bhaman travelled for 15 hours . he covered the first half of the distance at 40 kmph and remaining half of the distance at 10 kmph . find the distance travelled by bhaman ?

Explanation: let the distance travelled be x km . total time = ( x / 2 ) / 40 + ( x / 2 ) / 10 = 15 = > x / 80 + x / 20 = 15 = > ( x + 4 x ) / 80 = 15 = > x = 240 km answer : a

multiply(divide(15, add(divide(multiply(const_2, 40), const_10), divide(multiply(const_2, 10), const_10))), multiply(multiply(divide(multiply(const_2, 40), const_10), divide(multiply(const_2, 10), const_10)), const_10))

<gadget id="calculator">2 * 40</gadget>
<output>80</output>
<gadget id="calculator">80 / 10</gadget>
<output>8</output>
<gadget id="calculator">2 * 10</gadget>
<output>20</output>
<gadget id="calculator">20 / 10</gadget>
<output>2</output>
<gadget id="calculator">8 + 2</gadget>
<output>10</output>
<gadget id="calculator">15 / 10</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">8 * 2</gadget>
<output>16</output>
<gadget id="calculator">16 * 10</gadget>
<output>160</output>
<gadget id="calculator">(3/2) * 160</gadget>
<output>240</output>
<result>240</result>


in a survey of parents , exactly 7 / 8 of the mothers and 3 / 4 of the fathers held full - time jobs . if 40 percent of the parents surveyed were women , what percent of the parents did not hold full - time jobs ?

Explanation: fathers without full - time jobs are 1 / 4 * 3 / 5 = 3 / 20 of all the parents surveyed . mothers without full - time jobs are 1 / 8 * 2 / 5 = 1 / 20 of all the parents surveyed . the percent of parents without full - time jobs is 3 / 20 + 1 / 20 = 1 / 5 = 20 % the answer is a .

add(subtract(subtract(const_100, 40), multiply(divide(3, 4), subtract(const_100, 40))), subtract(40, multiply(divide(7, 8), 40)))

<gadget id="calculator">100 - 40</gadget>
<output>60</output>
<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(3/4) * 60</gadget>
<output>45</output>
<gadget id="calculator">60 - 45</gadget>
<output>15</output>
<gadget id="calculator">7 / 8</gadget>
<output>7/8 = around 0.875</output>
<gadget id="calculator">(7/8) * 40</gadget>
<output>35</output>
<gadget id="calculator">40 - 35</gadget>
<output>5</output>
<gadget id="calculator">15 + 5</gadget>
<output>20</output>
<result>20</result>


three pipes of same capacity can fill a tank in 8 hours . if there are only two pipes of same capacity , the tank can be filled in .

Explanation: the part of the tank filled by three pipes in one hour = 1 / 8 = > the part of the tank filled by two pipes in 1 hour = 2 / 3 * 1 / 8 = 1 / 12 . the tank can be filled in 12 hours . answer : b

inverse(multiply(divide(const_2, const_3), divide(const_1, 8)))

<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">(2/3) * (1/8)</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">1 / (1/12)</gadget>
<output>12</output>
<result>12</result>


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

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

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

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


a grocer has a sale of rs . 6435 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ?

Explanation: "let the sale in the sixth month = x then ( 6435 + 6927 + 6855 + 7230 + 6562 + x ) / 6 = 6500 = > 6435 + 6927 + 6855 + 7230 + 6562 + x = 6 × 6500 = > 34009 + x = 39000 = > x = 39000 − 34009 = 4991 answer is c ."

<gadget id="calculator">5 + 1</gadget>
<output>6</output>
<gadget id="calculator">6 * 6_500</gadget>
<output>39_000</output>
<gadget id="calculator">6_435 + 6_927</gadget>
<output>13_362</output>
<gadget id="calculator">13_362 + 6_855</gadget>
<output>20_217</output>
<gadget id="calculator">20_217 + 7_230</gadget>
<output>27_447</output>
<gadget id="calculator">27_447 + 6_562</gadget>
<output>34_009</output>
<gadget id="calculator">39_000 - 34_009</gadget>
<output>4_991</output>
<result>4_991</result>


calculate the number of bricks , each measuring 25 cm x 15 cm x 8 cm required to construct a wall of dimensions 10 m x 4 cm x 6 m when 10 % of its volume is occupied by mortar ?

Explanation: explanation : let the number of bricks be ' n ' 10 x 4 / 100 x 6 x 90 / 100 = 25 / 100 x 15 / 100 x 8 / 100 x n 10 x 4 x 6 x 90 = 15 x 2 x n = > n = 720 . answer is a

divide(multiply(multiply(multiply(10, divide(4, const_100)), 6), subtract(const_1, divide(10, const_100))), multiply(multiply(divide(25, const_100), divide(15, const_100)), divide(8, const_100)))

<gadget id="calculator">4 / 100</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">10 * (1/25)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) * 6</gadget>
<output>12/5 = around 2.4</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 - (1/10)</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">(12/5) * (9/10)</gadget>
<output>54/25 = around 2.16</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">(1/4) * (3/20)</gadget>
<output>3/80 = around 0.0375</output>
<gadget id="calculator">8 / 100</gadget>
<output>2/25 = around 0.08</output>
<gadget id="calculator">(3/80) * (2/25)</gadget>
<output>3/1_000 = around 0.003</output>
<gadget id="calculator">(54/25) / (3/1_000)</gadget>
<output>720</output>
<result>720</result>


the lcm and hcf of two numbers are 8 and 48 respectively . if one of them is 24 , find the other ?

Explanation: hcf x lcm = product of numbers 8 x 48 = 24 x the other number other number = ( 8 x 48 ) / 24 other number = 16 answer : d

<gadget id="calculator">8 * 48</gadget>
<output>384</output>
<gadget id="calculator">384 / 24</gadget>
<output>16</output>
<result>16</result>


one night a certain hotel rented 3 / 5 of its rooms , including 2 / 3 of their air conditioned rooms . if 3 / 5 of its rooms were air conditioned , what percent of the rooms that were not rented were air conditioned ?

