a vowel in set - 1 : 4 / 6 and not a vowel in ser - 2 : 5 / 6 now , 4 / 6 ∗ 5 / 6 = 5 / 9 this is for not a vowel . then for at least one vowel will be = 1 − 5 / 9 = 4 / 9 answer will be e .

subtract(1, multiply(divide(const_4, add(const_4, const_2)), divide(add(const_3, const_2), add(const_4, const_2))))

<gadget id="calculator">4 + 2</gadget>
<output>6</output>
<gadget id="calculator">4 / 6</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">5 / 6</gadget>
<output>5/6 = around 0.833333</output>
<gadget id="calculator">(2/3) * (5/6)</gadget>
<output>5/9 = around 0.555556</output>
<gadget id="calculator">1 - (5/9)</gadget>
<output>4/9 = around 0.444444</output>
<result>4/9 = around 0.444444</result>


if a no . when divided by 44 , gives 432 as quotient and 0 as remainder . what will be the remainder when dividing thesame no . by 31

Explanation: p ÷ 44 = 432 = > p = 432 * 44 = 19008 p / 31 = 19008 / 31 = 613 , remainder = 5 c

<gadget id="calculator">432 * 44</gadget>
<output>19_008</output>
<gadget id="calculator">19_008 % 31</gadget>
<output>5</output>
<result>5</result>


the age of somu is one - third his father ' s . 7 years back he was one - fifth of his father ' s age . what is his persent age ?

Explanation: "explanation : let somu ' s age be x and that of his father be 3 x . so , x - 7 = 3 x - 7 / 5 = x = 14 answer : option c"

divide(subtract(multiply(add(const_4, const_1), 7), 7), subtract(add(const_4, const_1), const_3))

<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">5 * 7</gadget>
<output>35</output>
<gadget id="calculator">35 - 7</gadget>
<output>28</output>
<gadget id="calculator">5 - 3</gadget>
<output>2</output>
<gadget id="calculator">28 / 2</gadget>
<output>14</output>
<result>14</result>


sam ’ s car was fined when he gave joe and peter a ride , so they decided to help sam pay the fine . joe paid $ 6 more than 1 / 4 of the fine and peter paid $ 6 less than 1 / 3 of the fine , leaving pay $ 10 less than 1 / 2 the fine to complete the payment . what fraction of the fine did sam pay ?

Explanation: "call the fine f . joe paid ( 1 / 4 ) f + 4 and peter paid ( 1 / 3 ) f – 4 , leaving ( 1 / 2 ) f – 5 left . if we add those three up , they should add up to f . f = [ ( 1 / 4 ) f + 6 ] + [ ( 1 / 3 ) f – 6 ] + [ ( 1 / 2 ) f – 10 ] f = ( 1 / 4 ) f + ( 1 / 3 ) f + ( 1 / 2 ) f – 10 multiply all terms by 12 to clear the fractions . 12 f = 3 f + 4 f + 6 f – 120 12 f = 13 f – 120 – f = – 120 f = 120 well , if the fine cost $ 120 , then sam paid the part not covered by joe or peter . half the fine is $ 60 , and sam paid $ 10 less than this : $ 50 . answer = a"

add(multiply(add(multiply(add(divide(1, 2), add(divide(1, 4), divide(1, 3))), 10), 10), 2), const_10)

<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 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/4) + (1/3)</gadget>
<output>7/12 = around 0.583333</output>
<gadget id="calculator">(1/2) + (7/12)</gadget>
<output>13/12 = around 1.083333</output>
<gadget id="calculator">(13/12) * 10</gadget>
<output>65/6 = around 10.833333</output>
<gadget id="calculator">(65/6) + 10</gadget>
<output>125/6 = around 20.833333</output>
<gadget id="calculator">(125/6) * 2</gadget>
<output>125/3 = around 41.666667</output>
<gadget id="calculator">(125/3) + 10</gadget>
<output>155/3 = around 51.666667</output>
<result>155/3 = around 51.666667</result>


the average wages of a worker during a fortnight comprising 15 consecutive working days was $ 90 per day . during the first 7 days , his average wages was $ 87 per day and the average wages during the last 7 days was $ 91 per day . what was his wage on the 8 th day ?

Explanation: "average daily wage of a worker for 15 consecutive working days = 90 $ during the first 7 days , the daily average daily wage = 87 $ during the last 7 days , the daily average daily wage = 91 $ wage on 8 th day = 90 * 15 - ( 87 * 7 + 91 * 7 ) = 1350 - ( 609 + 637 ) = 1350 - 1246 = 104 answer e"

subtract(multiply(90, 15), add(multiply(87, 7), multiply(91, 7)))

<gadget id="calculator">90 * 15</gadget>
<output>1_350</output>
<gadget id="calculator">87 * 7</gadget>
<output>609</output>
<gadget id="calculator">91 * 7</gadget>
<output>637</output>
<gadget id="calculator">609 + 637</gadget>
<output>1_246</output>
<gadget id="calculator">1_350 - 1_246</gadget>
<output>104</output>
<result>104</result>


in a class , there are 18 boys who are over 160 cm tall . if these constitute 3 - fourths of the boys and the total number of boys is two - thirds of the total number of students in the class , what is the number of girls in the class ?

Explanation: let the number of boys be x . then , ( 3 / 4 ) x = 18 or x = 18 x ( 4 / 3 ) = 24 . if total number of students is y , then ( 2 / 3 ) y = 24 or y = 24 x ( 3 / 2 ) = 36 . therefore number of girls in the class = ( 36 - 24 ) = 12 . answer : b

subtract(divide(divide(18, divide(3, const_4)), divide(const_2, 3)), divide(18, divide(3, const_4)))

<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">18 / (3/4)</gadget>
<output>24</output>
<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">24 / (2/3)</gadget>
<output>36</output>
<gadget id="calculator">36 - 24</gadget>
<output>12</output>
<result>12</result>


the perimeter of a triangle is 40 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle ?

