48 persons can repair a road in 12 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?

Explanation: "let the required number of days be x . less persons , more days ( indirect proportion ) more working hours per day , less days ( indirect proportion ) persons 30 : 48 : : 12 : x working hours / day 6 : 5 30 x 6 x x = 48 x 5 x 12 x = ( 48 x 5 x 12 ) / ( 30 x 6 ) x = 16 answer b"

divide(multiply(multiply(48, 12), 5), multiply(30, 6))

<gadget id="calculator">48 * 12</gadget>
<output>576</output>
<gadget id="calculator">576 * 5</gadget>
<output>2_880</output>
<gadget id="calculator">30 * 6</gadget>
<output>180</output>
<gadget id="calculator">2_880 / 180</gadget>
<output>16</output>
<result>16</result>


the operation is defined for all integers a and b by the equation ab = ( a - 1 ) ( b - 1 ) . if x 20 = 190 , what is the value of x ?

Explanation: "ab = ( a - 1 ) ( b - 1 ) x 20 = ( x - 1 ) ( 20 - 1 ) = 190 - - > x - 1 = 10 - - > x = 11 answer : c"

<gadget id="calculator">20 - 1</gadget>
<output>19</output>
<gadget id="calculator">190 / 19</gadget>
<output>10</output>
<gadget id="calculator">10 + 1</gadget>
<output>11</output>
<result>11</result>


how many 5 digit nos are there if the 2 leftmost digits are odd and the digit 4 ca n ' t appear more than once in the number ? could someone please provide a solution using a approach other than ( 1 - x ( none ) ) approach ?

Explanation: a . 4 is used once : oo * * 4 - - > ( 5 * 5 * 9 * 9 ) * 3 : 5 choices for the first digit as there are 5 odd numbers , 5 choices for the second digit for the same reason , 9 choices for one of the two * ( not - 4 digit ) , 9 choices for another * ( not - 4 digit ) , multiplied by 3 as 4 can take the place of any of the three last digits ( oo * * 4 , oo * 4 * , oo 4 * * ) ; b . 4 is not used : oo * * * - - > 5 * 5 * 9 * 9 * 9 : the same logic as above . 5 * 5 * 9 * 9 * 3 + 5 * 5 * 9 * 9 * 9 = 24300 . answer : a

multiply(multiply(multiply(multiply(subtract(multiply(4, 5), 1), 5), 5), 5), const_10)

<gadget id="calculator">4 * 5</gadget>
<output>20</output>
<gadget id="calculator">20 - 1</gadget>
<output>19</output>
<gadget id="calculator">19 * 5</gadget>
<output>95</output>
<gadget id="calculator">95 * 5</gadget>
<output>475</output>
<gadget id="calculator">475 * 5</gadget>
<output>2_375</output>
<gadget id="calculator">2_375 * 10</gadget>
<output>23_750</output>
<result>23_750</result>


a cat leaps 6 leaps for every 5 leaps of a dog , but 2 leaps of the dog are equal to 3 leaps of the cat . what is the ratio of the speed of the cat to that of the dog ?

Explanation: "given ; 2 dog = 3 cat ; or , dog / cat = 3 / 2 ; let cat ' s 1 leap = 2 meter and dogs 1 leap = 3 meter . then , ratio of speed of cat and dog = 2 * 6 / 3 * 5 = 4 : 5 ' ' answer : 4 : 5 ;"

<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) * 6</gadget>
<output>4</output>
<gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>
<result>4/5 = around 0.8</result>


a horse is tethered to one corner of a rectangular grassy field 36 m by 20 m with a rope 18 m long . over how much area of the field can it graze ?

Explanation: "area of the shaded portion = 1 ⁄ 4 × π × ( 18 ) 2 = 254 m 2 answer c"

divide(multiply(power(18, const_2), const_pi), const_4)

<gadget id="calculator">18 ** 2</gadget>
<output>324</output>
<gadget id="calculator">324 * pi</gadget>
<output>324*pi = around 1_017.87602</output>
<gadget id="calculator">(324*pi) / 4</gadget>
<output>81*pi = around 254.469005</output>
<result>81*pi = around 254.469005</result>


if the arithmetic mean of seventy 5 numbers is calculated , it is 35 . if each number is increased by 5 , then mean of new number is ?

Explanation: a . m . of 75 numbers = 35 sum of 75 numbers = 75 * 35 = 2625 total increase = 75 * 5 = 375 increased sum = 2625 + 375 = 3000 increased average = 3000 / 75 = 40 . answer : b

<gadget id="calculator">35 + 5</gadget>
<output>40</output>
<result>40</result>


Explanation: answer x = 13200 - 8873 = 4327 option : b

<gadget id="calculator">13_200 - 8_873</gadget>
<output>4_327</output>
<result>4_327</result>


a box contains 8 pairs of shoes ( 16 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ?

Explanation: "the problem with your solution is that we do n ' t choose 1 shoe from 16 , but rather choose the needed one after we just took one and need the second to be the pair of it . so , the probability would simply be : 1 / 1 * 1 / 15 ( as after taking one at random there are 15 shoes left and only one is the pair of the first one ) = 1 / 15 answer : e ."

<gadget id="calculator">16 - 1</gadget>
<output>15</output>
<gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>
<result>1/15 = around 0.066667</result>


sales price is $ 60 , gross profit is 140 % of cost , what is the value of gross profit ?

Explanation: "cost + profit = sales cost + ( 140 / 100 ) cost = 60 cost = 25 profit = 60 - 25 = 35 answer ( d )"

subtract(60, divide(60, add(const_1, divide(140, const_100))))

<gadget id="calculator">140 / 100</gadget>
<output>7/5 = around 1.4</output>
<gadget id="calculator">1 + (7/5)</gadget>
<output>12/5 = around 2.4</output>
<gadget id="calculator">60 / (12/5)</gadget>
<output>25</output>
<gadget id="calculator">60 - 25</gadget>
<output>35</output>
<result>35</result>


a , b , k start from the same place and travel in the same direction at speeds of 30 km / hr , 40 km / hr , 60 km / hr respectively . b starts 6 hours after a . if b and k overtake a at the same instant , how many hours after a did k start ?

Explanation: the table you made does n ' t make sense to me . all three meet at the same point means the distance they cover is the same . we know their rates are 30 , 40 and 60 . say the time taken by b is t hrs . then a takes 6 + t hrs . and we need to find the time taken by k . distance covered by a = distance covered by b 30 * ( 6 + t ) = 40 * t t = 18 hrs distance covered by b = distance covered by k 40 * t = 60 * time taken by k time taken by k = 40 * 18 / 60 = 12 hrs time taken by a = 6 + t = 6 + 18 = 24 hrs time taken by k = 12 hrs so k starts 24 - 12 = 12 hrs after a . ( answer d )

divide(multiply(30, add(6, divide(multiply(30, 6), subtract(40, 30)))), 60)

<gadget id="calculator">30 * 6</gadget>
<output>180</output>
<gadget id="calculator">40 - 30</gadget>
<output>10</output>
<gadget id="calculator">180 / 10</gadget>
<output>18</output>
<gadget id="calculator">6 + 18</gadget>
<output>24</output>
<gadget id="calculator">30 * 24</gadget>
<output>720</output>
<gadget id="calculator">720 / 60</gadget>
<output>12</output>
<result>12</result>


in an exam 80 % of the boys and 40 % of the girls passed . the number of girls who passed is 120 , which is 2 / 3 rd of the number of boys who failed . what is the total number of students who appeared for the exam ?

Explanation: let the number of boys = x , number of girls = y 40 y / 100 = 120 y = 300 120 = 2 / 3 * 20 x / 100 = 2 x / 15 x = 900 total = x + y = 300 + 900 = 1200 answer : a

add(divide(120, multiply(divide(subtract(const_100, 80), const_100), divide(2, 3))), divide(120, divide(40, const_100)))

<gadget id="calculator">100 - 80</gadget>
<output>20</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(1/5) * (2/3)</gadget>
<output>2/15 = around 0.133333</output>
<gadget id="calculator">120 / (2/15)</gadget>
<output>900</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">120 / (2/5)</gadget>
<output>300</output>
<gadget id="calculator">900 + 300</gadget>
<output>1_200</output>
<result>1_200</result>


pipe a fills a tank in 42 minutes . pipe b can fill the same tank 6 times as fast as pipe a . if both the pipes are kept open when the tank is empty , how many minutes will it take to fill the tank ?

Explanation: "a ' s rate is 1 / 42 and b ' s rate is 1 / 7 . the combined rate is 1 / 42 + 1 / 7 = 1 / 6 the pipes will fill the tank in 6 minutes . the answer is d ."

inverse(add(divide(const_1, 42), divide(6, 42)))

<gadget id="calculator">1 / 42</gadget>
<output>1/42 = around 0.02381</output>
<gadget id="calculator">6 / 42</gadget>
<output>1/7 = around 0.142857</output>
<gadget id="calculator">(1/42) + (1/7)</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">1 / (1/6)</gadget>
<output>6</output>
<result>6</result>


by weight , liquid x makes up 1.5 percent of solution p and 6.5 percent of solution q . if 200 grams of solution p are mixed with 800 grams of solution q , then liquid x accounts for what percent of the weight of the resulting solution ?

Explanation: "the number of grams of liquid x is 1.5 ( 200 ) / 100 + 6.5 ( 800 ) / 100 = 3 + 52 = 55 grams . 55 / 1000 = 5.5 % the answer is c ."

multiply(divide(add(const_1, divide(multiply(6.5, 800), const_100)), const_1000), const_100)

<gadget id="calculator">6.5 * 800</gadget>
<output>5_200</output>
<gadget id="calculator">5_200 / 100</gadget>
<output>52</output>
<gadget id="calculator">1 + 52</gadget>
<output>53</output>
<gadget id="calculator">53 / 1_000</gadget>
<output>53/1_000 = around 0.053</output>
<gadget id="calculator">(53/1_000) * 100</gadget>
<output>53/10 = around 5.3</output>
<result>53/10 = around 5.3</result>


900 men have provisions for 15 days . if 200 more men join them , for how many days will the provisions last now ?

Explanation: "900 * 15 = 1100 * x x = 12.27 . answer : e"

<gadget id="calculator">15 * 900</gadget>
<output>13_500</output>
<gadget id="calculator">900 + 200</gadget>
<output>1_100</output>
<gadget id="calculator">13_500 / 1_100</gadget>
<output>135/11 = around 12.272727</output>
<result>135/11 = around 12.272727</result>


set a { 3 , 3,3 , 4,5 , 5,5 } has a standard deviation of 1 . what will the standard deviation be if every number in the set is multiplied by 2 ?

Explanation: points to remember - 1 . if oneadd / subtractthe same amont from every term in a set , sd does n ' t change . 2 . if onemultiply / divideevery term by the same number in a set , sd changes by same number . hence the answer to the above question is b

<gadget id="calculator">2 * 1</gadget>
<output>2</output>
<result>2</result>


a snail , climbing a 24 feet high wall , climbs up 4 feet on the first day but slides down 2 feet on the second . it climbs 4 feet on the third day and slides down again 2 feet on the fourth day . if this pattern continues , how many days will it take the snail to reach the top of the wall ?

Explanation: total transaction in two days = 4 - 2 = 2 feet in 20 days it will climb 20 feet on the 21 st day , the snail will climb 4 feet , thus reaching the top therefore , total no of days required = 21 e

<gadget id="calculator">24 - 4</gadget>
<output>20</output>
<result>20</result>


a ’ s speed is 25 / 18 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?

Explanation: "we have the ratio of a ’ s speed and b ’ s speed . this means , we know how much distance a covers compared with b in the same time . this is what the beginning of the race will look like : ( start ) a _________ b ______________________________ if a covers 25 meters , b covers 18 meters in that time . so if the race is 25 meters long , when a reaches the finish line , b would be 7 meters behind him . if we want the race to end in a dead heat , we want b to be at the finish line too at the same time . this means b should get a head start of 7 meters so that he doesn ’ t need to cover that . in that case , the time required by a ( to cover 25 meters ) would be the same as the time required by b ( to cover 18 meters ) to reach the finish line . so b should get a head start of 7 / 25 th of the race . answer ( c )"

<gadget id="calculator">25 - 18</gadget>
<output>7</output>
<gadget id="calculator">7 / 25</gadget>
<output>7/25 = around 0.28</output>
<result>7/25 = around 0.28</result>


the marked price of a book is 20 % more than the cost price . after the book is sold , the vendor realizes that he had wrongly raised the cost price by a margin of 25 % . if the marked price of the book is rs . 30 , what is the original cost price of the book ?