Explanation: the rooms which were not rented is 2 / 5 the ac rooms which were not rented is ( 1 / 3 ) * ( 3 / 5 ) = 1 / 5 the percentage of unrented rooms which were ac rooms is ( 1 / 5 ) / ( 2 / 5 ) = 1 / 2 = 50 % the answer is a .

multiply(divide(multiply(subtract(const_1, divide(2, 3)), multiply(divide(3, 5), const_100)), subtract(const_100, multiply(divide(3, 5), const_100))), const_100)

<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">1 - (2/3)</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(3/5) * 100</gadget>
<output>60</output>
<gadget id="calculator">(1/3) * 60</gadget>
<output>20</output>
<gadget id="calculator">100 - 60</gadget>
<output>40</output>
<gadget id="calculator">20 / 40</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * 100</gadget>
<output>50</output>
<result>50</result>


in what time will a train 180 m long cross an electric pole , it its speed be 144 km / hr ?

Explanation: "speed = 144 * 5 / 18 = 40 m / sec time taken = 180 / 40 = 4.5 sec . answer : d"

<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">180 / 40</gadget>
<output>9/2 = around 4.5</output>
<result>9/2 = around 4.5</result>


the average monthly salary of 25 employees in an organisation is rs . 2500 . if the manager ' s salary is added , then the average salary increases by rs . 200 . what is the manager ' s monthly salary ?

Explanation: "manager ' s monthly salary = rs . ( 2700 * 26 - 2500 * 25 ) = rs . 7700 answer : a"

subtract(multiply(add(2500, 200), add(25, const_1)), multiply(2500, 25))

<gadget id="calculator">2_500 + 200</gadget>
<output>2_700</output>
<gadget id="calculator">25 + 1</gadget>
<output>26</output>
<gadget id="calculator">2_700 * 26</gadget>
<output>70_200</output>
<gadget id="calculator">2_500 * 25</gadget>
<output>62_500</output>
<gadget id="calculator">70_200 - 62_500</gadget>
<output>7_700</output>
<result>7_700</result>


we had $ 1400 left after spending 30 % of the money that we took for shopping . how much money did we start with ?

Explanation: "let x be the amount of money we started with . 0.7 x = 1400 x = 2000 the answer is a ."

divide(1400, subtract(const_1, divide(30, const_100)))

<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">1 - (3/10)</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">1_400 / (7/10)</gadget>
<output>2_000</output>
<result>2_000</result>


each of the cucumbers in 100 pounds of cucumbers is composed of 99 % water , by weight . after some of the water evaporates , the cucumbers are now 94 % water by weight . what is the new weight of the cucumbers , in pounds ?

Explanation: "out of 100 pounds 99 % or 99 pounds is water and 1 pound is non - water . after somewaterevaporates the cucumbers become 94 % water and 6 % of non - water , so now 1 pound of non - water composes 6 % of cucucmbers , which means that the new weight of cucumbers is 1 / 0.06 = 16 pounds . answer : b ."

multiply(divide(subtract(100, 99), subtract(100, 94)), 100)

<gadget id="calculator">100 - 99</gadget>
<output>1</output>
<gadget id="calculator">100 - 94</gadget>
<output>6</output>
<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/6) * 100</gadget>
<output>50/3 = around 16.666667</output>
<result>50/3 = around 16.666667</result>


in a party every person shakes hands with every other person . if there are 105 hands shakes , find the number of person in the party .

Explanation: "let n be the number of persons in the party . number of hands shake = 105 ; total number of hands shake is given by nc 2 . now , according to the question , nc 2 = 105 ; or , n ! / [ 2 ! * ( n - 2 ) ! ] = 105 ; or , n * ( n - 1 ) / 2 = 105 ; or , n 2 - n = 210 ; or , n 2 - n - 210 = 0 ; or , n = 15 , - 14 ; but , we can not take negative value of n . so , n = 15 i . e . number of persons in the party = 15 . option d"

divide(add(sqrt(add(multiply(multiply(105, const_2), const_4), const_1)), const_1), const_2)

<gadget id="calculator">105 * 2</gadget>
<output>210</output>
<gadget id="calculator">210 * 4</gadget>
<output>840</output>
<gadget id="calculator">840 + 1</gadget>
<output>841</output>
<gadget id="calculator">841 ** (1/2)</gadget>
<output>29</output>
<gadget id="calculator">29 + 1</gadget>
<output>30</output>
<gadget id="calculator">30 / 2</gadget>
<output>15</output>
<result>15</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 5 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 + 5 x = 20.5 minutes answer : a"

subtract(subtract(divide(const_60, const_2), 5), divide(const_60, divide(20, 1.5)))

<gadget id="calculator">60 / 2</gadget>
<output>30</output>
<gadget id="calculator">30 - 5</gadget>
<output>25</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">25 - 4.5</gadget>
<output>20.5</output>
<result>20.5</result>


a lawn is in the form of a rectangle having its sides in the ratio 2 : 3 . the area of the lawn is ( 1 / 6 ) hectares . find the length and breadth of the lawn .

Explanation: let length = 2 x meters and breadth = 3 x meter . now , area = ( 1 / 6 ) x 1000 m 2 = 5000 / 3 m 2 so , 2 x * 3 x = 5000 / 3 < = > x 2 = 2500 / 9 < = > x = 50 / 3 therefore length = 2 x = ( 100 / 3 ) m = 33 ( 1 / 3 ) m and breadth = 3 x = 3 ( 50 / 3 ) m = 50 m . answer is a

divide(multiply(divide(multiply(const_10, const_1000), 6), 3), const_100)

<gadget id="calculator">10 * 1_000</gadget>
<output>10_000</output>
<gadget id="calculator">10_000 / 6</gadget>
<output>5_000/3 = around 1_666.666667</output>
<gadget id="calculator">(5_000/3) * 3</gadget>
<output>5_000</output>
<gadget id="calculator">5_000 / 100</gadget>
<output>50</output>
<result>50</result>


12 men work 8 hours per day to complete the work in 10 days . to complete the same work in 8 days , working 10 hours a day , the number of men required ?