Explanation: "area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 40 / 2 = 50 cm 2 answer : e"

<gadget id="calculator">(2.5 * 40) / 2</gadget>
<output>50</output>
<result>50</result>


if 75 percent of a class answered the first question on a certain test correctly , 70 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?

Explanation: { total } = { first } + { second } - { both } + { neither } 100 % = 75 % + 70 % - { both } + 20 % - - > { both } = 65 % . answer : e .

subtract(add(add(75, 70), 20), const_100)

<gadget id="calculator">75 + 70</gadget>
<output>145</output>
<gadget id="calculator">145 + 20</gadget>
<output>165</output>
<gadget id="calculator">165 - 100</gadget>
<output>65</output>
<result>65</result>


if a man lost 4 % by selling oranges at the rate of 72 a rupee at how many a rupee must he sell them to gain 44 % ?

Explanation: "96 % - - - - 72 144 % - - - - ? 96 / 144 * 72 = 48 answer : b"

divide(multiply(subtract(const_100, 4), 72), add(const_100, 44))

<gadget id="calculator">100 - 4</gadget>
<output>96</output>
<gadget id="calculator">96 * 72</gadget>
<output>6_912</output>
<gadget id="calculator">100 + 44</gadget>
<output>144</output>
<gadget id="calculator">6_912 / 144</gadget>
<output>48</output>
<result>48</result>


Explanation: "| 5 - 2 | - | 6 - 9 | = | 3 | - | - 3 | = 3 - 3 = 0 correct answer d"

subtract(subtract(5, 2), subtract(9, 6))

<gadget id="calculator">5 - 2</gadget>
<output>3</output>
<gadget id="calculator">9 - 6</gadget>
<output>3</output>
<gadget id="calculator">3 - 3</gadget>
<output>0</output>
<result>0</result>


Explanation: 121 × 54 = 121 × ( 102 ) 4 = 121 × 1000016 = 7.5625 × 10000 = 75625 e

multiply(add(add(121, 121), divide(multiply(121, 121), const_2)), const_10)

<gadget id="calculator">121 + 121</gadget>
<output>242</output>
<gadget id="calculator">121 * 121</gadget>
<output>14_641</output>
<gadget id="calculator">14_641 / 2</gadget>
<output>14_641/2 = around 7_320.5</output>
<gadget id="calculator">242 + (14_641/2)</gadget>
<output>15_125/2 = around 7_562.5</output>
<gadget id="calculator">(15_125/2) * 10</gadget>
<output>75_625</output>
<result>75_625</result>


aishwarya rai walks into a bank to cash out her check . by mistake the bank teller gives her dollar amount in change , and her cent amount in dollars . on the way home she spends 5 cent , and then suddenly she notices that she has twice the amount of her check . how much was her check amount ?

Explanation: e the check was for dollars 31.63 . the bank teller gave her dollars 63.31 she spent . 05 , and then she had dollars 63.26 , which is twice the check . let x be the dollars of the check , and y be the cent . the check was for 100 x + y cent he was given 100 y + x cent also 100 y + x - 5 = 2 ( 100 x + y ) expanding this out and rearranging , we find : 98 y = 199 x + 5 or 199 x ≡ - 5 ( mod 98 ) or 98 * 2 * x + 3 x ≡ - 5 ( mod 98 ) 3 x ≡ - 5 ≡ 93 ( mod 98 ) this quickly leads to x = 31

divide(multiply(subtract(const_1, divide(5, subtract(const_100, const_2))), subtract(const_100, const_2)), const_3)

<gadget id="calculator">100 - 2</gadget>
<output>98</output>
<gadget id="calculator">5 / 98</gadget>
<output>5/98 = around 0.05102</output>
<gadget id="calculator">1 - (5/98)</gadget>
<output>93/98 = around 0.94898</output>
<gadget id="calculator">(93/98) * 98</gadget>
<output>93</output>
<gadget id="calculator">93 / 3</gadget>
<output>31</output>
<result>31</result>


the length of a room is 9 m and width is 4.75 m . what is the cost of paying the floor by slabs at the rate of rs . 900 per sq . metre .

Explanation: "area = 9 × 4.75 sq . metre . cost for 1 sq . metre . = rs . 900 hence total cost = 9 × 4.75 × 900 = 9 × 4275 = rs . 38475 answer is e ."

<gadget id="calculator">9 * 4.75</gadget>
<output>42.75</output>
<gadget id="calculator">900 * 42.75</gadget>
<output>38_475</output>
<result>38_475</result>


if 2 ^ 5 , 3 ^ 3 , and 13 ^ 2 are all factors of the product of 936 and w where w is a positive integer , what is the smallest possible value of w ?

Explanation: "here 156 has three two ' s two three ' s and one 13 rest of them must be in w so w = 13 * 3 * 4 = 156 answer : e"

multiply(multiply(multiply(power(2, 2), 3), divide(13, 2)), 2)

<gadget id="calculator">2 ** 2</gadget>
<output>4</output>
<gadget id="calculator">4 * 3</gadget>
<output>12</output>
<gadget id="calculator">13 / 2</gadget>
<output>13/2 = around 6.5</output>
<gadget id="calculator">12 * (13/2)</gadget>
<output>78</output>
<gadget id="calculator">78 * 2</gadget>
<output>156</output>
<result>156</result>


i chose a number and divide it by 12 . then i subtracted 240 from the result and got 8 . what was the number i chose ?

Explanation: "let x be the number i chose , then x / 12 − 240 = 8 x / 12 = 248 x = 2976 answer is a ."