Explanation: let the incorrect cost price be c 1 and let the original cost price be c 2 . marked price of book is rs . 30 . it is 20 % more than c 1 . therefore , ( 120 / 100 ) x c 1 = 30 or c 1 = 25 . c 1 is more than c 2 margin of 25 % . or c 1 = ( 125 / 100 ) c 2 therefore , c 2 = ( 100 / 125 ) x 25 = rs 20 answer : d

divide(divide(30, add(const_1, divide(20, const_100))), add(const_1, divide(25, const_100)))

<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">30 / (6/5)</gadget>
<output>25</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 + (1/4)</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">25 / (5/4)</gadget>
<output>20</output>
<result>20</result>


the h . c . f . of two numbers is 18 and the other two factors of their l . c . m . are 11 and 15 . the larger of the two numbers is :

Explanation: "the numbers are ( 18 x 11 ) and ( 18 x 15 ) . larger number = ( 18 x 15 ) = 270 . answer : a"

<gadget id="calculator">18 * 15</gadget>
<output>270</output>
<result>270</result>


the ratio of buses to cars on river road is 1 to 3 . if there are 20 fewer buses than cars on river road , how many cars are on river road ?

Explanation: "b / c = 1 / 3 c - b = 20 . . . . . . . . . > b = c - 20 ( c - 20 ) / c = 1 / 3 testing answers . clearly eliminate abce put c = 30 . . . . . . . . . > ( 30 - 20 ) / 30 = 10 / 30 = 1 / 3 answer : d"

<gadget id="calculator">3 - 1</gadget>
<output>2</output>
<gadget id="calculator">20 / 2</gadget>
<output>10</output>
<gadget id="calculator">10 * 3</gadget>
<output>30</output>
<result>30</result>


the total of 324 of 20 paise and 25 paise make a sum of rs . 71 . the no of 20 paise coins is

Explanation: "explanation : let the number of 20 paise coins be x . then the no of 25 paise coins = ( 324 - x ) . 0.20 * ( x ) + 0.25 ( 324 - x ) = 71 = > x = 200 . . answer : d ) 200"

divide(subtract(multiply(324, 25), multiply(71, const_100)), subtract(25, 20))

<gadget id="calculator">324 * 25</gadget>
<output>8_100</output>
<gadget id="calculator">71 * 100</gadget>
<output>7_100</output>
<gadget id="calculator">8_100 - 7_100</gadget>
<output>1_000</output>
<gadget id="calculator">25 - 20</gadget>
<output>5</output>
<gadget id="calculator">1_000 / 5</gadget>
<output>200</output>
<result>200</result>


if annual decrease in the population of a town is 5 % and the present number of people is 40000 what will the population be in 2 years ?

Explanation: population in 2 years = 40000 ( 1 - 5 / 100 ) ^ 2 = 40000 * 19 * 19 / 20 * 20 = 36100 answer is c

multiply(power(divide(subtract(const_100, 5), const_100), 2), 40000)

<gadget id="calculator">100 - 5</gadget>
<output>95</output>
<gadget id="calculator">95 / 100</gadget>
<output>19/20 = around 0.95</output>
<gadget id="calculator">(19/20) ** 2</gadget>
<output>361/400 = around 0.9025</output>
<gadget id="calculator">(361/400) * 40_000</gadget>
<output>36_100</output>
<result>36_100</result>


the price of lunch for 15 people was $ 206.00 , including a 15 percent gratuity for service . what was the average price per person , excluding the gratuity ?

Explanation: take the initial price before the gratuity is 100 the gratuity is calculated on the final price , so as we assumed the final bill before adding gratuity is 100 so gratuity is 15 % of 100 is 15 so the total price of meals is 115 so the given amount i . e 206 is for 115 then we have to calculate for 100 for 115 206 for 100 x so by cross multiplication we get 115 x = 100 * 206 = > x = 100 * 206 / 110 by simplifying we get x as 187.27 which is the price of lunch before gratuity so the gratuity is 18.73 so as the question ask the average price person excluding gratuity is 187.27 / 15 = 12.48 so our answer is b )

multiply(multiply(divide(206, add(const_100, 15)), const_100), divide(const_1, 15))

<gadget id="calculator">100 + 15</gadget>
<output>115</output>
<gadget id="calculator">206 / 115</gadget>
<output>206/115 = around 1.791304</output>
<gadget id="calculator">(206/115) * 100</gadget>
<output>4_120/23 = around 179.130435</output>
<gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">(4_120/23) * (1/15)</gadget>
<output>824/69 = around 11.942029</output>
<result>824/69 = around 11.942029</result>


joe drives 600 miles at 60 miles per hour , and then he drives the next 120 miles at 40 miles per hour . what is his average speed for the entire trip in miles per hour ?

Explanation: "t 1 = 600 / 60 = 10 hours t 2 = 120 / 40 = 3 hours t = t 1 + t 2 = 13 hours avg speed = total distance / t = 720 / 13 = 55 mph = b"

<gadget id="calculator">600 + 120</gadget>
<output>720</output>
<gadget id="calculator">600 / 60</gadget>
<output>10</output>
<gadget id="calculator">120 / 40</gadget>
<output>3</output>
<gadget id="calculator">10 + 3</gadget>
<output>13</output>
<gadget id="calculator">720 / 13</gadget>
<output>720/13 = around 55.384615</output>
<result>720/13 = around 55.384615</result>


a pet store regularly sells pet food at a discount of 10 percent to 30 percent from the manufacturer ’ s suggested retail price . if during a sale , the store discounts an additional 20 percent from the discount price , what would be the lowest possible price of a container of pet food that had a manufacturer ’ s suggested retail price o f $ 20.00 ?

Explanation: "for retail price = $ 20 first maximum discounted price = 20 - 30 % of 20 = 20 - 6 = 14 price after additional discount of 20 % = 14 - 20 % of 14 = 14 - 2.8 = 11.2 answer : option b"

multiply(divide(subtract(const_100, 20), const_100), multiply(divide(subtract(const_100, 30), const_100), 20.00))

<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">100 - 30</gadget>
<output>70</output>
<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">(7/10) * 20</gadget>
<output>14</output>
<gadget id="calculator">(4/5) * 14</gadget>
<output>56/5 = around 11.2</output>
<result>56/5 = around 11.2</result>


if 20 liters of chemical x are added to 80 liters of a mixture that is 15 % chemical x and 85 % chemical y , then what percentage of the resulting mixture is chemical x ?

Explanation: "the amount of chemical x in the solution is 20 + 0.15 ( 80 ) = 32 liters . 32 liters / 100 liters = 32 % the answer is b ."

add(20, multiply(divide(15, const_100), 80))

<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">(3/20) * 80</gadget>
<output>12</output>
<gadget id="calculator">20 + 12</gadget>
<output>32</output>
<result>32</result>


a set consists of 12 numbers , all are even or multiple of 5 . if 4 numbers are even and 10 numbers are multiple of 5 , how many numbers is multiple of 10 ?

Explanation: "{ total } = { even } + { multiple of 5 } - { both } + { nether } . since { neither } = 0 ( allare even or multiple of 5 ) then : 12 = 4 + 10 - { both } + 0 ; { both } = 2 ( so 1 number is both even and multiple of 5 , so it must be a multiple of 10 ) . answer : c ."

<gadget id="calculator">12 - 10</gadget>
<output>2</output>
<result>2</result>


two employees x and y are paid a total of rs . 506 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?

Explanation: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 506 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 506 ⇒ y [ 12 / 10 + 1 ] = 506 ⇒ 22 y / 10 = 506 ⇒ 22 y = 5060 ⇒ y = 5060 / 22 = 460 / 2 = rs . 230 e"

divide(multiply(506, multiply(add(const_1, const_4), const_2)), multiply(add(multiply(add(const_1, const_4), const_2), const_1), const_2))

<gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">506 * 10</gadget>
<output>5_060</output>
<gadget id="calculator">10 + 1</gadget>
<output>11</output>
<gadget id="calculator">11 * 2</gadget>
<output>22</output>
<gadget id="calculator">5_060 / 22</gadget>
<output>230</output>
<result>230</result>


the average age of 15 students of a class is 15 years . out of these , the average age of 4 students is 14 years and that of the other 10 students is 16 years . the age of the 15 th student is

Explanation: "solution age of the 15 th student = [ 15 x 15 - ( 14 x 4 + 16 x 10 ) ] = ( 225 - 216 ) = 9 years . answer e"

subtract(multiply(15, 15), add(multiply(4, 14), multiply(10, 16)))

<gadget id="calculator">15 * 15</gadget>
<output>225</output>
<gadget id="calculator">4 * 14</gadget>
<output>56</output>
<gadget id="calculator">10 * 16</gadget>
<output>160</output>
<gadget id="calculator">56 + 160</gadget>
<output>216</output>
<gadget id="calculator">225 - 216</gadget>
<output>9</output>
<result>9</result>


a certain sum of money is divided among a , b and c so that for each rs . a has , b has 65 paisa and c 40 paisa . if c ' s share is rs . 40 , find the sum of money ?

Explanation: "a : b : c = 100 : 65 : 40 = 20 : 13 : 8 8 - - - - 40 41 - - - - ? = > rs . 205 answer : d"

multiply(divide(40, 40), add(add(const_100, 65), 40))

<gadget id="calculator">40 / 40</gadget>
<output>1</output>
<gadget id="calculator">100 + 65</gadget>
<output>165</output>
<gadget id="calculator">165 + 40</gadget>
<output>205</output>
<gadget id="calculator">1 * 205</gadget>
<output>205</output>
<result>205</result>


two trains leave the train station at the same time . one train , on the blue line , heads east - while the other , on the red line , heads west . if the train on the blue line averages 40 km / hr and the other train averages 40 km / hr - how long will it take for the trains to be 100 km apart ?

Explanation: each train is averaging 40 km / hour in an opposite direction . after 1 hour , they will be 80 km apart , and after 1.25 hours , they will be 100 km apart . ( 80 * 1.25 = 100 ) answer is d

<gadget id="calculator">100 / 2</gadget>
<output>50</output>
<gadget id="calculator">50 / 40</gadget>
<output>5/4 = around 1.25</output>
<result>5/4 = around 1.25</result>


a certain college ' s enrollment at the beginning of 1992 was 30 percent greater than it was at the beginning of 1991 , and its enrollment at the beginning of 1993 was 10 percent greater than it was at the beginning of 1992 . the college ' s enrollment at the beginning of 1993 was what percent greater than its enrollment at the beginning of 1991 ?

Explanation: "suppose enrollment in 1991 was 100 then enrollment in 1992 will be 130 and enrollment in 1993 will be 130 * 1.1 = 143 increase in 1993 from 1991 = 143 - 100 = 43 answer : a"

subtract(multiply(add(const_100, 30), divide(add(const_100, 10), const_100)), const_100)

<gadget id="calculator">100 + 30</gadget>
<output>130</output>
<gadget id="calculator">100 + 10</gadget>
<output>110</output>
<gadget id="calculator">110 / 100</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">130 * (11/10)</gadget>
<output>143</output>
<gadget id="calculator">143 - 100</gadget>
<output>43</output>
<result>43</result>


a can give b 120 meters start and c 200 meters start in a kilometer race . how much start can b give c in a kilometer race ?