Explanation: "that is , 1 work done = 12 × 8 × 10 then , 12 8 × 10 = ? × 10 × 8 ? ( i . e . no . of men required ) = 12 × 8 × 10 / 10 × 8 = 12 days b )"

divide(multiply(multiply(12, 10), 8), multiply(8, 10))

<gadget id="calculator">12 * 10</gadget>
<output>120</output>
<gadget id="calculator">120 * 8</gadget>
<output>960</output>
<gadget id="calculator">8 * 10</gadget>
<output>80</output>
<gadget id="calculator">960 / 80</gadget>
<output>12</output>
<result>12</result>


there are 240 doctors and nurses at a hospital . if the ratio of doctors to nurses is 3 to 7 , how many nurses are at the hospital ?

Explanation: "the number of nurses at the hospital is ( 7 / 10 ) * 240 = 168 . the answer is a ."

<gadget id="calculator">3 + 7</gadget>
<output>10</output>
<gadget id="calculator">240 / 10</gadget>
<output>24</output>
<gadget id="calculator">24 * 7</gadget>
<output>168</output>
<result>168</result>


what annual payment will discharge a debt of rs . 1125 due in 2 years at the rate of 5 % compound interest ?

Explanation: "explanation : let each installment be rs . x . then , x / ( 1 + 5 / 100 ) + x / ( 1 + 5 / 100 ) 2 = 1125 820 x + 1125 * 441 x = 605.03 so , value of each installment = rs . 605.03 answer : option d"

divide(multiply(power(add(divide(5, const_100), const_1), 2), 1125), 2)

<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/20) + 1</gadget>
<output>21/20 = around 1.05</output>
<gadget id="calculator">(21/20) ** 2</gadget>
<output>441/400 = around 1.1025</output>
<gadget id="calculator">(441/400) * 1_125</gadget>
<output>19_845/16 = around 1_240.3125</output>
<gadget id="calculator">(19_845/16) / 2</gadget>
<output>19_845/32 = around 620.15625</output>
<result>19_845/32 = around 620.15625</result>


if x ¤ y = ( x + y ) ^ 2 - ( x - y ) ^ 2 . then √ 2 ¤ √ 2 =

Explanation: "x = √ 2 and y also = √ 2 applying the function ( √ 2 + √ 2 ) ^ 2 - ( √ 2 - √ 2 ) ^ 2 = ( 2 √ 2 ) ^ 2 - 0 = 4 x 2 = 8 . note : alternative approach is the entire function is represented as x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) which can be simplified as ( x + y + x - y ) ( x + y - ( x - y ) ) = ( 2 x ) ( 2 y ) = 4 xy . substituting x = √ 2 and y = √ 2 you get the answer 8 . answer b"

<gadget id="calculator">2 ** (1/2)</gadget>
<output>sqrt(2) = around 1.414214</output>
<gadget id="calculator">(sqrt(2)) + (sqrt(2))</gadget>
<output>2*sqrt(2) = around 2.828427</output>
<gadget id="calculator">(2*sqrt(2)) ** 2</gadget>
<output>8</output>
<result>8</result>


jamshid can paint a fence in 50 percent less time than taimour can when each works alone . when they work together , they can paint the fence in 4 hours . how long would it take taimour to paint the fence alone ?

Explanation: i believe the answer is c . please see below for explanation . if jamshid can paint a dence in 50 percent less time then taimour we can infer the following rate j = 2 t if working together they can do the job in 8 hours we can infer 1 = 2 t + t * 4 = > 1 / 12 working alone taimour can do the job in 1 = 1 / 12 * hours = > 12 answer c

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


Explanation: "answer let √ n / 20 = 4 then √ n = 20 x 4 = 80 ∴ n = 80 x 80 = 6400 . correct option : b"

<gadget id="calculator">4 * 20</gadget>
<output>80</output>
<gadget id="calculator">80 ** 2</gadget>
<output>6_400</output>
<result>6_400</result>


the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 45 kmph , find the speed of the stream ?

Explanation: "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 45 / 3 = 15 kmph answer : d"

subtract(45, divide(multiply(45, const_2), const_3))

<gadget id="calculator">45 * 2</gadget>
<output>90</output>
<gadget id="calculator">90 / 3</gadget>
<output>30</output>
<gadget id="calculator">45 - 30</gadget>
<output>15</output>
<result>15</result>


a box contains 14 pairs of shoes ( 28 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 28 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 / 27 ( as after taking one at random there are 27 shoes left and only one is the pair of the first one ) = 1 / 27 answer : d"

<gadget id="calculator">28 - 1</gadget>
<output>27</output>
<gadget id="calculator">1 / 27</gadget>
<output>1/27 = around 0.037037</output>
<result>1/27 = around 0.037037</result>


there are 1000 students in a school and among them 10 % of them attends chess class . 10 % of the students who are in the chess class are also enrolled for swimming . no other students are interested in swimming so how many will attend the swimming class if all enrolled attends ?

Explanation: "10 % of 1000 gives 100 . so 100 attends chess and 10 % of 100 gives 10 . so 10 enrolled for swimming answer : b"

divide(multiply(divide(multiply(10, 1000), const_100), 10), const_100)

<gadget id="calculator">10 * 1_000</gadget>
<output>10_000</output>
<gadget id="calculator">10_000 / 100</gadget>
<output>100</output>
<gadget id="calculator">100 * 10</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 / 100</gadget>
<output>10</output>
<result>10</result>


a furniture dealer purchased a desk for $ 150 and then set the selling price equal to the purchase price plus a markup that was 20 % of the selling price . if the dealer sold the desk at the selling price , what was the amount of the dealer ' s gross profit from the purchase and the sale of the desk ?