<gadget id="calculator">240 + 8</gadget>
<output>248</output>
<gadget id="calculator">248 * 12</gadget>
<output>2_976</output>
<result>2_976</result>


in what time will a train 100 meters long cross an electric pole , if its speed is 72 km / hr

Explanation: "first convert speed into m / sec speed = 72 * ( 5 / 18 ) = 20 m / sec time = distance / speed = 100 / 20 = 5 seconds answer : a"

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">72 * (5/18)</gadget>
<output>20</output>
<gadget id="calculator">100 / 20</gadget>
<output>5</output>
<result>5</result>


at joel ’ s bookstore , the current inventory is 30 % historical fiction . of the historical fiction books , 40 % are new releases , while 50 % of the other books are new releases . what fraction of all new releases are the historical fiction new releases ?

Explanation: let there be 100 books in all historic fiction books = 30 % of total = 30 other books = 70 new historic fiction = 40 % of 30 = 12 other new books = 50 % of 70 = 35 total new books = 35 + 12 = 47 fraction = 12 / 47 ans : b

divide(divide(multiply(30, 40), const_100), add(divide(multiply(30, 40), const_100), divide(multiply(50, subtract(const_100, 30)), const_100)))

<gadget id="calculator">30 * 40</gadget>
<output>1_200</output>
<gadget id="calculator">1_200 / 100</gadget>
<output>12</output>
<gadget id="calculator">100 - 30</gadget>
<output>70</output>
<gadget id="calculator">50 * 70</gadget>
<output>3_500</output>
<gadget id="calculator">3_500 / 100</gadget>
<output>35</output>
<gadget id="calculator">12 + 35</gadget>
<output>47</output>
<gadget id="calculator">12 / 47</gadget>
<output>12/47 = around 0.255319</output>
<result>12/47 = around 0.255319</result>


if 45 % of a class averages 95 % on a test , 50 % of the class averages 78 % on the test , and the remainder of the class averages 60 % on the test , what is the overall class average ? ( round final answer to the nearest percent ) .

Explanation: "this question is a weighted average question with a series of dependent variables . the remaining portion of the class represents 100 % - 45 % - 50 % = 5 % of the class converting the portions of the class population to decimal weights , we find : class average = 0.45 x 95 + 0.50 x 78 + 0.05 x 60 = 84.75 the class average ( rounded ) is 85 % final answer c ) 85 %"

divide(add(add(multiply(45, 95), multiply(50, 78)), multiply(subtract(const_100, add(45, 50)), 60)), const_100)

<gadget id="calculator">45 * 95</gadget>
<output>4_275</output>
<gadget id="calculator">50 * 78</gadget>
<output>3_900</output>
<gadget id="calculator">4_275 + 3_900</gadget>
<output>8_175</output>
<gadget id="calculator">45 + 50</gadget>
<output>95</output>
<gadget id="calculator">100 - 95</gadget>
<output>5</output>
<gadget id="calculator">5 * 60</gadget>
<output>300</output>
<gadget id="calculator">8_175 + 300</gadget>
<output>8_475</output>
<gadget id="calculator">8_475 / 100</gadget>
<output>339/4 = around 84.75</output>
<result>339/4 = around 84.75</result>


on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.30 per glass on the first day , what was the price per glass on the second day ?

Explanation: "on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.3 = 3 * x - - > x = $ 0.2 . answer : b ."

divide(multiply(add(const_1, const_1), 0.30), add(const_1, const_2))

<gadget id="calculator">1 + 1</gadget>
<output>2</output>
<gadget id="calculator">2 * 0.3</gadget>
<output>0.6</output>
<gadget id="calculator">1 + 2</gadget>
<output>3</output>
<gadget id="calculator">0.6 / 3</gadget>
<output>0.2</output>
<result>0.2</result>


calculate the effect changes in dimension of a rectangle will have on its area , if length is increased by 40 % and its breadth is decreased by 25 % ?

Explanation: "let l and b be 100 each 100 * 100 = 10000 l increase by 40 % = 140 b decrease by 25 % = 75 140 * 75 = 10500 5 % increase answer : a"

multiply(divide(subtract(multiply(add(const_100, 40), subtract(const_100, 25)), multiply(const_100, const_100)), multiply(const_100, const_100)), const_100)

<gadget id="calculator">100 + 40</gadget>
<output>140</output>
<gadget id="calculator">100 - 25</gadget>
<output>75</output>
<gadget id="calculator">140 * 75</gadget>
<output>10_500</output>
<gadget id="calculator">100 * 100</gadget>
<output>10_000</output>
<gadget id="calculator">10_500 - 10_000</gadget>
<output>500</output>
<gadget id="calculator">500 / 10_000</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/20) * 100</gadget>
<output>5</output>
<result>5</result>


if 3 / w + 3 / x = 3 / y and wx = y , then the average ( arithmetic mean ) of w and x is

Explanation: "given : 3 / w + 3 / x = 3 / ywx = y find : ( w + x ) / 2 = ? 3 ( 1 / w + 1 / x ) = 3 ( 1 / y ) - divide both sides by 3 ( 1 / w + 1 / x ) = 1 / y ( x + w ) / wx = 1 / wx - sub ' d in y = wx x + w - 1 = 0 x + w = 1 therefore ( w + x ) / 2 = 1 / 2 ans : a"

<gadget id="calculator">3 + 3</gadget>
<output>6</output>
<gadget id="calculator">3 / 6</gadget>
<output>1/2 = around 0.5</output>
<result>1/2 = around 0.5</result>


- - - - - - - - - - - - - - - - yes - - - - - - - - - no - - - - unsure subject m - - - - 500 - - - - - - - - 200 - - - - - 100 subject r - - - - 400 - - - - - - - - 100 - - - - - 300 a total of 800 students were asked whether they found two subjects , m and r , interesting . each answer was either yes or no or unsure , and the numbers of students who gave these answers are listed in the table above . if 140 students answered yes only for subject m , how many of the students did not answer yes for either subject ?

Explanation: "since 140 students answered yes only for subject m , then the remaining 360 students who answered yes for subject m , also answered yes for subject r . so , 360 students answered yes for both subjects . if 360 students answered yes for both subjects , then 400 - 360 = 40 students answered yes only for subject r . so , we have that : 200 students answered yes only for subject m ; 40 students answered yes only for subject r ; 300 students answered yes for both subjects ; therefore 800 - ( 200 + 40 + 300 ) = 260 students did not answer yes for either subject . answer : b ."