Explanation: "explanation : a runs 1000 meters while b runs 880 meters and c runs 800 meters . therefore , b runs 880 meters while c runs 800 meters . so , the number of meters that c runs when b runs 1000 meters = ( 1000 x 800 ) / 880 = 909.09 meters thus , b can give c ( 1000 - 909.09 ) = 90.09 meters start answer : a"

subtract(multiply(const_100, const_10), divide(multiply(multiply(const_100, const_10), subtract(multiply(const_100, const_10), 200)), subtract(multiply(const_100, const_10), 120)))

<gadget id="calculator">100 * 10</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 - 200</gadget>
<output>800</output>
<gadget id="calculator">1_000 * 800</gadget>
<output>800_000</output>
<gadget id="calculator">1_000 - 120</gadget>
<output>880</output>
<gadget id="calculator">800_000 / 880</gadget>
<output>10_000/11 = around 909.090909</output>
<gadget id="calculator">1_000 - (10_000/11)</gadget>
<output>1_000/11 = around 90.909091</output>
<result>1_000/11 = around 90.909091</result>


a merchant marks his goods up by 30 % and then offers a discount of 20 % on the marked price . what % profit does the merchant make after the discount ?

Explanation: "let the price be 100 . the price becomes 130 after a 30 % markup . now a discount of 20 % on 130 . profit = 104 - 100 4 % answer e"

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

<gadget id="calculator">30 + 100</gadget>
<output>130</output>
<gadget id="calculator">130 * 20</gadget>
<output>2_600</output>
<gadget id="calculator">2_600 / 100</gadget>
<output>26</output>
<gadget id="calculator">130 - 26</gadget>
<output>104</output>
<gadget id="calculator">104 - 100</gadget>
<output>4</output>
<result>4</result>


the owner of a furniture shop charges his customer 42 % more than the cost price . if a customer paid rs . 8300 for a computer table , then what was the cost price of the computer table ?

Explanation: cp = sp * ( 100 / ( 100 + profit % ) ) = 8300 ( 100 / 142 ) = rs . 5845 . answer : b

divide(8300, add(const_1, divide(42, const_100)))

<gadget id="calculator">42 / 100</gadget>
<output>21/50 = around 0.42</output>
<gadget id="calculator">1 + (21/50)</gadget>
<output>71/50 = around 1.42</output>
<gadget id="calculator">8_300 / (71/50)</gadget>
<output>415_000/71 = around 5_845.070423</output>
<result>415_000/71 = around 5_845.070423</result>


an article with cost price of 320 is sold at 18 % profit . what is the selling price ?

Explanation: "sp = 1.18 * 320 = 378 answer : d"

add(320, multiply(320, divide(18, const_100)))

<gadget id="calculator">18 / 100</gadget>
<output>9/50 = around 0.18</output>
<gadget id="calculator">320 * (9/50)</gadget>
<output>288/5 = around 57.6</output>
<gadget id="calculator">320 + (288/5)</gadget>
<output>1_888/5 = around 377.6</output>
<result>1_888/5 = around 377.6</result>


given that 100.48 = x , 100.70 = y and xz = y 2 , then the value of z is close to :

Explanation: "xz = y 2 10 ( 0.48 z ) = 10 ( 2 x 0.70 ) = 101.40 0.48 z = 1.40 z = 140 = 35 = 2.9 ( approx . ) 48 12 answer : c"

divide(multiply(subtract(100.70, const_100), const_2), subtract(100.48, const_100))

<gadget id="calculator">100.7 - 100</gadget>
<output>0.7</output>
<gadget id="calculator">0.7 * 2</gadget>
<output>1.4</output>
<gadget id="calculator">100.48 - 100</gadget>
<output>0.48</output>
<gadget id="calculator">1.4 / 0.48</gadget>
<output>2.916667</output>
<result>2.916667</result>


how many digits are required to number a book containing 250 pages ?

Explanation: "9 pages from 1 to 9 will require 9 digits . 90 pages from 10 to 99 will require 90 * 2 = 180 digits . 250 - ( 90 + 9 ) = 151 pages will require 151 * 3 = 453 digits . the total number of digits is 9 + 180 + 453 = 642 . the answer is b ."

add(add(subtract(const_10, const_1), multiply(multiply(subtract(const_10, const_1), const_10), const_2)), multiply(add(subtract(250, const_100), const_1), const_3))

<gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">9 * 10</gadget>
<output>90</output>
<gadget id="calculator">90 * 2</gadget>
<output>180</output>
<gadget id="calculator">9 + 180</gadget>
<output>189</output>
<gadget id="calculator">250 - 100</gadget>
<output>150</output>
<gadget id="calculator">150 + 1</gadget>
<output>151</output>
<gadget id="calculator">151 * 3</gadget>
<output>453</output>
<gadget id="calculator">189 + 453</gadget>
<output>642</output>
<result>642</result>


at scratch and dents rent - a - car , it costs $ 34.95 a day plus $ 0.23 per mile to rent a car . at rent - a - lemon , the charge is $ 25.00 a day plus $ 1.31 per mile . if you need to rent a car for 3 days , how many miles ( to nearest tenth ) must you drive for a car from both agencies to cost the same amount ?

Explanation: for sad : saddaily = $ 34.95 / day sadmile = $ 0.23 / mile for ral : raldaily = $ 25.00 / day ralmile = $ 1.31 / mile we want the raltotal = sadtotal , so we get ( raldaily * days ) + ( ralmile * miles ) = ( saddaily * days ) + ( sadmile * miles ) = > miles = ( ( saddaily * days ) - ( raldaily * days ) ) / ( ralmiles - sadmiles ) = ( ( saddaily - raldaily ) * days ) / ( ralmiles - sadmiles ) miles = ( ( $ 34.95 * 3 ) - ( $ 25.00 * 3 ) ) / ( $ 1.31 - $ 0.23 ) = 27.6 miles c . 27.6 miles

divide(subtract(multiply(34.95, 3), multiply(25, 3)), subtract(1.31, 0.23))

<gadget id="calculator">34.95 * 3</gadget>
<output>104.85</output>
<gadget id="calculator">25 * 3</gadget>
<output>75</output>
<gadget id="calculator">104.85 - 75</gadget>
<output>29.85</output>
<gadget id="calculator">1.31 - 0.23</gadget>
<output>1.08</output>
<gadget id="calculator">29.85 / 1.08</gadget>
<output>27.638889</output>
<result>27.638889</result>


pipe a can fill a tank in 9 hours . due to a leak at the bottom , it takes 12 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?

Explanation: "let the leak can empty the full tank in x hours 1 / 9 - 1 / x = 1 / 12 = > 1 / x = 1 / 9 - 1 / 12 = 1 / 12 = > x = 36 . answer : a"

divide(multiply(12, 9), subtract(12, 9))

<gadget id="calculator">12 * 9</gadget>
<output>108</output>
<gadget id="calculator">12 - 9</gadget>
<output>3</output>
<gadget id="calculator">108 / 3</gadget>
<output>36</output>
<result>36</result>


if p is a prime number greater than 3 , find the remainder when p ^ 2 + 16 is divided by 12 .

Explanation: every prime number greater than 3 can be written 6 n + 1 or 6 n - 1 . if p = 6 n + 1 , then p ^ 2 + 16 = 36 n ^ 2 + 12 n + 1 + 16 = 36 n ^ 2 + 12 n + 12 + 5 if p = 6 n - 1 , then p ^ 2 + 16 = 36 n ^ 2 - 12 n + 1 + 16 = 36 n ^ 2 - 12 n + 12 + 5 when divided by 12 , it must leave a remainder of 5 . the answer is a .

subtract(add(16, power(add(const_1, const_4), const_2)), multiply(12, 3))

<gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">5 ** 2</gadget>
<output>25</output>
<gadget id="calculator">16 + 25</gadget>
<output>41</output>
<gadget id="calculator">12 * 3</gadget>
<output>36</output>
<gadget id="calculator">41 - 36</gadget>
<output>5</output>
<result>5</result>


if x is 20 percent greater than 55 , then x =

Explanation: x is 20 % greater than 55 means x is 1.2 times 55 ( in other words 55 + 20 / 100 * 55 = 1.2 * 55 ) therefore , x = 1.2 * 55 = 66 answer : d

add(55, multiply(divide(20, const_100), 55))

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 55</gadget>
<output>11</output>
<gadget id="calculator">55 + 11</gadget>
<output>66</output>
<result>66</result>


Explanation: "72519 x 9999 = 72519 x ( 10000 - 1 ) = 72519 x 10000 - 72519 x 1 = 725190000 - 72519 = 725117481 d"

<gadget id="calculator">9_999 - 4</gadget>
<output>9_995</output>
<gadget id="calculator">9_995 * 72_519</gadget>
<output>724_827_405</output>
<result>724_827_405</result>


a bag contains 12 red marbles . if someone were to remove 2 marbles from the bag , one at a time , and replace the first marble after it was removed , the probability that neither marble would be red is 49 / 64 . how many marbles are in the bag ?

Explanation: "ok let me see if i can explain what went on in the previous post lets say i have x marbles in the bag in total - - > out of them 12 are red so the probability of pulling a non - red marble is ( x - 12 ) / x now the marble is placed back in the bag and we have x marbles again , of which again 12 are red . so the probability of pulling a non - red marble out is ( x - 12 ) / x probability theorm states that if the probability of event a occuring is m and the probability of event b occuring is n then the probability of both a and b occuring is m * n so therefore the probability of 2 non - red marbles getting pulled out is [ ( x - 12 ) / x ] * [ ( x - 12 ) / x ] this is given as 49 / 64 - - > ( x - 12 ) ^ 2 = 49 / 64 x ^ 2 square rooting u have x - 12 / x = 7 / 8 or x = 96 d"

divide(12, subtract(const_1, sqrt(divide(49, 64))))

<gadget id="calculator">49 / 64</gadget>
<output>49/64 = around 0.765625</output>
<gadget id="calculator">(49/64) ** (1/2)</gadget>
<output>7/8 = around 0.875</output>
<gadget id="calculator">1 - (7/8)</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">12 / (1/8)</gadget>
<output>96</output>
<result>96</result>


average of 15 results is 43 . if the average of first 7 results is 41 and average of last 7 results is 45 then find the eighth result ?

Explanation: option ' c '

subtract(multiply(15, 43), add(multiply(7, 41), multiply(7, 45)))

<gadget id="calculator">15 * 43</gadget>
<output>645</output>
<gadget id="calculator">7 * 41</gadget>
<output>287</output>
<gadget id="calculator">7 * 45</gadget>
<output>315</output>
<gadget id="calculator">287 + 315</gadget>
<output>602</output>
<gadget id="calculator">645 - 602</gadget>
<output>43</output>
<result>43</result>


the difference between the compound interest compounded annually and simple interest for 2 years at 20 % per annum is rs . 432 . find the principal ?

Explanation: p = 432 ( 100 / 5 ) ^ 2 = > p = 10800 answer : e

divide(432, subtract(power(add(divide(20, const_100), const_1), 2), add(multiply(divide(20, const_100), 2), const_1)))

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) + 1</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">(6/5) ** 2</gadget>
<output>36/25 = around 1.44</output>
<gadget id="calculator">(1/5) * 2</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) + 1</gadget>
<output>7/5 = around 1.4</output>
<gadget id="calculator">(36/25) - (7/5)</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">432 / (1/25)</gadget>
<output>10_800</output>
<result>10_800</result>


a sprinter starts running on a circular path of radius r metres . her average speed ( in metres / minute ) is π r during the first 30 seconds , π r / 2 during next one minute , π r / 4 during next 2 minutes , π r / 8 during next 4 minutes , and so on . what is the ratio of the time taken for the nth round to that for the previous round ?

Explanation: explanation : there is more than 1 way to approach the solution ; however , i will detail the easiest way to go about it here . we want to find the ratio of time taken for nth round : time taken for ( n - 1 ) th round it will be same as finding the ratio of time taken for 2 nd round : time taken for 1 st round . 1 round = circumference of the circle = 2 π r 1 st round : speed = π r for 30 seconds . so , total distance travelled = π r / 2 . speed = π r / 2 for 1 minute . so , total distance travelled = π r / 2 . speed = π r / 4 for 2 minutes . so , total distance travelled = π r / 2 . speed = π r / 8 for 4 minutes . so , total distance travelled = π r / 2 . so , for a distance of 2 π r , time taken is 7.5 minutes . 2 nd round : speed = π r / 16 for 8 minutes . so , total distance travelled = π r / 2 . speed = π r / 32 for 16 minutes . so , total distance travelled = π r / 2 . speed = π r / 64 for 32 minutes . so , total distance travelled = π r / 2 . speed = π r / 128 for 64 minutes . so , total distance travelled = π r / 2 . so , for a distance of 2 π r , time taken is 120 minutes . ratio is 120 : 7.5 = 16 : 1 . answer : c

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


. a car covers a distance of 1028 km in 4 hours . find its speed ?