Explanation: anyway , in this question , there is no discount but the mark up is given as 40 % of the selling price . so it is not 20 % of $ 150 but instead , 20 % of selling price which is obtained by adding mark up to $ 150 . so if selling price is s , 150 + 20 % of s = s s = 150 / 0.8 profit = 150 / 0.8 - 150 = which is calculated on cost price in % terms . so 37.5 / 150 * 100 = 25 % is profit . e

divide(multiply(subtract(divide(150, subtract(const_1, divide(20, const_100))), 150), const_100), 150)

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">150 / (4/5)</gadget>
<output>375/2 = around 187.5</output>
<gadget id="calculator">(375/2) - 150</gadget>
<output>75/2 = around 37.5</output>
<gadget id="calculator">(75/2) * 100</gadget>
<output>3_750</output>
<gadget id="calculator">3_750 / 150</gadget>
<output>25</output>
<result>25</result>


a and b start walking towards each other at 4 pm at speed of 2 kmph and 3 kmph . they were initially 15 km apart . at what time do they meet ?

Explanation: time of meeting = distance / relative speed = 15 / 3 + 2 = 15 / 5 = 3 hrs after 4 pm = 7 pm answer is c

<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">15 / 5</gadget>
<output>3</output>
<gadget id="calculator">4 + 3</gadget>
<output>7</output>
<result>7</result>


in a certain parallelogram the degree measure of one angle exceeds that of the other by 20 what is the degree measure of the smaller angle ?

Explanation: "in a parallelogram opposite angles are equal and the angles at each side are supplementary to each other ( supplementary angles are two angles that add up to 180 ° ) . given : x + ( x + 20 ) = 180 - - > x = 80 . answer : b ."

divide(subtract(divide(const_3600, const_10), multiply(20, const_2)), const_4)

<gadget id="calculator">3_600 / 10</gadget>
<output>360</output>
<gadget id="calculator">20 * 2</gadget>
<output>40</output>
<gadget id="calculator">360 - 40</gadget>
<output>320</output>
<gadget id="calculator">320 / 4</gadget>
<output>80</output>
<result>80</result>


3 years ago , the average age of a , b and c was 27 years and that of b and c 5 years ago was 20 years . a ’ s present age is :

Explanation: explanation : sum of the present ages of a , b and c = ( 27 × 3 + 3 × 3 ) years = 90 years . sum of the present ages of b and c = ( 20 × 2 + 5 × 2 ) years = 50 years . a ' s present age = 90 – 50 = 40 years . answer : c

subtract(add(multiply(27, 3), multiply(3, 3)), add(multiply(20, const_2), multiply(5, const_2)))

<gadget id="calculator">27 * 3</gadget>
<output>81</output>
<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">81 + 9</gadget>
<output>90</output>
<gadget id="calculator">20 * 2</gadget>
<output>40</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">40 + 10</gadget>
<output>50</output>
<gadget id="calculator">90 - 50</gadget>
<output>40</output>
<result>40</result>


if the perimeter of a rectangular garden is 600 m , its length when its breadth is 120 m is ?

Explanation: "2 ( l + 120 ) = 600 = > l = 180 m answer : b"

<gadget id="calculator">600 / 2</gadget>
<output>300</output>
<gadget id="calculator">300 - 120</gadget>
<output>180</output>
<result>180</result>


the average of 5 consecutive even numbers a , b , c , d and e is 20 . what percent of e is d ?

Explanation: explanation : in such a case the middle number ( c ) is the average ∴ c = 20 and d = 22 and e = 24 required percentage = 22 / 24 x 100 = 91.7 answer : option b

multiply(divide(add(add(add(subtract(20, divide(add(add(add(const_2, multiply(const_2, const_2)), multiply(const_2, const_3)), multiply(const_2, const_4)), 5)), const_2), const_2), const_2), add(add(add(add(subtract(20, divide(add(add(add(const_2, multiply(const_2, const_2)), multiply(const_2, const_3)), multiply(const_2, const_4)), 5)), const_2), const_2), const_2), const_2)), const_100)

<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">2 + 4</gadget>
<output>6</output>
<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">6 + 6</gadget>
<output>12</output>
<gadget id="calculator">2 * 4</gadget>
<output>8</output>
<gadget id="calculator">12 + 8</gadget>
<output>20</output>
<gadget id="calculator">20 / 5</gadget>
<output>4</output>
<gadget id="calculator">20 - 4</gadget>
<output>16</output>
<gadget id="calculator">16 + 2</gadget>
<output>18</output>
<gadget id="calculator">18 + 2</gadget>
<output>20</output>
<gadget id="calculator">20 + 2</gadget>
<output>22</output>
<gadget id="calculator">22 + 2</gadget>
<output>24</output>
<gadget id="calculator">22 / 24</gadget>
<output>11/12 = around 0.916667</output>
<gadget id="calculator">(11/12) * 100</gadget>
<output>275/3 = around 91.666667</output>
<result>275/3 = around 91.666667</result>


the length of rectangle is thrice its breadth and its perimeter is 72 m , find the area of the rectangle ?

Explanation: "2 ( 3 x + x ) = 72 l = 27 b = 9 lb = 27 * 9 = 243 answer : c"

multiply(multiply(divide(72, add(multiply(const_3, const_2), multiply(const_1, const_2))), const_3), divide(72, add(multiply(const_3, const_2), multiply(const_1, const_2))))

<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">1 * 2</gadget>
<output>2</output>
<gadget id="calculator">6 + 2</gadget>
<output>8</output>
<gadget id="calculator">72 / 8</gadget>
<output>9</output>
<gadget id="calculator">9 * 3</gadget>
<output>27</output>
<gadget id="calculator">27 * 9</gadget>
<output>243</output>
<result>243</result>


there are 5 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair . what is the number of pair that can be formed .