<gadget id="calculator">500 - 140</gadget>
<output>360</output>
<gadget id="calculator">140 + 360</gadget>
<output>500</output>
<gadget id="calculator">400 - 360</gadget>
<output>40</output>
<gadget id="calculator">500 + 40</gadget>
<output>540</output>
<gadget id="calculator">800 - 540</gadget>
<output>260</output>
<result>260</result>


the area of a square field is 7201 sq m . how long will a lady take to cross the field diagonally at the rate of 2.4 km / hr ?

Explanation: area of a square field = 7201 sq m let the side of square = a a ^ 2 = 7201 = > a = 84.86 diagonal = ( 2 ) ^ ( 1 / 2 ) * a = 1.414 * 84.86 = 120 speed of lady = 2.4 km / hour = 2400 m / hour = 40 m / min time taken by lady to cross the field diagonally = 120 / 40 = 3 min answer b

<gadget id="calculator">2.4 * 1_000</gadget>
<output>2_400</output>
<gadget id="calculator">7_201 / 2_400</gadget>
<output>7_201/2_400 = around 3.000417</output>
<result>7_201/2_400 = around 3.000417</result>


running at the same constant rate , 6 identical machines can produce a total of 270 bottles per minute . at this rate , how many bottles could 8 such machines produce in 4 minutes ?

Explanation: "solution let the required number of bottles be x . more machines , more bottles ( direct proportion ) more minutes , more bottles ( direct proportion ) â ˆ ´ 6 ã — 1 ã — x = 8 ã — 4 ã — 270 â ‡ ” x = 8 x 4 x 270 / 6 = 1440 . answer d"

multiply(multiply(divide(270, 6), 4), 8)

<gadget id="calculator">270 / 6</gadget>
<output>45</output>
<gadget id="calculator">45 * 4</gadget>
<output>180</output>
<gadget id="calculator">180 * 8</gadget>
<output>1_440</output>
<result>1_440</result>


a number when divided b the sum of 555 and 445 gives two times their difference as quotient and 30 as the remainder . the number is :

Explanation: required number = ( 555 + 445 ) * 2 * 110 + 30 = 220000 + 30 = 220030 . answer : d

add(multiply(multiply(subtract(555, 445), const_2), const_100), 30)

<gadget id="calculator">555 - 445</gadget>
<output>110</output>
<gadget id="calculator">110 * 2</gadget>
<output>220</output>
<gadget id="calculator">220 * 100</gadget>
<output>22_000</output>
<gadget id="calculator">22_000 + 30</gadget>
<output>22_030</output>
<result>22_030</result>


compound x contains elements a and b at an approximate ratio , by weight , of 2 : 10 . approximately how many grams of element b are there in 108 grams of compound x ?

Explanation: "total number of fractions = 2 + 10 = 12 element b constitutes = 10 out of 12 parts of x so in 108 gms of x have 108 * 10 / 12 = 90 gms of b and 108 - 90 = 18 gms of a . cross check : - a / b = 18 / 90 = 2 / 10 ( as given ) ans a"

<gadget id="calculator">108 * 10</gadget>
<output>1_080</output>
<gadget id="calculator">2 + 10</gadget>
<output>12</output>
<gadget id="calculator">1_080 / 12</gadget>
<output>90</output>
<result>90</result>


tough and tricky questions : ratios 4 / 5 of a certain class left on a field trip . 1 / 3 of the students who stayed behind did not want to go on the field trip ( all the others did want to go ) . when another vehicle was located , 1 / 2 of the students who did want to go on the field trip but had been left behind were able to join . what fraction of the class ended up going on the field trip ?

Explanation: let total no . of students be 30 students left on a field trip = 4 / 5 ( 30 ) = 24 thus 6 students left behind 1 / 3 ( 6 ) = 2 students did not want to go . thus 4 students want to go on the trip 1 / 2 ( 4 ) = 2 were able to join the other students on the field trip . thus total number of students that went on a field trip = 24 + 2 = 26 thus required fraction = 26 / 30 = 13 / 15 c

divide(add(multiply(divide(1, 2), subtract(subtract(lcm(lcm(3, 5), 2), multiply(divide(4, 5), lcm(lcm(3, 5), 2))), multiply(divide(1, 3), subtract(lcm(lcm(3, 5), 2), multiply(divide(4, 5), lcm(lcm(3, 5), 2)))))), multiply(divide(4, 5), lcm(lcm(3, 5), 2))), lcm(lcm(3, 5), 2))

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">lcm(3, 5)</gadget>
<output>15</output>
<gadget id="calculator">lcm(15, 2)</gadget>
<output>30</output>
<gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(4/5) * 30</gadget>
<output>24</output>
<gadget id="calculator">30 - 24</gadget>
<output>6</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/3) * 6</gadget>
<output>2</output>
<gadget id="calculator">6 - 2</gadget>
<output>4</output>
<gadget id="calculator">(1/2) * 4</gadget>
<output>2</output>
<gadget id="calculator">2 + 24</gadget>
<output>26</output>
<gadget id="calculator">26 / 30</gadget>
<output>13/15 = around 0.866667</output>
<result>13/15 = around 0.866667</result>


if x ^ 2 + 9 / x ^ 2 = 10 , what is the value of x - 3 / x

Explanation: to find : x - 3 / x . let it be t . = > x - 3 / x = t = > ( x ^ 2 + 9 / x ^ 2 ) - 2 * x * 3 / x = t ^ 2 ( squaring both sides ) . = > ( 10 ) - 2 * 3 = 4 = > t ^ 2 = 4 . thus t = 2 or t = - 2 . answer c

<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">10 - 6</gadget>
<output>4</output>
<gadget id="calculator">4 ** (1/2)</gadget>
<output>2</output>
<result>2</result>


the average salary / head of all the workers in a workshop is rs . 1100 , if the average salary / head of 9 technician is rs . 1300 and the average salary / head of the rest is rs . 880 , the total no . of workers in the work - shop is ?