Explanation: "1028 / 4 = 257 kmph answer : d"

<gadget id="calculator">1_028 / 4</gadget>
<output>257</output>
<result>257</result>


the weight of a hollow sphere is directly dependent on its surface area . the surface area of a sphere is 4 π · r ^ 2 , where r is the radius of the sphere . if a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams , a hollow sphere of radius 0.3 cm made of the same metal would weigh how many grams t ?

Explanation: "weight directly proportional to 4 pi r ^ 2 now , 4 pi is constant , so , weight is directly proportional to r ^ 2 . when radius = 0.15 , weight = 8 , so ( 0.15 ) ^ 2 proportional to 8 ; ( 0.15 ) ^ 2 * 4 proportional to 8 * 4 , solving further ( 0.15 ) ^ 2 * 2 ^ 2 = ( 0.15 * 2 ) ^ 2 = 0.3 ^ 2 ; so answer = 32 ( b )"

<gadget id="calculator">8 * 4</gadget>
<output>32</output>
<result>32</result>


an enterprising businessman earns an income of re 5 on the first day of his business . on every subsequent day , he earns an income which is just thrice of that made on the previous day . on the 10 th day of business , he earns an income of :

Explanation: 2 nd day he earns = 3 ( 2 – 5 ) 3 rd day he earns = 3 ( 3 – 5 ) on 20 th day he earns 3 ( 20 - 5 ) = 45 rupees answer : d

<gadget id="calculator">5 * 10</gadget>
<output>50</output>
<gadget id="calculator">50 - 5</gadget>
<output>45</output>
<result>45</result>


a student chose a number , multiplied it by 3 , then subtracted 138 from the result and got 102 . what was the number he chose ?

Explanation: "solution : let xx be the number he chose , then 3 ⋅ x − 138 = 102 3 x = 240 x = 80 answer a"

<gadget id="calculator">102 + 138</gadget>
<output>240</output>
<gadget id="calculator">240 / 3</gadget>
<output>80</output>
<result>80</result>


two goods train each 500 m long , are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively find the time taken by the slower train to pass the driver of the faster one .

Explanation: solution relative speed = ( 45 + 30 ) km / hr = ( 75 x 5 / 18 ) m / sec = ( 125 / 6 ) m / sec total distance covered = ( 500 + 500 ) m = 1000 m required time = ( 1000 x 6 / 125 ) sec = 48 sec answer c

multiply(divide(500, divide(multiply(const_1000, add(45, 30)), const_3600)), const_2)

<gadget id="calculator">45 + 30</gadget>
<output>75</output>
<gadget id="calculator">1_000 * 75</gadget>
<output>75_000</output>
<gadget id="calculator">75_000 / 3_600</gadget>
<output>125/6 = around 20.833333</output>
<gadget id="calculator">500 / (125/6)</gadget>
<output>24</output>
<gadget id="calculator">24 * 2</gadget>
<output>48</output>
<result>48</result>


the population of a village is 14300 . it increases annually at the rate of 15 % p . a . what will be its population after 2 years ?

Explanation: formula : ( after = 100 denominator ago = 100 numerator ) 14300 × 115 / 100 × 115 / 100 = 18911 a

multiply(14300, power(add(const_1, divide(15, const_100)), 2))

<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">1 + (3/20)</gadget>
<output>23/20 = around 1.15</output>
<gadget id="calculator">(23/20) ** 2</gadget>
<output>529/400 = around 1.3225</output>
<gadget id="calculator">14_300 * (529/400)</gadget>
<output>75_647/4 = around 18_911.75</output>
<result>75_647/4 = around 18_911.75</result>


what is the sum of all possible solutions to | x - 3 | ^ 2 + | x - 3 | = 20 ?

Explanation: "first of all | x - 3 | ^ 2 = ( x - 3 ) ^ 2 , so we have : ( x - 3 ) ^ 2 + | x - 3 | = 20 . when x < 3 , x - 3 is negative , thus | x - 3 | = - ( x - 3 ) . in this case we ' ll have ( x - 3 ) ^ 2 - ( x - 3 ) = 20 - - > x = - 1 or x = 8 . discard x = 8 because it ' s not in the range we consider ( < 3 ) . when x > = 3 , x - 3 is non - negative , thus | x - 3 | = x - 3 . in this case we ' ll have ( x - 3 ) ^ 2 + ( x - 3 ) = 20 - - > x = - 2 or x = 7 . discard x = - 2 because it ' s not in the range we consider ( > = 3 ) . thus there are two solutions : x = - 1 and x = 7 - - > the sum = 6 . answer : b ."

add(add(const_4, 3), subtract(3, const_4))

<gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">3 - 4</gadget>
<output>-1</output>
<gadget id="calculator">7 + (-1)</gadget>
<output>6</output>
<result>6</result>


a closed cylindrical tank contains 36 pie cubic feet of water and its filled to half its capacity . when the tank is placed upright on its circular base on level ground , the height of water in the tank is 4 feet . when the tank is placed on its side on level ground , what is the height , in feet , of the surface of the water above the ground ?

Explanation: 36 pie cubic feet of water and its filled to half tank ' s capacity . . . volume of tank = 72 pie cubic feet height of tank = 4 * 2 = 8 feet ( since tank is placed upright on its circular base on level ground , the height of water in the tank is 4 feet . ) 72 pie = pie * r 2 * 8 r 2 = 9 r = 3 feet answer : d

sqrt(divide(divide(multiply(36, const_pi), 4), const_pi))

<gadget id="calculator">36 * pi</gadget>
<output>36*pi = around 113.097336</output>
<gadget id="calculator">(36*pi) / 4</gadget>
<output>9*pi = around 28.274334</output>
<gadget id="calculator">(9*pi) / pi</gadget>
<output>9</output>
<gadget id="calculator">9 ** (1/2)</gadget>
<output>3</output>
<result>3</result>


shopkeeper rise price by 33 % and gives successive discount of 10 % and 15 % . what is overall % gain or loss ?

Explanation: "let d initial price be 100 33 % rise now price = 133 / 100 * 100 = 133 10 % discount then price = 133 * 90 / 100 = 119.7 15 % discount then price = 119.7 * 85 / 100 = 101.745 so gain = 101.745 - 100 = 1.745 gain % = gain * 100 / cp = = > 1.745 * 100 / 100 = 1.745 % answer : a"

subtract(multiply(multiply(add(const_100, 33), divide(subtract(const_100, 10), const_100)), divide(subtract(const_100, 15), const_100)), const_100)

<gadget id="calculator">100 + 33</gadget>
<output>133</output>
<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">90 / 100</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">133 * (9/10)</gadget>
<output>1_197/10 = around 119.7</output>
<gadget id="calculator">100 - 15</gadget>
<output>85</output>
<gadget id="calculator">85 / 100</gadget>
<output>17/20 = around 0.85</output>
<gadget id="calculator">(1_197/10) * (17/20)</gadget>
<output>20_349/200 = around 101.745</output>
<gadget id="calculator">(20_349/200) - 100</gadget>
<output>349/200 = around 1.745</output>
<result>349/200 = around 1.745</result>


in a certain pet shop , the ratio of dogs to cats to bunnies in stock is 3 : 7 : 13 . if the shop carries 352 dogs and bunnies total in stock , how many dogs are there ?

Explanation: "let us assume the number of dogs , cats and bunnies to be 3 x , 7 x and 13 x total dogs and bunnies = 16 x . and we are given that 16 x = 352 . hence x = 22 . dogs = 3 x = 3 * 22 = 66 ( option b )"

<gadget id="calculator">3 + 13</gadget>
<output>16</output>
<gadget id="calculator">352 / 16</gadget>
<output>22</output>
<gadget id="calculator">22 * 3</gadget>
<output>66</output>
<result>66</result>


when the price of an article was reduced by 25 % its sale increased by 80 % . what was the net effect on the sale ?

Explanation: "if n items are sold for $ p each , revenue is $ np . if we reduce the price by 25 % , the new price is 0.75 p . if we increase the number sold by 80 % , the new number sold is 1.8 n . so the new revenue is ( 0.75 p ) ( 1.8 n ) = 1.35 np , which is 1.35 times the old revenue , so is 35 % greater . answer : a"

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

<gadget id="calculator">80 + 100</gadget>
<output>180</output>
<gadget id="calculator">100 - 25</gadget>
<output>75</output>
<gadget id="calculator">180 * 75</gadget>
<output>13_500</output>
<gadget id="calculator">13_500 / 100</gadget>
<output>135</output>
<gadget id="calculator">135 - 100</gadget>
<output>35</output>
<result>35</result>


5 years ago , the average age of a and b was 15 years . average age of a , b and c today is 20 years . how old will c be after 14 years ?

Explanation: explanation : ( a + b ) , five years ago = ( 15 * 2 ) = 30 years . ( a + b ) , now = ( 30 + 5 * 2 ) years = 40 years . ( a + b + c ) , now = ( 20 x 3 ) years = 60 years . c , now = ( 60 - 40 ) years = 20 years . c , after 14 years = ( 20 + 14 ) years = 34 years . answer : b

add(subtract(multiply(20, const_3), add(add(multiply(15, const_2), 5), 5)), 14)

<gadget id="calculator">20 * 3</gadget>
<output>60</output>
<gadget id="calculator">15 * 2</gadget>
<output>30</output>
<gadget id="calculator">30 + 5</gadget>
<output>35</output>
<gadget id="calculator">35 + 5</gadget>
<output>40</output>
<gadget id="calculator">60 - 40</gadget>
<output>20</output>
<gadget id="calculator">20 + 14</gadget>
<output>34</output>
<result>34</result>


one fourth of a solution that was 10 % sugar by weight was replaced with by a second solution resulting in a solution that was 16 percent sugar by weight . the second solution was what percent sugar by weight ?

Explanation: "say the second solution ( which was 1 / 4 th of total ) was x % sugar , then 3 / 4 * 0.1 + 1 / 4 * x = 1 * 0.16 - - > x = 0.34 . alternately you can consider total solution to be 100 liters and in this case you ' ll have : 75 * 0.1 + 25 * x = 100 * 0.16 - - > x = 0.34 . answer : a ."

multiply(divide(subtract(multiply(const_100, divide(16, const_100)), multiply(subtract(const_100, multiply(divide(const_1, const_4), const_100)), divide(10, const_100))), multiply(divide(const_1, const_4), const_100)), const_100)

<gadget id="calculator">16 / 100</gadget>
<output>4/25 = around 0.16</output>
<gadget id="calculator">100 * (4/25)</gadget>
<output>16</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<gadget id="calculator">100 - 25</gadget>
<output>75</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">75 * (1/10)</gadget>
<output>15/2 = around 7.5</output>
<gadget id="calculator">16 - (15/2)</gadget>
<output>17/2 = around 8.5</output>
<gadget id="calculator">(17/2) / 25</gadget>
<output>17/50 = around 0.34</output>
<gadget id="calculator">(17/50) * 100</gadget>
<output>34</output>
<result>34</result>


a can give b 100 meters start and c 120 meters start in a kilometer race . how much start can b give c in a kilometer race ?