Explanation: "first of all you should remember that there is a difference in left and right sock . now no . of way to select any of the sock = 5 and for second = 4 so total methods = 5 * 4 = 20 answer : b"

<gadget id="calculator">binomial(5, 2)</gadget>
<output>10</output>
<gadget id="calculator">10 + 10</gadget>
<output>20</output>
<result>20</result>


if m is a positive integer and m ^ 2 is divisible by 36 , then the largest positive integer that must divide m is ?

Explanation: "m ^ 2 is divisible by 48 so m ^ 2 must be multiple of 48 . if the value of m is multiples of 12 then it will satisfy the condition . if we if m is 12 or 24 or 36 then it ans is d but if m = 48 then answer should be 16 . is the question right ? or am i missing some thing ? d"

multiply(const_3, divide(divide(36, const_3), const_3))

<gadget id="calculator">36 / 3</gadget>
<output>12</output>
<gadget id="calculator">12 / 3</gadget>
<output>4</output>
<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<result>12</result>


on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.60 per glass on the first day , what was the price per f glass on the second day ?

Explanation: "on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.6 = 3 * x - - > x = $ 0.4 . answer : d ."

divide(multiply(add(const_1, const_1), 0.60), add(const_1, const_2))

<gadget id="calculator">1 + 1</gadget>
<output>2</output>
<gadget id="calculator">2 * 0.6</gadget>
<output>1.2</output>
<gadget id="calculator">1 + 2</gadget>
<output>3</output>
<gadget id="calculator">1.2 / 3</gadget>
<output>0.4</output>
<result>0.4</result>


in what time will a train 110 m long cross an electric pole , it its speed be 128 km / hr ?

Explanation: "speed = 128 * 5 / 18 = 36 m / sec time taken = 110 / 36 = 3.1 sec . answer : c"

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">128 * (5/18)</gadget>
<output>320/9 = around 35.555556</output>
<gadget id="calculator">110 / (320/9)</gadget>
<output>99/32 = around 3.09375</output>
<result>99/32 = around 3.09375</result>


two trains 160 m and 160 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?

Explanation: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 160 + 160 = 320 m . required time = 320 * 9 / 250 = 288 / 25 = 11.52 sec . answer : e"

<gadget id="calculator">160 + 160</gadget>
<output>320</output>
<gadget id="calculator">60 + 40</gadget>
<output>100</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">100 * (5/18)</gadget>
<output>250/9 = around 27.777778</output>
<gadget id="calculator">320 / (250/9)</gadget>
<output>288/25 = around 11.52</output>
<result>288/25 = around 11.52</result>


two trains 200 m and 150 m long are running on parallel rails at the rate of 40 kmph and 48 kmph respectively . in how much time will they cross each other , if they are running in the same direction ?

Explanation: "solution relative speed = ( 48 - 40 ) kmph = 8 kmph = ( 8 x 5 / 18 ) m / sec = ( 40 / 18 ) m / sec time taken = ( 350 x 18 / 40 ) sec = 157.5 sec . answer c"

multiply(const_3600, divide(divide(add(200, 150), const_1000), subtract(48, 40)))

<gadget id="calculator">200 + 150</gadget>
<output>350</output>
<gadget id="calculator">350 / 1_000</gadget>
<output>7/20 = around 0.35</output>
<gadget id="calculator">48 - 40</gadget>
<output>8</output>
<gadget id="calculator">(7/20) / 8</gadget>
<output>7/160 = around 0.04375</output>
<gadget id="calculator">3_600 * (7/160)</gadget>
<output>315/2 = around 157.5</output>
<result>315/2 = around 157.5</result>


a trader cheats both his supplier and customer by using faulty weights . when he buys from the supplier , he takes 10 % more than the indicated weight . when he sells to his customer , he gives the customer a weight such that 10 % of that is added to the weight , the weight claimed by the trader is obtained . if he charges the cost price of the weight that he claims , find his profit percentage .

Explanation: "lets say the indicated weight is x for $ 10 but the trader actually get 1.1 x for $ 10 now he tells to the customer that its 1.1 ( 1.1 x ) = 1.21 x and charges the price accordingly i . e . 1.21 x * 10 / x = 12.1 so profit % = ( 12.1 - 10 ) / 10 = 0.21 = 21 % answer : b"

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

<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">(11/10) * 110</gadget>
<output>121</output>
<gadget id="calculator">121 - 100</gadget>
<output>21</output>
<result>21</result>


if the wheel is 14 cm then the number of revolutions to cover a distance of 2288 cm is ?

Explanation: "2 * 22 / 7 * 14 * x = 2288 = > x = 26 answer : a"

divide(2288, multiply(multiply(const_2, divide(add(add(multiply(const_3, const_100), multiply(const_1, const_10)), const_4), const_100)), 14))

<gadget id="calculator">3 * 100</gadget>
<output>300</output>
<gadget id="calculator">1 * 10</gadget>
<output>10</output>
<gadget id="calculator">300 + 10</gadget>
<output>310</output>
<gadget id="calculator">310 + 4</gadget>
<output>314</output>
<gadget id="calculator">314 / 100</gadget>
<output>157/50 = around 3.14</output>
<gadget id="calculator">2 * (157/50)</gadget>
<output>157/25 = around 6.28</output>
<gadget id="calculator">(157/25) * 14</gadget>
<output>2_198/25 = around 87.92</output>
<gadget id="calculator">2_288 / (2_198/25)</gadget>
<output>28_600/1_099 = around 26.023658</output>
<result>28_600/1_099 = around 26.023658</result>


in the seaside summer camp there are 50 children . 90 % of the children are boys and the rest are girls . the camp administrator decided to make the number of girls only 5 % of the total number of children in the camp . how many more boys must she bring to make that happen ?