Explanation: let the total number of workers be y . so sum of salary for all workers = sum of salary of 9 technician + sum of salary for other y - 9 workers . 9 x 1300 + 880 ( y - 9 ) = 1100 y ⇒ 11700 + 880 y - 7920 = 1100 y ⇒ 220 y = 3780 ∴ y = 17 so total number of workers = 17 d

divide(subtract(multiply(9, 1300), multiply(880, 9)), subtract(1100, 880))

<gadget id="calculator">9 * 1_300</gadget>
<output>11_700</output>
<gadget id="calculator">880 * 9</gadget>
<output>7_920</output>
<gadget id="calculator">11_700 - 7_920</gadget>
<output>3_780</output>
<gadget id="calculator">1_100 - 880</gadget>
<output>220</output>
<gadget id="calculator">3_780 / 220</gadget>
<output>189/11 = around 17.181818</output>
<result>189/11 = around 17.181818</result>


joe invested a certain sum of money in a simple interest bond whose value grew to $ 310 at the end of 3 years and to $ 410 at the end of another 5 years . what was the rate of interest in which he invested his sum ?

Explanation: "in 5 years , the value grew $ 100 , so the simple interest was $ 20 per year . in 3 years , the total interest was 3 * $ 20 = $ 60 the principal is $ 310 - $ 60 = 250 . the interest rate is $ 20 / $ 250 = 8 % the answer is c ."

multiply(divide(divide(subtract(410, 310), 5), subtract(310, multiply(divide(subtract(410, 310), 5), 3))), const_100)

<gadget id="calculator">410 - 310</gadget>
<output>100</output>
<gadget id="calculator">100 / 5</gadget>
<output>20</output>
<gadget id="calculator">20 * 3</gadget>
<output>60</output>
<gadget id="calculator">310 - 60</gadget>
<output>250</output>
<gadget id="calculator">20 / 250</gadget>
<output>2/25 = around 0.08</output>
<gadget id="calculator">(2/25) * 100</gadget>
<output>8</output>
<result>8</result>


a rhombus has area 432 sq m , one diagonal is 36 cm . find other diagonal ?

Explanation: area of rhombus = 1 / 2 * d 1 * d 2 432 = 1 / 2 * d 1 * . 36 d 1 = 2400 m answer : a

divide(multiply(432, const_2), divide(36, const_100))

<gadget id="calculator">432 * 2</gadget>
<output>864</output>
<gadget id="calculator">36 / 100</gadget>
<output>9/25 = around 0.36</output>
<gadget id="calculator">864 / (9/25)</gadget>
<output>2_400</output>
<result>2_400</result>


if { x } is the product of all even integers from 1 to x inclusive , what is the greatest prime factor of { 12 } + { 10 } ?

Explanation: "soln : { 12 } + { 10 } = 12 * { 10 } + { 10 } = 13 * { 10 } answer : c"

add(divide(add(12, 10), const_2), multiply(1, const_2))

<gadget id="calculator">12 + 10</gadget>
<output>22</output>
<gadget id="calculator">22 / 2</gadget>
<output>11</output>
<gadget id="calculator">1 * 2</gadget>
<output>2</output>
<gadget id="calculator">11 + 2</gadget>
<output>13</output>
<result>13</result>


a , b and c invested rs . 2400 , rs . 7200 and rs . 9600 respectively , in a partnership business . find the share of a in profit of rs . 9000 after a year ?

Explanation: "explanation : 2400 : 7200 : 9600 1 : 3 : 4 1 / 8 * 9000 = 1125 answer : a"

<gadget id="calculator">2_400 + 7_200</gadget>
<output>9_600</output>
<gadget id="calculator">9_600 + 9_600</gadget>
<output>19_200</output>
<gadget id="calculator">2_400 / 19_200</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">(1/8) * 9_000</gadget>
<output>1_125</output>
<result>1_125</result>


a women purchased 3 towels @ rs . 100 each , 5 towels @ rs . 150 each and two towels at a certain rate which is now slipped off from his memory . but she remembers that the average price of the towels was rs . 165 . find the unknown rate of two towels ?

Explanation: "10 * 150 = 1650 3 * 100 + 5 * 150 = 1050 1650 – 1050 = 600 e"

subtract(subtract(multiply(add(add(3, 5), const_2), 165), multiply(5, 150)), multiply(3, 100))

<gadget id="calculator">3 + 5</gadget>
<output>8</output>
<gadget id="calculator">8 + 2</gadget>
<output>10</output>
<gadget id="calculator">10 * 165</gadget>
<output>1_650</output>
<gadget id="calculator">5 * 150</gadget>
<output>750</output>
<gadget id="calculator">1_650 - 750</gadget>
<output>900</output>
<gadget id="calculator">3 * 100</gadget>
<output>300</output>
<gadget id="calculator">900 - 300</gadget>
<output>600</output>
<result>600</result>


aaron will jog from home at 2 miles per hour and then walk back home by the same route at 4 miles per hour . how many miles from home can aaron jog so that he spends a total of 3 hours jogging and walking ?

Explanation: xyt / ( x + y ) x = 2 , y = 4 t = 3 2 * 4 * 3 / 2 + 4 = 18 / 6 = 3 answer : c

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

<gadget id="calculator">2 * 4</gadget>
<output>8</output>
<gadget id="calculator">8 * 3</gadget>
<output>24</output>
<gadget id="calculator">24 / 8</gadget>
<output>3</output>
<result>3</result>


every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 57600 ?