Explanation: "explanation : a runs 1000 meters while b runs 900 meters and c runs 880 meters . therefore , b runs 900 meters while c runs 880 meters . so , the number of meters that c runs when b runs 1000 meters = ( 1000 x 880 ) / 900 = 977.778 meters thus , b can give c ( 1000 - 977.77 ) = 22.22 meters start answer : c"

subtract(multiply(const_100, const_10), divide(multiply(multiply(const_100, const_10), subtract(multiply(const_100, const_10), 120)), subtract(multiply(const_100, const_10), 100)))

<gadget id="calculator">100 * 10</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 - 120</gadget>
<output>880</output>
<gadget id="calculator">1_000 * 880</gadget>
<output>880_000</output>
<gadget id="calculator">1_000 - 100</gadget>
<output>900</output>
<gadget id="calculator">880_000 / 900</gadget>
<output>8_800/9 = around 977.777778</output>
<gadget id="calculator">1_000 - (8_800/9)</gadget>
<output>200/9 = around 22.222222</output>
<result>200/9 = around 22.222222</result>


a train 450 metres long is moving at a speed of 25 kmph . it will cross a man coming from the opposite direction at a speed of 2 km per hour in :

Explanation: "relative speed = ( 25 + 2 ) km / hr = 27 km / hr = ( 27 × 5 / 18 ) m / sec = 15 / 2 m / sec . time taken by the train to pass the man = ( 450 × 2 / 15 ) sec = 60 sec answer : e"

multiply(const_3600, divide(divide(450, const_1000), add(25, 2)))

<gadget id="calculator">450 / 1_000</gadget>
<output>9/20 = around 0.45</output>
<gadget id="calculator">25 + 2</gadget>
<output>27</output>
<gadget id="calculator">(9/20) / 27</gadget>
<output>1/60 = around 0.016667</output>
<gadget id="calculator">3_600 * (1/60)</gadget>
<output>60</output>
<result>60</result>


a rectangular with dimensions 35 inches by 45 inches is to be divided into squares of equal size . which of the following could be a length of a side of the squares ?

Explanation: you need to divide the width and length of the rectangular to equal pieces where l = w you can solve this using gcf 35 = 5 * 7 45 = 3 * 3 * 5 gcf = 5 p . s you can make squares with side of 5 answer : c

<gadget id="calculator">45 - 35</gadget>
<output>10</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<result>5</result>


the function f ( p ) represents the number of ways that prime numbers can be uniquely summed to form a certain number p such that p = a + b + c + d … where those summed variables are each prime and a ≤ b ≤ c ≤ d . . . for instance f ( 8 ) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5 . what is f ( 12 ) ?

Explanation: so we can start with 2 and check whether sum of two primes is primes is even . 1 ) 2 ( 6 times ) 2 ) 2 ( 3 times ) + 3 ( 2 times ) 3 ) 2 ( 2 times ) + 3 + 5 4 ) 2 + 3 + 7 5 ) 2 + 5 + 5 6 ) 3 ( 4 times ) 7 ) 5 + 7 answer : d

<gadget id="calculator">12 / 4</gadget>
<output>3</output>
<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<result>7</result>


in what time will a train 175 m long cross an electric pole , it its speed be 144 km / hr ?

Explanation: "speed = 144 * 5 / 18 = 40 m / sec time taken = 175 / 40 = 4.37 sec . answer : c"

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">144 * (5/18)</gadget>
<output>40</output>
<gadget id="calculator">175 / 40</gadget>
<output>35/8 = around 4.375</output>
<result>35/8 = around 4.375</result>


a student chose a number , multiplied it by 5 , then subtracted 275 from the result and got 135 . what was the number he chose ?

Explanation: "let x be the number he chose , then 5 ⋅ x − 275 = 135 5 x = 410 x = 82 correct answer b"

<gadget id="calculator">135 + 275</gadget>
<output>410</output>
<gadget id="calculator">410 / 5</gadget>
<output>82</output>
<result>82</result>


in a can , there is a mixture of milk and water in the ratio 3 : 2 . if the can is filled with an additional 6 liters of milk , the can would be full and the ratio of milk and water would become 2 : 1 . find the capacity of the can ?

Explanation: "let c be the capacity of the can . ( 3 / 5 ) * ( c - 6 ) + 6 = ( 2 / 3 ) * c 9 c - 54 + 90 = 10 c c = 36 the answer is a ."

add(add(multiply(divide(multiply(1, 6), subtract(multiply(2, 2), multiply(1, 3))), 3), 6), multiply(divide(multiply(1, 6), subtract(multiply(2, 2), multiply(1, 3))), 2))

<gadget id="calculator">1 * 6</gadget>
<output>6</output>
<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">1 * 3</gadget>
<output>3</output>
<gadget id="calculator">4 - 3</gadget>
<output>1</output>
<gadget id="calculator">6 / 1</gadget>
<output>6</output>
<gadget id="calculator">6 * 3</gadget>
<output>18</output>
<gadget id="calculator">18 + 6</gadget>
<output>24</output>
<gadget id="calculator">6 * 2</gadget>
<output>12</output>
<gadget id="calculator">24 + 12</gadget>
<output>36</output>
<result>36</result>


susan drives from city a to city b . after two hours of driving she noticed that she covered 80 km and calculated that , if she continued driving at the same speed , she would end up been 15 minutes late . so she increased her speed by 10 km / hr and she arrived at city b 36 minutes earlier than she planned . find the distance between cities a and b .

Explanation: let xx be the distance between a and b . since susan covered 80 km in 2 hours , her speed was v = 802 = 40 v = 802 = 40 km / hr . if she continued at the same speed she would be 1515 minutes late , i . e . the planned time on the road is x 40 − 1560 x 40 − 1560 hr . the rest of the distance is ( x − 80 ) ( x − 80 ) km . v = 40 + 10 = 50 v = 40 + 10 = 50 km / hr . so , she covered the distance between a and b in 2 + x − 80502 + x − 8050 hr , and it was 36 min less than planned . therefore , the planned time was 2 + x − 8050 + 36602 + x − 8050 + 3660 . when we equalize the expressions for the scheduled time , we get the equation : x 40 − 1560 = 2 + x − 8050 + 3660 x 40 − 1560 = 2 + x − 8050 + 3660 x − 1040 = 100 + x − 80 + 3050 x − 1040 = 100 + x − 80 + 3050 x − 104 = x + 505 x − 104 = x + 505 5 x − 50 = 4 x + 2005 x − 50 = 4 x + 200 x = 250 x = 250 so , the distance between cities a and b is 250 km . answer : c

add(divide(subtract(add(subtract(divide(36, const_60), divide(80, add(divide(80, const_2), 10))), const_2), divide(15, const_60)), subtract(divide(const_1, divide(80, const_2)), divide(const_1, add(divide(80, const_2), 10)))), const_100)

<gadget id="calculator">36 / 60</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">80 / 2</gadget>
<output>40</output>
<gadget id="calculator">40 + 10</gadget>
<output>50</output>
<gadget id="calculator">80 / 50</gadget>
<output>8/5 = around 1.6</output>
<gadget id="calculator">(3/5) - (8/5)</gadget>
<output>-1</output>
<gadget id="calculator">(-1) + 2</gadget>
<output>1</output>
<gadget id="calculator">15 / 60</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 - (1/4)</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">1 / 40</gadget>
<output>1/40 = around 0.025</output>
<gadget id="calculator">1 / 50</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">(1/40) - (1/50)</gadget>
<output>1/200 = around 0.005</output>
<gadget id="calculator">(3/4) / (1/200)</gadget>
<output>150</output>
<gadget id="calculator">150 + 100</gadget>
<output>250</output>
<result>250</result>


a train running at the speed of 40 km / hr crosses a pole in 9 sec . what is the length of the train ?

Explanation: "speed = 40 * 5 / 18 = 100 / 9 m / sec length of the train = speed * time = 100 / 9 * 9 = 100 m answer : a"

multiply(divide(multiply(40, const_1000), const_3600), 9)

<gadget id="calculator">40 * 1_000</gadget>
<output>40_000</output>
<gadget id="calculator">40_000 / 3_600</gadget>
<output>100/9 = around 11.111111</output>
<gadget id="calculator">(100/9) * 9</gadget>
<output>100</output>
<result>100</result>


what is the remainder if 7 ^ 16 is divided by 100 ?

Explanation: "7 ^ 16 can be written as ( 7 ^ 4 ) ^ 4 if we divide 7 ^ 4 by 100 the reminder is 1 so , ( 7 ^ 4 ) ^ 4 by 100 , the reminder is 1 ^ 4 = 1 answer : d"

subtract(divide(100, const_2), multiply(7, 7))

<gadget id="calculator">100 / 2</gadget>
<output>50</output>
<gadget id="calculator">7 * 7</gadget>
<output>49</output>
<gadget id="calculator">50 - 49</gadget>
<output>1</output>
<result>1</result>


a large box contains 17 small boxes and each small box contains 25 chocolate bars . how many chocolate bars are in the large box ?

Explanation: "the number of chocolate bars is equal to 17 * 25 = 425 correct answer c"

<gadget id="calculator">17 * 25</gadget>
<output>425</output>
<result>425</result>


what is the product of all the possible values of x if x ^ 2 + 5 x + 6 ?

Explanation: explanation : = > y = x ^ 2 + 5 x + 6 = > y = ( x + 2 ) ( x + 3 ) = > x = - 2 , x = - 3 product x = ( - 2 ) ( - 3 ) = 6 answer option 6 answer : d

<gadget id="calculator">6 / 1</gadget>
<output>6</output>
<result>6</result>


jo ' s collection contains us , indian and british stamps . if the ratio of us to indian stamps is 6 to 2 and the ratio of indian to british stamps is 5 to 1 , what is the ratio of us to british stamps ?

Explanation: "u / i = 6 / 2 i / b = 5 / 1 since i is multiple of both 2 ( as per first ratio ) and 5 ( as per second ratio ) so let ' s assume that i = 10 i . e . multiplying teh first ratio by 5 and second ration by 2 in each numerator and denominator then , u : i : b = 30 : 18 : 2 i . e . u : b = 30 : 2 answer : option b"

<gadget id="calculator">6 * 5</gadget>
<output>30</output>
<gadget id="calculator">1 * 2</gadget>
<output>2</output>
<gadget id="calculator">30 / 2</gadget>
<output>15</output>
<result>15</result>


a man walking at a constant rate of 9 miles per hour is passed by a woman traveling in the same direction along the same path at a constant rate of 15 miles per hour . the woman stops to wait for the man 3 minutes after passing him , while the man continues to walk at his constant rate . how many minutes must the woman wait until the man catches up ?

Explanation: when the woman passes the man , they are aligned ( m and w ) . they are moving in the same direction . after 5 minutes , the woman ( w ) will be ahead the man ( m ) : m - - - - - - m - - - - - - - - - - - - - - - w w in the 5 minutes , after passing the man , the woman walks the distance mw = ww , which is 3 * 15 / 60 = 15 / 20 miles and the man walks the distance mm , which is 3 * 9 / 60 = 9 / 20 mile . the difference of 15 / 20 - 9 / 20 = 3 / 10 miles ( mw ) will be covered by the man in ( 3 / 10 ) / 9 = 1 / 30 of an hour , which is 2 minutes . answer b .

multiply(const_60, divide(multiply(divide(3, const_60), subtract(15, 9)), 9))

<gadget id="calculator">3 / 60</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">15 - 9</gadget>
<output>6</output>
<gadget id="calculator">(1/20) * 6</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(3/10) / 9</gadget>
<output>1/30 = around 0.033333</output>
<gadget id="calculator">60 * (1/30)</gadget>
<output>2</output>
<result>2</result>


in a certain state , the ratio of registered republicans to registered democrats is 3 to 2 , and every registered voter is either a republican or a democrat . if 80 percent of the republicans and 20 percent of the democrats are expected to vote for candidate x , and everyone else is expected to vote for candidate y , by what percent is candidate x expected to win the election ?