Explanation: given there are 50 students in the seaside summer camp , 90 % of 50 = 45 boys and remaining 5 girls . now here 90 % are boys and 10 % are girls . now question is asking about how many boys do we need to add , to make the girls percentage to 5 or 5 % . . if we add 50 to existing 45 then the count will be 95 and the girls number will be 5 as it . now boys are 95 % and girls are 5 % . ( out of 100 students = 95 boys + 5 girls ) . imo option a is correct .

subtract(divide(multiply(subtract(50, divide(multiply(90, 50), const_100)), const_100), 5), 50)

<gadget id="calculator">90 * 50</gadget>
<output>4_500</output>
<gadget id="calculator">4_500 / 100</gadget>
<output>45</output>
<gadget id="calculator">50 - 45</gadget>
<output>5</output>
<gadget id="calculator">5 * 100</gadget>
<output>500</output>
<gadget id="calculator">500 / 5</gadget>
<output>100</output>
<gadget id="calculator">100 - 50</gadget>
<output>50</output>
<result>50</result>


the average price of 3 items of furniture is rs . 15000 . if their prices are in the ratio 2 : 4 : 8 , the price of the cheapest item is ?

Explanation: let their prices be 3 x , 5 x and 7 x . then , 2 x + 6 x + 8 x = ( 15000 * 3 ) or x = 2812.5 . cost of cheapest item = 2 x = rs . 5625 . answer : c

<gadget id="calculator">3 * 15_000</gadget>
<output>45_000</output>
<gadget id="calculator">45_000 / 8</gadget>
<output>5_625</output>
<result>5_625</result>


in a group of 15 people , 8 read english , 7 read french while 3 of them read none of these two . how many of them read french and english both ?

Explanation: in the following venn diagram , f and e represent people who read french and english respectively . now , [ f + ( { f ∩ e } ) + e ] = 15 - 3 ( or ) f + e + ( f ∩ e ) = 12 . . . . . . ( 1 ) also , f + ( f ∩ e ) = 7 ; e + ( f ∩ e ) = 8 . by adding , f + e + 2 ( f ∩ e ) = 15 - - - - - - - - - - ( 2 ) by subtracting ( 1 ) from ( 2 ) , we get ( f ∩ e ) = 3 . ∴ 3 of them read both french and english . answer : b

<gadget id="calculator">8 + 7</gadget>
<output>15</output>
<gadget id="calculator">15 - 3</gadget>
<output>12</output>
<gadget id="calculator">15 - 12</gadget>
<output>3</output>
<result>3</result>


if a person walks at 14 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance traveled by him is ?

Explanation: "let the actual distance traveled be x km . then , x / 10 = ( x + 20 ) / 14 4 x - 200 = > x = 50 km . answer : a"

multiply(10, divide(20, subtract(14, 10)))

<gadget id="calculator">14 - 10</gadget>
<output>4</output>
<gadget id="calculator">20 / 4</gadget>
<output>5</output>
<gadget id="calculator">10 * 5</gadget>
<output>50</output>
<result>50</result>


Explanation: "sum of 1 st n odd no . s = 1 + 3 + 5 + 7 + . . . = n ^ 2 so , sum of 1 st 36 odd numbers = 36 ^ 2 = 1296 answer : c"

multiply(multiply(36, const_2), divide(36, const_2))

<gadget id="calculator">36 * 2</gadget>
<output>72</output>
<gadget id="calculator">36 / 2</gadget>
<output>18</output>
<gadget id="calculator">72 * 18</gadget>
<output>1_296</output>
<result>1_296</result>


15 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ?

Explanation: "though 2 * ( 15 c 2 ) is the correct approcah to do this , but for people like me who find perm , comb n prob a nightmare , an easy approach can be used . the first guy has to play 2 matches with the rest of 14 , so he ' ll play 28 matches . similarly , second guy has to play with the rest of 13 as his 2 games with the first guy are already played . so he plays 26 matches . this continues like this and the total matches are 28 + 26 + 24 . . . + 2 28 + 26 + . . . + 2 = 2 ( 14 + 13 + . . . + 1 ) = 2 ( ( 14 * 15 ) / 2 ) = 14 * 15 = 210 . answer : c"

<gadget id="calculator">15 - 1</gadget>
<output>14</output>
<gadget id="calculator">15 * 14</gadget>
<output>210</output>
<result>210</result>


the height of the wall is 6 times its width and length of the wall is 8 times its height . if the volume of the wall be 36000 cu . m . its width is

Explanation: "explanation : let width = x then , height = 6 x and length = 48 x 48 x ã — 6 x ã — x = 36000 x = 5 answer : b"

power(divide(36000, multiply(multiply(6, 8), 6)), divide(const_1, const_3))

<gadget id="calculator">6 * 8</gadget>
<output>48</output>
<gadget id="calculator">48 * 6</gadget>
<output>288</output>
<gadget id="calculator">36_000 / 288</gadget>
<output>125</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">125 ** (1/3)</gadget>
<output>5</output>
<result>5</result>


one - third of 600 is what percent of 120 ?

Explanation: answer let one - third of 600 is n % of 120 . ∵ 600 / 3 = ( n x 120 ) / 100 ∴ n = ( 200 x 100 ) / 120 = 166.6 correct option : e

multiply(const_100, divide(divide(600, const_3), 120))

<gadget id="calculator">600 / 3</gadget>
<output>200</output>
<gadget id="calculator">200 / 120</gadget>
<output>5/3 = around 1.666667</output>
<gadget id="calculator">100 * (5/3)</gadget>
<output>500/3 = around 166.666667</output>
<result>500/3 = around 166.666667</result>


how many diagonals does a 58 - sided convex polygon have ?