Explanation: 57600 * 9 / 8 * 9 / 8 = 72900 . answer : d

<gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">(1/8) * 57_600</gadget>
<output>7_200</output>
<gadget id="calculator">57_600 + 7_200</gadget>
<output>64_800</output>
<gadget id="calculator">(1/8) * 64_800</gadget>
<output>8_100</output>
<gadget id="calculator">64_800 + 8_100</gadget>
<output>72_900</output>
<result>72_900</result>


for each of her sales , a saleswoman receives a commission equal to 20 percent of the first $ 500 of the total amount of the sale , plus 35 percent of the total amount in excess of $ 500 . if the total amount of one of her sales was $ 800 , the saleswoman ’ s commission was approximately what percent of the total amount of the sale ?

Explanation: "total sales = 800 comission = ( 20 / 100 ) * 500 + ( 35 / 100 ) * 300 = 100 + 105 = 205 % comission = ( 205 / 800 ) * 100 = 25.6 ~ 26 % answer is d"

multiply(divide(add(multiply(divide(20, const_100), 500), multiply(divide(35, const_100), subtract(800, 500))), 800), const_100)

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 500</gadget>
<output>100</output>
<gadget id="calculator">35 / 100</gadget>
<output>7/20 = around 0.35</output>
<gadget id="calculator">800 - 500</gadget>
<output>300</output>
<gadget id="calculator">(7/20) * 300</gadget>
<output>105</output>
<gadget id="calculator">100 + 105</gadget>
<output>205</output>
<gadget id="calculator">205 / 800</gadget>
<output>41/160 = around 0.25625</output>
<gadget id="calculator">(41/160) * 100</gadget>
<output>205/8 = around 25.625</output>
<result>205/8 = around 25.625</result>


a boat can travel with a speed of 22 km / hr in still water . if the speed of the stream is 5 km / hr , find the time taken by the boat to go 135 km downstream

Explanation: "explanation : speed of the boat in still water = 22 km / hr speed of the stream = 5 km / hr speed downstream = ( 22 + 5 ) = 27 km / hr distance travelled downstream = 135 km time taken = distance / speed = 135 / 27 = 5 hours . answer : option a"

<gadget id="calculator">22 + 5</gadget>
<output>27</output>
<gadget id="calculator">135 / 27</gadget>
<output>5</output>
<result>5</result>


a bag contains 5 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is

Explanation: "drawing two balls of same color from five green balls can be done in 5 c ₂ ways . similarly from eight white balls two can be drawn in ⁸ c ₂ ways . p = 5 c ₂ / ¹ ⁵ c ₂ + ⁸ c ₂ / ¹ ⁵ c ₂ = 19 / 39 answer : e"

add(multiply(divide(8, add(5, 8)), divide(subtract(8, const_1), subtract(add(5, 8), const_1))), multiply(divide(5, add(5, 8)), divide(subtract(5, const_1), subtract(add(5, 8), const_1))))

<gadget id="calculator">5 + 8</gadget>
<output>13</output>
<gadget id="calculator">8 / 13</gadget>
<output>8/13 = around 0.615385</output>
<gadget id="calculator">8 - 1</gadget>
<output>7</output>
<gadget id="calculator">13 - 1</gadget>
<output>12</output>
<gadget id="calculator">7 / 12</gadget>
<output>7/12 = around 0.583333</output>
<gadget id="calculator">(8/13) * (7/12)</gadget>
<output>14/39 = around 0.358974</output>
<gadget id="calculator">5 / 13</gadget>
<output>5/13 = around 0.384615</output>
<gadget id="calculator">5 - 1</gadget>
<output>4</output>
<gadget id="calculator">4 / 12</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(5/13) * (1/3)</gadget>
<output>5/39 = around 0.128205</output>
<gadget id="calculator">(14/39) + (5/39)</gadget>
<output>19/39 = around 0.487179</output>
<result>19/39 = around 0.487179</result>


find the 10 th term of an arithmetic progression whose first term is 8 and the common difference is 2 .

Explanation: "n th term of a . p = a + ( n - 1 ) * d = 8 + ( 10 - 1 ) * 2 , = 8 + 18 = 26 . answer : b"

add(multiply(subtract(10, const_1), 2), 8)

<gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">9 * 2</gadget>
<output>18</output>
<gadget id="calculator">18 + 8</gadget>
<output>26</output>
<result>26</result>


Explanation: ( 10 x + 2 ) / 4 - ( 3 x - 6 ) / 18 = ( 2 x + 4 ) / 3 = > 18 ( 10 x + 2 ) / 4 - ( 3 x - 6 ) = 18 ( 2 x + 4 ) / 3 = > 4.5 ( 10 x + 2 ) - 3 x + 6 = 6 ( 2 x + 4 ) = > 45 x + 9 - 3 x + 6 = 12 x + 24 = > 45 x - 3 x - 12 x = 24 - 9 - 6 = > 30 x = 9 = > x = 9 / 30 = > x = 3 / 10 answer : d

divide(subtract(subtract(multiply(divide(lcm(lcm(4, 18), 3), 3), 4), multiply(divide(lcm(lcm(4, 18), 3), 4), 2)), multiply(divide(lcm(lcm(4, 18), 3), 18), 6)), subtract(subtract(multiply(divide(lcm(lcm(4, 18), 3), 4), 10), multiply(divide(lcm(lcm(4, 18), 3), 18), 3)), multiply(divide(lcm(lcm(4, 18), 3), 3), 2)))

<gadget id="calculator">lcm(4, 18)</gadget>
<output>36</output>
<gadget id="calculator">lcm(36, 3)</gadget>
<output>36</output>
<gadget id="calculator">36 / 3</gadget>
<output>12</output>
<gadget id="calculator">12 * 4</gadget>
<output>48</output>
<gadget id="calculator">36 / 4</gadget>
<output>9</output>
<gadget id="calculator">9 * 2</gadget>
<output>18</output>
<gadget id="calculator">48 - 18</gadget>
<output>30</output>
<gadget id="calculator">36 / 18</gadget>
<output>2</output>
<gadget id="calculator">2 * 6</gadget>
<output>12</output>
<gadget id="calculator">30 - 12</gadget>
<output>18</output>
<gadget id="calculator">9 * 10</gadget>
<output>90</output>
<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">90 - 6</gadget>
<output>84</output>
<gadget id="calculator">12 * 2</gadget>
<output>24</output>
<gadget id="calculator">84 - 24</gadget>
<output>60</output>
<gadget id="calculator">18 / 60</gadget>
<output>3/10 = around 0.3</output>
<result>3/10 = around 0.3</result>


the area of a circular field is 13.86 hectares . find the cost of fencing it at the rate of rs . 4.80 per metre .