Explanation: "since we were expected to find a percentage figure - it thought that it might be easier to pick a ' smart number ' to represent the total number of voters ( republicans and democrats ) . therefore , i picked 100 ( as the total number of voters ) and thus 30 : 20 represents the number ratio of republicans : democrats . if 80 % of republicans ( which is ( 60 * 0.8 ) = 48 ) and 20 % of democrats ( 40 * 0.2 = 8 ) voted for candidate x , means that out of total of 100 voters ; 56 ( 48 + 8 ) voters voted for candidate x and 44 voted for candidate y . thus we can infer that candidate x is expected to win the election by 12 ( 56 - 44 ) votes . therefore candidate x is expected to win the election by ( 12 / 100 ) votes which is equivalent to 12 % . i think the answer is e ."

multiply(divide(subtract(add(multiply(divide(20, const_100), 2), multiply(divide(80, const_100), 3)), add(subtract(3, multiply(divide(80, const_100), 3)), subtract(2, multiply(divide(20, const_100), 2)))), add(3, 2)), const_100)

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 2</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(4/5) * 3</gadget>
<output>12/5 = around 2.4</output>
<gadget id="calculator">(2/5) + (12/5)</gadget>
<output>14/5 = around 2.8</output>
<gadget id="calculator">3 - (12/5)</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">2 - (2/5)</gadget>
<output>8/5 = around 1.6</output>
<gadget id="calculator">(3/5) + (8/5)</gadget>
<output>11/5 = around 2.2</output>
<gadget id="calculator">(14/5) - (11/5)</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">(3/5) / 5</gadget>
<output>3/25 = around 0.12</output>
<gadget id="calculator">(3/25) * 100</gadget>
<output>12</output>
<result>12</result>


the sides of a square region , measured to the nearest centimeter , are 10 centimeters long . the least possible value of the actual area of the square region is

Explanation: "though there might be some technicalities concerning the termnearest ( as 9.5 is equidistant from both 9 and 10 ) the answer still should be : 9.5 ^ 2 = 90.25 . answer : e"

power(subtract(subtract(10, const_0_25), const_0_25), const_2)

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">10 - (1/4)</gadget>
<output>39/4 = around 9.75</output>
<gadget id="calculator">(39/4) - (1/4)</gadget>
<output>19/2 = around 9.5</output>
<gadget id="calculator">(19/2) ** 2</gadget>
<output>361/4 = around 90.25</output>
<result>361/4 = around 90.25</result>


if tim had lunch at $ 50.50 and he gave 10 % tip , how much did he spend ?

Explanation: "the tip is 20 % of what he paid for lunch . hence tip = 20 % of 50.50 = ( 10 / 100 ) * 50.50 = $ 5.05 total spent 50.50 + 5.05 = $ 55.55 correct answer d"

<gadget id="calculator">50.5 * 10</gadget>
<output>505</output>
<gadget id="calculator">505 / 100</gadget>
<output>101/20 = around 5.05</output>
<gadget id="calculator">50.5 + (101/20)</gadget>
<output>55.55</output>
<result>55.55</result>


a 240 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds . what is the lenght of other train .

Explanation: "relative speeds = ( 120 + 80 ) km / hr = 200 km / hr = ( 200 * 5 / 18 ) m / s = ( 500 / 9 ) m / s let length of train be xm x + 240 / 9 = 500 / 9 x = 260 ans is 260 m answer : a"

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

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


company a imported 12,000 widgets made of either brass or aluminum . the widgets are painted blue , red or green . if 10 percent of the widgets are made of brass and of those 20 percent are painted green and 40 percent are painted red how many brass widgets painted blue were imported ?

Explanation: answer a . we are told that 10 % of all imported widgets are made of brass and of those , 20 % are green and 40 % are red . since we know that there are only three colors , the remaining 40 % must be blue . 40 % blue of 10 % brass widgets leads to 4 % blue brass widgets out of the total 10,550 widgets . 12,000 / 100 * 4 = 480 . answer b .

multiply(multiply(multiply(multiply(divide(10, const_100), divide(40, const_100)), divide(add(10, const_2), 10)), const_100), const_100)

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(1/10) * (2/5)</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">10 + 2</gadget>
<output>12</output>
<gadget id="calculator">12 / 10</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">(1/25) * (6/5)</gadget>
<output>6/125 = around 0.048</output>
<gadget id="calculator">(6/125) * 100</gadget>
<output>24/5 = around 4.8</output>
<gadget id="calculator">(24/5) * 100</gadget>
<output>480</output>
<result>480</result>


mr . das decided to walk down the escalator of a mall . he found that if he walks down 26 steps , he requires 30 seconds to reach the bottom . however , if he steps down 34 stair she would only require 18 seconds to get to the bottom . if the time is measured from the moment the top step begins to descend to the time he steps off the last step at the bottom , find out the height of the stair way insteps ?

Explanation: here when he step down 26 steps he has 30 seconds for remaining steps . if he step down 34 stairs he has only 18 sec . 30 - 18 = 12 12 secs for 8 steps . . 18 secs for 12 steps . 12 + 34 = 46 so ans is 46 . . answer : b

subtract(add(multiply(divide(subtract(34, 26), subtract(30, 18)), 30), 26), multiply(const_4, const_10))

<gadget id="calculator">34 - 26</gadget>
<output>8</output>
<gadget id="calculator">30 - 18</gadget>
<output>12</output>
<gadget id="calculator">8 / 12</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) * 30</gadget>
<output>20</output>
<gadget id="calculator">20 + 26</gadget>
<output>46</output>
<gadget id="calculator">4 * 10</gadget>
<output>40</output>
<gadget id="calculator">46 - 40</gadget>
<output>6</output>
<result>6</result>


solution x is 30 % chemical a and 70 % chemical b by volume . solution y is 40 % chemical a and 60 % chemical b by volume . if a mixture of x and y is 36 % chemical a , what percent of the mixture is solution x ?

Explanation: "the volume of the mixture be x + y . 0.3 x + 0.4 y = 0.36 ( x + y ) x = 2 y / 3 x / ( x + y ) = ( 2 y / 3 ) / ( 5 y / 3 ) = 2 / 5 = 40 % . the answer is c ."

multiply(divide(divide(subtract(40, 36), subtract(36, 30)), add(divide(subtract(40, 36), subtract(36, 30)), const_1)), const_100)

<gadget id="calculator">40 - 36</gadget>
<output>4</output>
<gadget id="calculator">36 - 30</gadget>
<output>6</output>
<gadget id="calculator">4 / 6</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) + 1</gadget>
<output>5/3 = around 1.666667</output>
<gadget id="calculator">(2/3) / (5/3)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) * 100</gadget>
<output>40</output>
<result>40</result>


jim ’ s taxi service charges an initial fee of $ 2.45 at the beginning of a trip and an additional charge of $ 0.35 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?

Explanation: "let the fixed charge of jim ’ s taxi service = 2.45 $ and charge per 2 / 5 mile ( . 4 mile ) = . 35 $ total charge for a trip of 3.6 miles = 2.45 + ( 3.6 / . 4 ) * . 35 = 2.45 + 9 * . 35 = 5.6 $ answer e"

<gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">3.6 / (2/5)</gadget>
<output>9</output>
<gadget id="calculator">0.35 * 9</gadget>
<output>3.15</output>
<gadget id="calculator">2.45 + 3.15</gadget>
<output>5.6</output>
<result>5.6</result>


a bowl contains equal numbers of red , orange , green , blue , and yellow candies . kaz eats all of the green candies and half of the orange ones . next , he eats half of the remaining pieces of each color . finally , he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 24 % of the original number . what percent of the red candies remain ?

Explanation: let x be the original number of each color so there are a total of 5 x candies . kaz eats all of the green candies and half of the orange ones . there are 0 green candies and 0.5 x orange candies remaining . he eats half of the remaining pieces of each color . there are 0.25 x orange candies , and 0.5 x each of red , yellow , and blue candies . he eats red and yellow candies in equal proportions . orange + blue + red + yellow = 0.75 x + red + yellow = 1.2 x red + yellow = 0.45 x red = 0.225 x , since red = yellow . the answer is c .

multiply(divide(divide(subtract(24, add(divide(divide(const_100, add(const_2, const_3)), const_2), divide(divide(divide(const_100, add(const_2, const_3)), const_2), const_2))), const_2), divide(const_100, add(const_2, const_3))), const_100)

<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">100 / 5</gadget>
<output>20</output>
<gadget id="calculator">20 / 2</gadget>
<output>10</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">10 + 5</gadget>
<output>15</output>
<gadget id="calculator">24 - 15</gadget>
<output>9</output>
<gadget id="calculator">9 / 2</gadget>
<output>9/2 = around 4.5</output>
<gadget id="calculator">(9/2) / 20</gadget>
<output>9/40 = around 0.225</output>
<gadget id="calculator">(9/40) * 100</gadget>
<output>45/2 = around 22.5</output>
<result>45/2 = around 22.5</result>


on selling 9 balls at rs . 720 , there is a loss equal to the cost price of 5 balls . the cost price of a ball is :

Explanation: "( c . p . of 9 balls ) - ( s . p . of 9 balls ) = ( c . p . of 5 balls ) c . p . of 4 balls = s . p . of 9 balls = rs . 720 . c . p . of 1 ball = rs . 720 / 4 = rs . 180 . answer : option e"

<gadget id="calculator">9 - 5</gadget>
<output>4</output>
<gadget id="calculator">720 / 4</gadget>
<output>180</output>
<result>180</result>


boy sells a book for rs . 630 he gets a loss of 10 % , to gain 10 % , what should be the sp ?

Explanation: "cost price = 630 / 90 x 100 = 700 to gain 10 % = 700 x 10 / 100 = 70 sp = cp + gain = 700 + 70 = 770 answer : d"

add(divide(630, subtract(const_1, divide(10, const_100))), multiply(divide(630, subtract(const_1, divide(10, const_100))), divide(10, const_100)))

<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">630 / (9/10)</gadget>
<output>700</output>
<gadget id="calculator">700 * (1/10)</gadget>
<output>70</output>
<gadget id="calculator">700 + 70</gadget>
<output>770</output>
<result>770</result>


a train 310 meters long is running with a speed of 60 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?

Explanation: "speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 310 * 3 / 55 ] sec = 17 sec answer : d"

multiply(const_3600, divide(divide(310, const_1000), add(60, 6)))

<gadget id="calculator">310 / 1_000</gadget>
<output>31/100 = around 0.31</output>
<gadget id="calculator">60 + 6</gadget>
<output>66</output>
<gadget id="calculator">(31/100) / 66</gadget>
<output>31/6_600 = around 0.004697</output>
<gadget id="calculator">3_600 * (31/6_600)</gadget>
<output>186/11 = around 16.909091</output>
<result>186/11 = around 16.909091</result>


Explanation: start with the prime factorization : 210 = 2 * 3 * 5 * 7 for odd factors , we put aside the factor of two , and look at the other prime factors . set of exponents = { 1 , 1 , 1 } plus 1 to each = { 2 , 2 , 2 } product = 2 * 2 * 2 = 8 therefore , there are 8 odd factors of 210 . in case you are curious , they are { 1 , 3 , 5 , 7 , 15 , 21 , 35 , and 105 } answer : e .

add(add(add(const_4, const_2), const_1), const_1)

<gadget id="calculator">4 + 2</gadget>
<output>6</output>
<gadget id="calculator">6 + 1</gadget>
<output>7</output>
<gadget id="calculator">7 + 1</gadget>
<output>8</output>
<result>8</result>


sarah operated her lemonade stand monday through friday over a two week period and made a total profit of 350 dollars . on hot days she sold cups of lemonade for a price that was 25 percent higher than the regular days . each cup she sold had a total cost of 75 cents and sarah did not incur any other costs . if every day she sold exactly 32 cups and 3 of the days were hot , then what was the price of 1 cup on a hot day ?

Explanation: "7 regular days - - > sales = 7 * 32 * x = 224 x ; 3 hot days - - > sales = 3 * 32 * ( 1.25 x ) = 120 x ; total sales = 224 x + 120 x = 344 x . total cost = 10 * 32 * 0.75 = 240 . profit = 344 x - 240 = 350 - - > x = 1.715 . 1.25 x = ~ 2.14 . answer : c ."

multiply(divide(add(multiply(multiply(32, divide(75, const_100)), multiply(add(const_4, 1), const_2)), 350), add(multiply(subtract(multiply(add(const_4, 1), const_2), 3), 32), multiply(multiply(divide(add(const_100, 25), const_100), 3), 32))), divide(add(const_100, 25), const_100))

<gadget id="calculator">75 / 100</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">32 * (3/4)</gadget>
<output>24</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">24 * 10</gadget>
<output>240</output>
<gadget id="calculator">240 + 350</gadget>
<output>590</output>
<gadget id="calculator">10 - 3</gadget>
<output>7</output>
<gadget id="calculator">7 * 32</gadget>
<output>224</output>
<gadget id="calculator">100 + 25</gadget>
<output>125</output>
<gadget id="calculator">125 / 100</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">(5/4) * 3</gadget>
<output>15/4 = around 3.75</output>
<gadget id="calculator">(15/4) * 32</gadget>
<output>120</output>
<gadget id="calculator">224 + 120</gadget>
<output>344</output>
<gadget id="calculator">590 / 344</gadget>
<output>295/172 = around 1.715116</output>
<gadget id="calculator">(295/172) * (5/4)</gadget>
<output>1_475/688 = around 2.143895</output>
<result>1_475/688 = around 2.143895</result>


a man has $ 480 in the denominations of one - dollar , 5 - dollar notes and 10 - dollar . the number of dollars of each denomination is equal . what is the total number of dollar that he has ?