Explanation: "a 58 - sided convex polygon has 58 vertices . if we examine a single vertex , we can see that we can connect it with 55 other vertices to create a diagonal . note that we ca n ' t connect the vertex to itself and we ca n ' t connect it to its adjacent vertices , since this would not create a diagonal . if each of the 58 vertices can be connected with 55 vertices to create a diagonal then the total number of diagonals would be ( 58 ) ( 55 ) = 3190 however , we must recognize that we have counted every diagonal twice . to account for counting each diagonal twice , we must divide 3190 by 2 to get 1595 . the answer is c ."

divide(factorial(58), multiply(factorial(subtract(58, const_2)), factorial(const_2)))


a side of beef lost 35 percent of its weight in processing . if the side of beef weighed 545 pounds after processing , how many pounds did it weigh before processing ?

Explanation: let weight of side of beef before processing = x ( 65 / 100 ) * x = 545 = > x = ( 545 * 100 ) / 65 = 838 answer d

divide(multiply(545, const_100), subtract(const_100, 35))

<gadget id="calculator">545 * 100</gadget>
<output>54_500</output>
<gadget id="calculator">100 - 35</gadget>
<output>65</output>
<gadget id="calculator">54_500 / 65</gadget>
<output>10_900/13 = around 838.461538</output>
<result>10_900/13 = around 838.461538</result>


miller street begins at baker street and runs directly east for 4.5 kilometers until it ends when it meets turner street . miller street is intersected every 250 meters by a perpendicular street , and each of those streets other than baker street and turner street is given a number beginning at 1 st street ( one block east of baker street ) and continuing consecutively ( 2 nd street , 3 rd street , etc . . . ) until the highest - numbered street one block west of turner street . what is the highest - numbered street that intersects miller street ?

Explanation: 4.5 km / 250 m = 18 . however , the street at the 4.5 - km mark is not 18 th street ; it is turner street . therefore , the highest numbered street is 17 th street . the answer is c .

subtract(divide(4.5, divide(250, const_1000)), 1)

<gadget id="calculator">250 / 1_000</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">4.5 / (1/4)</gadget>
<output>18</output>
<gadget id="calculator">18 - 1</gadget>
<output>17</output>
<result>17</result>


the pressure someone experiences as he or she dives deeper and deeper in the ocean increases linearly . on the surface , the pressure is close to 15 pounds per square inch . 33 feet below the surface , the pressure is 30 pounds . if 25000 pounds per sq inch can crush your bones , what depth is extremely dangerous for humans ?

Explanation: solution : first , model the pressure ( p ) in terms of depth ( d ) with a linear equation . we will find the equation p = md + b use ( 0 , 15 ) and ( 33 , 30 ) to find m m = 30 - 15 / 33 - 0 m = 15 / 33 = 0.45 p = 0.45 d + b use ( 0 , 15 ) to find b 15 = 0.45 × 0 + b 15 = b p = 0.45 d + 15 25000 = 0.45 d + 15 25000 - 15 = 0.45 d + 15 - 15 24985 = 0.45 d d = 24985 / 0.45 = 55522 feet answer a

divide(divide(subtract(25000, 15), divide(subtract(30, 15), multiply(33, multiply(const_4, const_3)))), multiply(const_4, const_3))

<gadget id="calculator">25_000 - 15</gadget>
<output>24_985</output>
<gadget id="calculator">30 - 15</gadget>
<output>15</output>
<gadget id="calculator">4 * 3</gadget>
<output>12</output>
<gadget id="calculator">33 * 12</gadget>
<output>396</output>
<gadget id="calculator">15 / 396</gadget>
<output>5/132 = around 0.037879</output>
<gadget id="calculator">24_985 / (5/132)</gadget>
<output>659_604</output>
<gadget id="calculator">659_604 / 12</gadget>
<output>54_967</output>
<result>54_967</result>


in a class total 34 students , 16 are have a brother , 15 are have sisters , 9 students do n ' t have either brothers or sisters . find the number of students having both brother and sisters .

Explanation: total number of students = 34 let a be the number of students have a brothers . let b be the number of students have a sisters . aub = number of students have either brothers or sisters = 34 - 9 = 25 n ( aub ) = n ( a ) + n ( b ) - n ( anb ) 25 = 16 + 15 - n ( anb ) n ( anb ) = 31 - 25 n ( anb ) = 6 the number of students having both brother and sisters = 6 answer : c

<gadget id="calculator">16 + 15</gadget>
<output>31</output>
<gadget id="calculator">34 - 9</gadget>
<output>25</output>
<gadget id="calculator">31 - 25</gadget>
<output>6</output>
<result>6</result>


find the area of a parallelogram with base 26 cm and height 12 cm ?

Explanation: "area of a parallelogram = base * height = 26 * 12 = 312 cm 2 answer : e"

<gadget id="calculator">26 * 12</gadget>
<output>312</output>
<result>312</result>


a can do a piece of work in 90 days & y can do it in 80 days . they began working together but a leaves after some days and then b completed the remaining work in 46 days . the number of days after which a left the work was ?

Explanation: a and b did the work for some days . after that , b completed the remaining work in 46 days . in 46 days , word done by b = 1 80 x 46 = 23 45 remaining work = 1 – 23 / 45 = 17 / 45 remaining work is done by both a and b together = 17 / 45 x 90 x 80 / 90 + 80 = 16 days c

subtract(divide(subtract(const_1, multiply(divide(const_1, 80), 46)), add(divide(const_1, 80), divide(const_1, 90))), const_2)

<gadget id="calculator">1 / 80</gadget>
<output>1/80 = around 0.0125</output>
<gadget id="calculator">(1/80) * 46</gadget>
<output>23/40 = around 0.575</output>
<gadget id="calculator">1 - (23/40)</gadget>
<output>17/40 = around 0.425</output>
<gadget id="calculator">1 / 90</gadget>
<output>1/90 = around 0.011111</output>
<gadget id="calculator">(1/80) + (1/90)</gadget>
<output>17/720 = around 0.023611</output>
<gadget id="calculator">(17/40) / (17/720)</gadget>
<output>18</output>
<gadget id="calculator">18 - 2</gadget>
<output>16</output>
<result>16</result>


by selling 10 pencils for a rupee a man loses 25 % . how many for a rupee should he sell in order to gain 25 % ?