Explanation: "explanation : area = ( 13.86 x 10000 ) sq . m = 138600 sq . m circumference = cost of fencing = rs . ( 1320 x 4.80 ) = rs . 6336 . answer : b ) 6336"

multiply(circumface(multiply(sqrt(divide(13.86, const_pi)), const_100)), 4.80)


a train 150 m long is running at a speed of 68 kmph . how long does it take to pass a man who is running at 8 kmph in the same direction as the train ?

Explanation: "d 9 sec speed of the train relative to man = ( 68 - 8 ) kmph = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec time taken by the train to cross the man = time taken by it to cover 150 m at 50 / 3 m / sec = 150 * 3 / 50 sec = 9 sec"

divide(150, multiply(subtract(68, 8), const_0_2778))

<gadget id="calculator">68 - 8</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">150 / (50/3)</gadget>
<output>9</output>
<result>9</result>


annie and sam set out together on bicycles traveling at 15 and 12 km per hour respectively . after 40 minutes , annie stops to fix a flat tire . if it takes annie 30 minutes to fix the flat tire and sam continues to ride during this time , how many minutes will it take annie to catch up with sam assuming that annie resumes riding at 15 km per hour ?

Explanation: annie gains 3 km per hour ( or 1 km every 20 minutes ) on sam . after 40 minutes annie is 2 km ahead . sam rides 1 km every 5 minutes . in the next 30 minutes , sam rides 6 km so sam will be 4 km ahead . it will take annie 80 minutes to catch sam . the answer is d .

multiply(divide(subtract(divide(12, multiply(subtract(15, 12), divide(40, const_60))), multiply(subtract(15, 12), divide(40, const_60))), subtract(15, 12)), const_60)

<gadget id="calculator">15 - 12</gadget>
<output>3</output>
<gadget id="calculator">40 / 60</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">3 * (2/3)</gadget>
<output>2</output>
<gadget id="calculator">12 / 2</gadget>
<output>6</output>
<gadget id="calculator">6 - 2</gadget>
<output>4</output>
<gadget id="calculator">4 / 3</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">(4/3) * 60</gadget>
<output>80</output>
<result>80</result>


john and jane went out for a dinner and they ordered the same dish . both used a 10 % discount coupon . john paid a 15 % tip over the original price of the dish , while jane paid the tip over the discounted price for the coupon . if john paid $ 0.60 more than jane , what was the original price of the dish ?

Explanation: "the difference between the amounts john paid and jane paid is the deference between 15 % of p and 15 % of 0.9 p : 0.15 p - 0.15 * 0.9 p = 0.60 - - > 15 p - 13.5 p = 60 - - > p = 40 . answer : d ."

divide(0.60, subtract(divide(15, const_100), multiply(subtract(const_1, divide(10, const_100)), divide(15, const_100))))

<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 - (1/10)</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">(9/10) * (3/20)</gadget>
<output>27/200 = around 0.135</output>
<gadget id="calculator">(3/20) - (27/200)</gadget>
<output>3/200 = around 0.015</output>
<gadget id="calculator">0.6 / (3/200)</gadget>
<output>40</output>
<result>40</result>


a certain industrial loom weaves 0.126 meters of cloth every second . approximately how many seconds will it take for the loom to weave 15 meters of cloth ?

Explanation: "let the required number of seconds be x more cloth , more time , ( direct proportion ) hence we can write as ( cloth ) 0.126 : 15 : : 1 : x = > 0.126 * x = 15 = > x = 15 / 0.126 = > x = 119 answer : e"

<gadget id="calculator">15 / 0.126</gadget>
<output>119.047619</output>
<result>119.047619</result>


a cistern is normally filled in 8 hrs , but takes 2 hrs longer to fill because of a leak on its bottom , if cistern is full , how much time citern would empty ?

Explanation: if leakage / hour = 1 / x , then 1 / 8 - 1 / x = 1 / 10 , solving 1 / x = 1 / 40 so in 40 hours full cistern will be empty . answer : d

inverse(subtract(divide(const_1, 8), divide(const_1, add(8, 2))))

<gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">8 + 2</gadget>
<output>10</output>
<gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/8) - (1/10)</gadget>
<output>1/40 = around 0.025</output>
<gadget id="calculator">1 / (1/40)</gadget>
<output>40</output>
<result>40</result>


oil cans x and y are right circular cylinders and the height and radius of y are each 4 times those of x . if the oil in can x filled to capacity sells for $ 2 , how much does the oil in y sell for if y is only half filled ?

Explanation: formula for vol of a cyl is pi * r ^ 2 * h so vy = 64 * vy y when half filled will cost 32 times x so ans is d

<gadget id="calculator">4 ** 2</gadget>
<output>16</output>
<gadget id="calculator">16 * 4</gadget>
<output>64</output>
<result>64</result>


how many distinct integer values of n satisfy the inequality | | n - 3 | + 4 | ≤ 15 ?

Explanation: so i can write this as in - 3 i + 4 < = 15 or in - 3 i < = 11 so n can have - 8 to 14 = 13 true values . . . . e

<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">12 + 1</gadget>
<output>13</output>
<result>13</result>


a man rows his boat 75 km downstream and 45 km upstream , taking 5 hours each time . find the speed of the stream ?