Explanation: c $ 90 let number of notes of each denomination be x . then x + 5 x + 10 x = 480 16 x = 480 x = 30 . hence , total number of notes = 3 x = 90 .

add(divide(multiply(480, 10), const_60), 10)

<gadget id="calculator">480 * 10</gadget>
<output>4_800</output>
<gadget id="calculator">4_800 / 60</gadget>
<output>80</output>
<gadget id="calculator">80 + 10</gadget>
<output>90</output>
<result>90</result>


find how many positive integers less than 10000 are there such thatthe sum of the digits of the no . is divisible by 3 ?

Explanation: if sum of the digits is divisible by 3 , the number is divisible by 3 . therefore , required number of non - negative integers is equal to count of numbers less than 10000 which are divisible by 3 . such numbers are ( 3 , 6 , 9 , . . . , 9999 ) ( arithmetic progression with first term = 3 , last term = 9999 , common difference = 3 ) . count of such numbers = 9999 3 = 3333 99993 = 3333 but zero is also divisible by 3 . this makes our total count 3334 d

<gadget id="calculator">10_000 / 3</gadget>
<output>10_000/3 = around 3_333.333333</output>
<gadget id="calculator">floor(10_000/3)</gadget>
<output>3_333</output>
<gadget id="calculator">3_333 + 1</gadget>
<output>3_334</output>
<result>3_334</result>


two persons a and b can complete a piece of work in 30 days and 45 days respectively . if they work together , what part of the work will be completed in 6 days ?

Explanation: "a ' s one day ' s work = 1 / 30 b ' s one day ' s work = 1 / 45 ( a + b ) ' s one day ' s work = 1 / 30 + 1 / 45 = 1 / 18 the part of the work completed in 6 days = 6 ( 1 / 18 ) = 1 / 3 . answer c"

multiply(6, add(divide(const_1, 30), divide(const_1, 45)))

<gadget id="calculator">1 / 30</gadget>
<output>1/30 = around 0.033333</output>
<gadget id="calculator">1 / 45</gadget>
<output>1/45 = around 0.022222</output>
<gadget id="calculator">(1/30) + (1/45)</gadget>
<output>1/18 = around 0.055556</output>
<gadget id="calculator">6 * (1/18)</gadget>
<output>1/3 = around 0.333333</output>
<result>1/3 = around 0.333333</result>


in how many ways 4 boys and 4 girls can be seated in a row so that they are alternate .

Explanation: "solution : let the arrangement be , b g b g b g b g 4 boys can be seated in 4 ! ways . girl can be seated in 4 ! ways . required number of ways , = 4 ! * 4 ! = 576 . answer : option d"

<gadget id="calculator">factorial(4)</gadget>
<output>24</output>
<gadget id="calculator">24 * 24</gadget>
<output>576</output>
<result>576</result>


kavi spends 50 % of his monthly salary on food and saves 80 % of the remaining amount . if his monthly salary is rs . 19000 , how much money does he save every month ?

Explanation: explanation : kavi ' s monthly income = rs . 19,000 he spends 50 % on food . the total money spent on food = 50 / 100 * 19000 = rs . 9500 now , his monthly remaining income = rs . 19000 – rs . 9500 = rs . 9500 out of rs . 9500 , he saves 40 % . amount saved = 40 / 100 * 9500 = rs . 3800 answer : d

divide(divide(multiply(divide(multiply(19000, 50), const_100), 80), const_100), const_2)

<gadget id="calculator">19_000 * 50</gadget>
<output>950_000</output>
<gadget id="calculator">950_000 / 100</gadget>
<output>9_500</output>
<gadget id="calculator">9_500 * 80</gadget>
<output>760_000</output>
<gadget id="calculator">760_000 / 100</gadget>
<output>7_600</output>
<gadget id="calculator">7_600 / 2</gadget>
<output>3_800</output>
<result>3_800</result>


a man can row upstream at 40 kmph and downstream at 52 kmph , and then find the speed of the man in still water ?

Explanation: "us = 40 ds = 52 m = ( 40 + 52 ) / 2 = 46 answer : d"

<gadget id="calculator">40 + 52</gadget>
<output>92</output>
<gadget id="calculator">92 / 2</gadget>
<output>46</output>
<result>46</result>


a can do a piece of work in 10 days and b alone can do it in 20 days . how much time will both take to finish the work ?

Explanation: "this question can be solved by different methods . we need to conserve time in exams so solving this problem using equations is the good idea . time taken to finish the job = xy / ( x + y ) = 10 x 20 / ( 10 + 20 ) = 200 / 30 = 6.666 days answer : c"

divide(const_1, add(divide(const_1, 10), divide(const_1, 20)))

<gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/10) + (1/20)</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">1 / (3/20)</gadget>
<output>20/3 = around 6.666667</output>
<result>20/3 = around 6.666667</result>


a ferry can transport 100 tons of vehicles . automobiles range in weight from 1,600 to 3,000 pounds . what is the greatest number of automobiles that can be loaded onto the ferry ?

Explanation: "to get maximum vehicles we must take into consideration the minimum weight i . e 1600 pounds here since , 1 ton = 2000 pounds 100 tons will be 200,000 pounds from the answer choices : let max number of vehicles be 120 total weight will be = 120 * 1600 = 192000 pounds , which is lesser than the maximum weight allowed . ans : e"

divide(multiply(multiply(100, const_2), const_1000), add(add(add(add(add(add(const_1000, const_100), const_100), const_100), const_100), const_100), const_100))

<gadget id="calculator">100 * 2</gadget>
<output>200</output>
<gadget id="calculator">200 * 1_000</gadget>
<output>200_000</output>
<gadget id="calculator">1_000 + 100</gadget>
<output>1_100</output>
<gadget id="calculator">1_100 + 100</gadget>
<output>1_200</output>
<gadget id="calculator">1_200 + 100</gadget>
<output>1_300</output>
<gadget id="calculator">1_300 + 100</gadget>
<output>1_400</output>
<gadget id="calculator">1_400 + 100</gadget>
<output>1_500</output>
<gadget id="calculator">1_500 + 100</gadget>
<output>1_600</output>
<gadget id="calculator">200_000 / 1_600</gadget>
<output>125</output>
<result>125</result>


the simple interest on rs . 10 for 4 months at the rate of 3 paise per rupeeper month is

Explanation: "sol . s . i . = rs . [ 10 * 3 / 100 * 4 ] = rs . 1.20 answer a"

divide(multiply(multiply(10, 4), 3), const_100)

<gadget id="calculator">10 * 4</gadget>
<output>40</output>
<gadget id="calculator">40 * 3</gadget>
<output>120</output>
<gadget id="calculator">120 / 100</gadget>
<output>6/5 = around 1.2</output>
<result>6/5 = around 1.2</result>


a bowl contains equal numbers of red , orange , green , blue , and yellow candies . kaz eats all of the green candies and half of the orange ones . next , he eats half of the remaining pieces of each color . finally , he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 25 % of the original number . what percent of the red candies remain ?

Explanation: "let x be the original number of each color . kaz eats all of the green candies and half of the orange ones . there are 0 green candies and 0.5 x orange candies remaining . he eats half of the remaining pieces of each color . there are 0.25 x orange candies , and 0.5 x each of red , yellow , and blue candies . he eats red and yellow candies in equal proportions . orange + blue + red + yellow = 0.75 x + red + yellow = 1.25 x red + yellow = 0.5 x red = 0.25 x , since red = yellow . the answer is c ."

multiply(divide(divide(subtract(25, add(divide(divide(const_100, add(const_2, const_3)), const_2), divide(divide(divide(const_100, add(const_2, const_3)), const_2), const_2))), const_2), divide(const_100, add(const_2, const_3))), const_100)

<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">100 / 5</gadget>
<output>20</output>
<gadget id="calculator">20 / 2</gadget>
<output>10</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">10 + 5</gadget>
<output>15</output>
<gadget id="calculator">25 - 15</gadget>
<output>10</output>
<gadget id="calculator">5 / 20</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<result>25</result>


if - 4 and - 8 are negative integers , then - 4 * - 8 + 2 is

Explanation: answer : c

<gadget id="calculator">-4</gadget>
<output>-4</output>
<gadget id="calculator">-8</gadget>
<output>-8</output>
<gadget id="calculator">(-4) * (-8)</gadget>
<output>32</output>
<gadget id="calculator">32 + 2</gadget>
<output>34</output>
<result>34</result>


the maximum number of students among them 1234 pens and 874 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :

Explanation: "explanation : required number of students = h . c . f of 1234 and 874 = 2 . answer : b"

<gadget id="calculator">gcd(1_234, 874)</gadget>
<output>2</output>
<result>2</result>


a boatman selling a boat along river flow . if he sell boat in steal water at 3 m / sec and flow of river is 2 m / sec . how much time he will take to sell 100 m .

Explanation: net speed = 3 + 2 = 5 m / sec distance = 100 m time = 100 / 5 = 20 sec answer d

<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">100 / 5</gadget>
<output>20</output>
<result>20</result>


a man can row his boat with the stream at 12 km / h and against the stream in 8 km / h . the man ' s rate is ?

Explanation: explanation : ds = 12 us = 8 s = ? s = ( 12 - 8 ) / 2 = 2 kmph answer : a

<gadget id="calculator">12 - 8</gadget>
<output>4</output>
<gadget id="calculator">4 / 2</gadget>
<output>2</output>
<result>2</result>


a vessel of capacity 2 litre has 25 % of alcohol and another vessel of capacity 6 litre had 30 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?

Explanation: "25 % of 2 litres = 0.5 litres 30 % of 6 litres = 1.8 litres therefore , total quantity of alcohol is 2.3 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 23 % answer : a"

multiply(divide(add(multiply(divide(25, const_100), 2), multiply(divide(30, const_100), 6)), 10), const_100)

<gadget id="calculator">25 / 100</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">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(3/10) * 6</gadget>
<output>9/5 = around 1.8</output>
<gadget id="calculator">(1/2) + (9/5)</gadget>
<output>23/10 = around 2.3</output>
<gadget id="calculator">(23/10) / 10</gadget>
<output>23/100 = around 0.23</output>
<gadget id="calculator">(23/100) * 100</gadget>
<output>23</output>
<result>23</result>


jack and jill work at a hospital with 4 other workers . for an internal review , 2 of the 6 workers will be randomly chosen to be interviewed . what is the probability that jack and jill will both be chosen ?

Explanation: "total number of ways to choose 2 out of 6 workers = 6 ! / 2 ! 4 ! = 15 number of ways to choose both jack and jill = 1 probability = 1 / 15 c should be the answer"

<gadget id="calculator">factorial(6)</gadget>
<output>720</output>
<gadget id="calculator">factorial(2)</gadget>
<output>2</output>
<gadget id="calculator">factorial(4)</gadget>
<output>24</output>
<gadget id="calculator">2 * 24</gadget>
<output>48</output>
<gadget id="calculator">720 / 48</gadget>
<output>15</output>
<gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>
<result>1/15 = around 0.066667</result>


a fashion designer sold a pair of jeans to a retail store for 40 percent more than it cost to manufacture the pair of jeans . a customer bought the pair of jeans for 35 percent more than the retailer paid for them . the price the customer paid was what percent greater than the cost of manufacturing the jeans ?