Explanation: "speed downstream = d / t = 75 / ( 5 ) = 15 kmph speed upstream = d / t = 45 / ( 5 ) = 9 kmph the speed of the stream = ( 15 - 9 ) / 2 = 3 kmph answer : d"

divide(subtract(divide(75, 5), divide(45, 5)), const_2)

<gadget id="calculator">75 / 5</gadget>
<output>15</output>
<gadget id="calculator">45 / 5</gadget>
<output>9</output>
<gadget id="calculator">15 - 9</gadget>
<output>6</output>
<gadget id="calculator">6 / 2</gadget>
<output>3</output>
<result>3</result>


an industrial loom weaves 0.128 metres of cloth every second . approximately , how many seconds will it take for the loom to weave 25 metre of cloth ?

Explanation: "explanation : let the time required by x seconds . then , more cloth means more time ( direct proportion ) so , 0.128 : 1 : : 25 : x = > x = 25 ∗ 1 / 0.128 = > x = 195.31 so time will be approx 195 seconds option b"

<gadget id="calculator">25 / 0.128</gadget>
<output>195.3125</output>
<result>195.3125</result>


at what time between 5 and 6 o ' clock are the hands of a 3 minutes apart ?

Explanation: in this type of problems the formuae is ( 5 * x + or - t ) * 12 / 11 here x is replaced by the first interval of given time . here x is 5 . t is spaces apart case 1 : ( 5 * x + t ) * 12 / 11 ( 5 * 5 + 3 ) * 12 / 11 28 * 12 / 11 = 336 / 11 = min therefore the hands will be 3 min apart at 31 5 / 11 min past 5 . case 2 : ( 5 * x - t ) * 12 / 11 ( 5 * 5 - 3 ) * 12 / 11 22 * 12 / 11 = 24 min therefore the hands will be 3 min apart at 24 min past 5 answer : a ) 24 min

multiply(subtract(multiply(5, 5), 3), divide(add(6, 6), add(6, 5)))

<gadget id="calculator">5 * 5</gadget>
<output>25</output>
<gadget id="calculator">25 - 3</gadget>
<output>22</output>
<gadget id="calculator">6 + 6</gadget>
<output>12</output>
<gadget id="calculator">6 + 5</gadget>
<output>11</output>
<gadget id="calculator">12 / 11</gadget>
<output>12/11 = around 1.090909</output>
<gadget id="calculator">22 * (12/11)</gadget>
<output>24</output>
<result>24</result>


the probability is 1 / 2 that a certain coin turns up heads on any given toss . if the coin is tossed 6 times , what is the probability that the coin turns up tails on at least one of the tosses ?

Explanation: p ( 6 heads ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 64 . p ( at least one tail ) = 1 - 1 / 64 = 63 / 64 . the answer is d .

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) ** 6</gadget>
<output>1/64 = around 0.015625</output>
<gadget id="calculator">1 - (1/64)</gadget>
<output>63/64 = around 0.984375</output>
<result>63/64 = around 0.984375</result>


a football field is 8400 square yards . if 1200 pounds of fertilizer are spread evenly across the entire field , how many pounds of fertilizer were spread over an area of the field totaling 3500 square yards ?

Explanation: "answer a ) 4800 yards need 1200 lbs 1 yard will need 1200 / 8400 = 1 / 7 lbs 3600 yards will need 1 / 7 * 3500 yards = 500 lbs c"

<gadget id="calculator">1_200 / 8_400</gadget>
<output>1/7 = around 0.142857</output>
<gadget id="calculator">3_500 * (1/7)</gadget>
<output>500</output>
<result>500</result>


the lowest number which should be added to 11390 so that the sum is exactly divisible by 7 , 9 , 10 and 12 is :

Explanation: l . c . m . of 7 , 9 , 10 and 12 = 1260 . on dividing 11390 by 1260 , the remainder is 50 . number to be added = ( 1260 - 50 ) = 1210 . answer : option ' d '


a telephone company needs to create a set of 3 - digit area codes . the company is entitled to use only digits 2 , 4 and 3 , which can be repeated . if the product of the digits in the area code must be even , how many different codes can be created ?

Explanation: "total # of codes possible is 3 * 3 * 3 = 27 . oit of those 27 codes only the product of 333 will be odd , the remaining 26 will have either 2 or 4 in them , which ensures that their product will be even . therefore the number of codes where the product of the digits is even = ( total ) - ( restriction ) = 27 - 1 = 26 . answer : b"

<gadget id="calculator">3 ** 3</gadget>
<output>27</output>
<gadget id="calculator">27 - 1</gadget>
<output>26</output>
<result>26</result>


120 students represent x percent of the boys at a school . if the boys at the school make up 30 % of the total school population of x students , what is x ?

Explanation: "let b be the number of boys in the school . 120 = xb / 100 b = 0.3 x 12000 = 0.3 x ^ 2 x ^ 2 = 40000 x = 200 the answer is d ."

sqrt(divide(multiply(120, const_100), divide(30, const_100)))

<gadget id="calculator">120 * 100</gadget>
<output>12_000</output>
<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">12_000 / (3/10)</gadget>
<output>40_000</output>
<gadget id="calculator">40_000 ** (1/2)</gadget>
<output>200</output>
<result>200</result>


of the diplomats attending a summit conference , 17 speak french , 32 do not speak russian , and 20 % of the diplomats speak neither french nor russian . if 10 % of the diplomats speak both languages , then how many diplomats attended the conference ?

Explanation: "{ total } = { french } + { russian } - { both } + { neither } { total } = 17 + ( { total } - 32 ) - ( 0.1 * { total } ) + 0.2 * { total } solving gives { total } = 150 . answer : e ."

divide(subtract(32, 17), subtract(divide(20, const_100), divide(10, const_100)))

<gadget id="calculator">32 - 17</gadget>
<output>15</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/5) - (1/10)</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">15 / (1/10)</gadget>
<output>150</output>
<result>150</result>