Explanation: "find the product of the two increases : ( 1.4 ) * ( 1.35 ) which is 1.89 and a 89 % increase . d"

multiply(subtract(divide(multiply(multiply(const_100, add(const_1, divide(40, const_100))), add(const_1, divide(35, const_100))), const_100), const_1), const_100)

<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">1 + (2/5)</gadget>
<output>7/5 = around 1.4</output>
<gadget id="calculator">100 * (7/5)</gadget>
<output>140</output>
<gadget id="calculator">35 / 100</gadget>
<output>7/20 = around 0.35</output>
<gadget id="calculator">1 + (7/20)</gadget>
<output>27/20 = around 1.35</output>
<gadget id="calculator">140 * (27/20)</gadget>
<output>189</output>
<gadget id="calculator">189 / 100</gadget>
<output>189/100 = around 1.89</output>
<gadget id="calculator">(189/100) - 1</gadget>
<output>89/100 = around 0.89</output>
<gadget id="calculator">(89/100) * 100</gadget>
<output>89</output>
<result>89</result>


solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 150 milliliters of solution x to create a solution that is 25 percent alcohol by volume ?

Explanation: "we know that x is 10 % , y is 30 % and w . avg = 25 % . what does this mean with respect to w . avg technique ? w . avg is 1 portion away from y and 3 portion away from x so for every 1 portion of x we will have to add 3 portions of y . if x = 150 then y = 450 answer : d"

multiply(divide(subtract(25, 10), subtract(30, 25)), 150)

<gadget id="calculator">25 - 10</gadget>
<output>15</output>
<gadget id="calculator">30 - 25</gadget>
<output>5</output>
<gadget id="calculator">15 / 5</gadget>
<output>3</output>
<gadget id="calculator">3 * 150</gadget>
<output>450</output>
<result>450</result>


a cycle is bought for rs . 750 and sold for rs . 1080 , find the gain percent ?

Explanation: "750 - - - - 180 100 - - - - ? = > 44 % answer : b"

multiply(divide(subtract(1080, 750), 750), const_100)

<gadget id="calculator">1_080 - 750</gadget>
<output>330</output>
<gadget id="calculator">330 / 750</gadget>
<output>11/25 = around 0.44</output>
<gadget id="calculator">(11/25) * 100</gadget>
<output>44</output>
<result>44</result>


the average ( arithmetic mean ) of 16 students first quiz scores in a difficult english class is 62.5 . when one student dropped the class , the average of the remaining scores increased to 65.0 . what is the quiz score of the student who dropped the class ?

Explanation: "total score of 16 students is 16 * 62.50 = 1000 total score of 15 students is 15 * 65 = 975 so , the score of the person who left is 25 ( 1000 - 975 ) answer will be ( b )"

subtract(multiply(16, 62.5), multiply(subtract(16, const_1), 65.0))

<gadget id="calculator">16 * 62.5</gadget>
<output>1_000</output>
<gadget id="calculator">16 - 1</gadget>
<output>15</output>
<gadget id="calculator">15 * 65</gadget>
<output>975</output>
<gadget id="calculator">1_000 - 975</gadget>
<output>25</output>
<result>25</result>


when positive integer x is divided by positive integer y , the remainder is 8 . if x / y = 96.12 , what is the value of y ?

Explanation: "when positive integer x is divided by positive integer y , the remainder is 8 - - > x = qy + 8 ; x / y = 96.12 - - > x = 96 y + 0.12 y ( so q above equals to 96 ) ; 0.12 y = 8 - - > y = 66.7 . answer : c ."

<gadget id="calculator">floor(96.12)</gadget>
<output>96</output>
<gadget id="calculator">96.12 - 96</gadget>
<output>0.12</output>
<gadget id="calculator">8 / 0.12</gadget>
<output>66.666667</output>
<result>66.666667</result>


a bullock cart has to cover a distance of 80 km in 10 hrs . if it covers half of the journey in 3 / 5 th time . what should be its speed to cover the remaining distance in the time left .

Explanation: a 10 kmph time left = 10 - 3 / 5 * 10 = 4 hr 10 km / h speed = 40 km / 4 hr = 10 kmph

divide(divide(80, const_2), subtract(10, multiply(divide(10, 5), 3)))

<gadget id="calculator">80 / 2</gadget>
<output>40</output>
<gadget id="calculator">10 / 5</gadget>
<output>2</output>
<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">10 - 6</gadget>
<output>4</output>
<gadget id="calculator">40 / 4</gadget>
<output>10</output>
<result>10</result>


reena took a loan of $ . 1200 with simple interest for as many years as the rate of interest . if she paid $ 300 as interest at the end of the loan period , what was the rate of interest ?

Explanation: "let rate = r % and time = r years . then , 1200 x r x r / 100 = 300 12 r 2 = 300 r 2 = 25 r = 5 . answer : a"

<gadget id="calculator">300 * 100</gadget>
<output>30_000</output>
<gadget id="calculator">30_000 / 1_200</gadget>
<output>25</output>
<gadget id="calculator">25 ** (1/2)</gadget>
<output>5</output>
<result>5</result>


darcy lives 1.5 miles from work . she can walk to work at a constant rate of 3 miles per hour , or she can ride the train to work at a constant rate of 20 miles per hour . if she rides the train , there is an additional x minutes spent walking to the nearest train station , waiting for the train , and walking from the final train station to her work . if it takes darcy a total of 20 more minutes to commute to work by walking than it takes her to commute to work by riding the train , what is the value of x ?

Explanation: "the time it takes darcy to walk to work is ( 1.5 / 3 ) * 60 = 30 minutes the time it takes darcy to take the train is ( 1.5 / 20 ) * 60 + x = 4.5 + x minutes it takes 15 minutes longer to walk , so 30 = 4.5 + x + 20 x = 5.5 minutes answer : a"

subtract(subtract(divide(const_60, const_2), 20), divide(const_60, divide(20, 1.5)))

<gadget id="calculator">60 / 2</gadget>
<output>30</output>
<gadget id="calculator">30 - 20</gadget>
<output>10</output>
<gadget id="calculator">20 / 1.5</gadget>
<output>13.333333</output>
<gadget id="calculator">60 / 13.333333</gadget>
<output>4.5</output>
<gadget id="calculator">10 - 4.5</gadget>
<output>5.5</output>
<result>5.5</result>


one ball will drop from a certain height . the height it will reach after rebounding from the floor is 50 percent of the previous height . the total travel is 150 cm when it touches the floor on third time . what is the value of the original height ?

Explanation: "when ball comes down , then i have indicated the distance covered in green when ball goes up , then i have indicated the distance covered in red distance travelled uptil the ball touches the floor 3 rd time : h + 0.5 h + 0.5 h + 0.5 * 0.5 h + 0.5 * 0.5 h h + 2 * 0.5 * h + 2 * 0.25 * h = h ( 1 + 2 * 0.5 + 2 * 0.25 ) = h ( 1 + 1 + 0.5 ) = 150 2.5 h = 150 h = 60 . a is the answer ."

divide(150, add(const_2, divide(50, const_100)))

<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">2 + (1/2)</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">150 / (5/2)</gadget>
<output>60</output>
<result>60</result>


a furniture manufacturer has two machines , but only one can be used at a time . machine w is utilized during the first shift and machine b during the second shift , while both work half of the third shift . if machine w can do the job in 12 days working two shifts and machine b can do the job in 15 days working two shifts , how many days will it take to do the job with the current work schedule ?

Explanation: ' approximately ' could actually make such a question ambiguous . not this one though but a similar question with the answer as 9.2 days . you round off 8.89 days as 9 days and everything is fine in this question . what do you do when you get 9.2 days ? do you need 9 days or 10 days ? can you round off 9.2 as 9 even though that is what you do with numbers ? no , because in 9 days your work is not over . you do need 10 days . to finish a work machine w say you need to work full 9 days and a part of the 10 th day . if i ask you how many days do you need to complete the work , will you say 9 or 10 ? you will say 10 even if you do n ' t use the 10 th day fully = d

inverse(add(inverse(divide(multiply(12, const_2), add(const_1, divide(const_1, const_2)))), inverse(divide(multiply(15, const_2), add(const_1, divide(const_1, const_2))))))

<gadget id="calculator">12 * 2</gadget>
<output>24</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 + (1/2)</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">24 / (3/2)</gadget>
<output>16</output>
<gadget id="calculator">1 / 16</gadget>
<output>1/16 = around 0.0625</output>
<gadget id="calculator">15 * 2</gadget>
<output>30</output>
<gadget id="calculator">30 / (3/2)</gadget>
<output>20</output>
<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/16) + (1/20)</gadget>
<output>9/80 = around 0.1125</output>
<gadget id="calculator">1 / (9/80)</gadget>
<output>80/9 = around 8.888889</output>
<result>80/9 = around 8.888889</result>


Explanation: "answer 469200 x 9999 = 469200 x ( 10000 - 1 ) = 4692000000 - 469200 = 4691100843 . option : e"


how many seconds will a train 100 meters long take to cross a bridge 130 meters long if the speed of the train is 36 kmph ?

Explanation: "explanation : d = 100 + 130 = 230 s = 36 * 5 / 18 = 10 mps t = 230 / 10 = 23 sec answer : option d"

<gadget id="calculator">130 + 100</gadget>
<output>230</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">36 * (5/18)</gadget>
<output>10</output>
<gadget id="calculator">230 / 10</gadget>
<output>23</output>
<result>23</result>


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

Explanation: "c age x , then b age is 2 x so a age is 2 x + 2 . ( 2 x + 2 ) + 2 x + x = 27 5 x = 25 x = 5 so b is 2 x = 2 ( 5 ) 2 x 5 = 10 answer : b"

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

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


a certain debt will be paid in 52 installments from january 1 to december 31 of a certain year . each of the first 22 payments is to be $ 410 ; each of the remaining payments is to be $ 65 more than each of the first 22 payments . what is the average ( arithmetic mean ) payment that will be made on the debt for the year ?

Explanation: total number of installments = 52 payment per installment for the first 22 installments = 410 payment per installment for the remaining 30 installments = 410 + 65 = 475 average = ( 22 * 410 + 30 * 475 ) / 52 = 447.50 answer a

divide(add(multiply(22, 410), multiply(add(410, 65), subtract(52, 22))), 52)

<gadget id="calculator">22 * 410</gadget>
<output>9_020</output>
<gadget id="calculator">410 + 65</gadget>
<output>475</output>
<gadget id="calculator">52 - 22</gadget>
<output>30</output>
<gadget id="calculator">475 * 30</gadget>
<output>14_250</output>
<gadget id="calculator">9_020 + 14_250</gadget>
<output>23_270</output>
<gadget id="calculator">23_270 / 52</gadget>
<output>895/2 = around 447.5</output>
<result>895/2 = around 447.5</result>


the ratio of numbers is 5 : 6 and their h . c . f is 4 . their l . c . m is :

Explanation: "let the numbers be 5 x and 6 x . then their h . c . f = x . so , x = 4 . so , the numbers are 20 and 24 . l . c . m of 20 and 24 = 120 . answer : e"

<gadget id="calculator">5 * 4</gadget>
<output>20</output>
<gadget id="calculator">6 * 4</gadget>
<output>24</output>
<gadget id="calculator">lcm(20, 24)</gadget>
<output>120</output>
<result>120</result>


a number when divided by a certain divisor left remainder 241 , when twice the number was divided by the same divisor , the remainder was 102 . find the divisor ?

Explanation: "easy solution : n = dq 1 + 241 2 n = 2 dq 1 + 482 - ( 1 ) 2 n = dq 2 + 102 - ( 2 ) as ( 1 ) = ( 2 ) = 2 n d * ( q 2 - 2 q 1 ) = 380 d * some integer = 380 checking all options only ( c ) syncs with it . answer c"

<gadget id="calculator">241 * 2</gadget>
<output>482</output>
<gadget id="calculator">482 - 102</gadget>
<output>380</output>
<result>380</result>


the banker â € ™ s discount of a certain sum of money is rs . 90 and the true discount on the same sum for the same time is rs . 60 . the sum due is

Explanation: "sol . sum = b . d . * t . d . / b . d . - t . d . = rs . [ 90 * 60 / 90 - 60 ] = rs . [ 90 * 60 / 30 ] = rs . 180 answer b"

divide(multiply(90, 60), subtract(90, 60))

<gadget id="calculator">90 * 60</gadget>
<output>5_400</output>
<gadget id="calculator">90 - 60</gadget>
<output>30</output>
<gadget id="calculator">5_400 / 30</gadget>
<output>180</output>
<result>180</result>