Explanation: "75 % - - - 10 125 % - - - ? 75 / 125 * 10 = 6 answer : a"

multiply(divide(const_1, multiply(add(const_100, 25), divide(const_1, subtract(const_100, 25)))), 10)

<gadget id="calculator">100 + 25</gadget>
<output>125</output>
<gadget id="calculator">100 - 25</gadget>
<output>75</output>
<gadget id="calculator">1 / 75</gadget>
<output>1/75 = around 0.013333</output>
<gadget id="calculator">125 * (1/75)</gadget>
<output>5/3 = around 1.666667</output>
<gadget id="calculator">1 / (5/3)</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(3/5) * 10</gadget>
<output>6</output>
<result>6</result>


Explanation: "explanation : 1 / 0.05 = ( 1 * 100 ) / 5 = 100 / 5 = 20 option d"

<gadget id="calculator">1 / 0.05</gadget>
<output>20</output>
<result>20</result>


amit and ananthu can do a work in 15 days and 60 days respectively . amit started the work and left after 3 days . ananthu took over and completed the work . in how many days was the total work completed ?

Explanation: "amit ’ s one day ’ s work = 1 / 15 amit ’ s 3 day ’ s work = 1 / 15 * 3 = 1 / 5 work left = 1 - 1 / 5 = 4 / 5 ananthu ’ s one day ’ s work = 1 / 60 ananthu can do work in = 4 / 5 * 60 = 48 days so total days = 48 + 3 = 51 days answer : e"

add(divide(subtract(const_1, multiply(inverse(15), 3)), inverse(60)), 3)

<gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">(1/15) * 3</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">1 / 60</gadget>
<output>1/60 = around 0.016667</output>
<gadget id="calculator">(4/5) / (1/60)</gadget>
<output>48</output>
<gadget id="calculator">48 + 3</gadget>
<output>51</output>
<result>51</result>


a and b together can do a work in 7 days . if a alone can do it in 56 days . in how many days can b alone do it ?

Explanation: "b 8 1 / 7 â € “ 1 / 56 = 1 / 8 = > 8"

add(inverse(subtract(divide(const_1, 7), divide(const_1, 56))), divide(const_2, add(const_2, const_3)))

<gadget id="calculator">1 / 7</gadget>
<output>1/7 = around 0.142857</output>
<gadget id="calculator">1 / 56</gadget>
<output>1/56 = around 0.017857</output>
<gadget id="calculator">(1/7) - (1/56)</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">1 / (1/8)</gadget>
<output>8</output>
<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">8 + (2/5)</gadget>
<output>42/5 = around 8.4</output>
<result>42/5 = around 8.4</result>


a car gets 20 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 180 kilometers ?

Explanation: "each 20 kilometers , 1 gallon is needed . we need to know how many 20 kilometers are there in 180 kilometers ? 180 / 20 = 9 * 1 gallon = 9 gallons correct answer b"

<gadget id="calculator">180 / 20</gadget>
<output>9</output>
<result>9</result>


a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 680 sq . feet , how many feet of fencing will be required ?

Explanation: "explanation : we have : l = 20 ft and lb = 680 sq . ft . so , b = 34 ft . length of fencing = ( l + 2 b ) = ( 20 + 68 ) ft = 88 ft . answer : d"

add(multiply(divide(680, 20), const_2), 20)

<gadget id="calculator">680 / 20</gadget>
<output>34</output>
<gadget id="calculator">34 * 2</gadget>
<output>68</output>
<gadget id="calculator">68 + 20</gadget>
<output>88</output>
<result>88</result>


the average salary of all the workers in a workshop is rs . 8000 . the average salary of 9 technicians is rs . 18000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is :

Explanation: "explanation : lot the total number of workers be v then , 8 ooov = ( 18000 * 9 ) + 6000 ( v - 9 ) < = > 2000 v = 108000 < = > v = 54 answer : b ) 54"

<gadget id="calculator">18_000 - 8_000</gadget>
<output>10_000</output>
<gadget id="calculator">9 * 10_000</gadget>
<output>90_000</output>
<gadget id="calculator">8_000 - 6_000</gadget>
<output>2_000</output>
<gadget id="calculator">90_000 / 2_000</gadget>
<output>45</output>
<gadget id="calculator">9 + 45</gadget>
<output>54</output>
<result>54</result>


a shopkeeper sold an book offering a discount of 5 % and earned a profit of 25 % . what would have been the percentage of profit earned if no discount was offered ?

Explanation: "let c . p . be $ 100 . then , s . p . = $ 125 let marked price be $ x . then , 95 / 100 x = 125 x = 12500 / 95 = $ 131.6 now , s . p . = $ 131.6 , c . p . = $ 100 profit % = 31.6 % . a"

multiply(const_100, divide(add(const_100, 25), subtract(const_100, 5)))

<gadget id="calculator">100 + 25</gadget>
<output>125</output>
<gadget id="calculator">100 - 5</gadget>
<output>95</output>
<gadget id="calculator">125 / 95</gadget>
<output>25/19 = around 1.315789</output>
<gadget id="calculator">100 * (25/19)</gadget>
<output>2_500/19 = around 131.578947</output>
<result>2_500/19 = around 131.578947</result>


find the sum the difference between the compound and s . i . on a certain sum of money for 2 years at 10 % per annum is rs . 10 of money ?

Explanation: "p = 10 ( 100 / 10 ) 2 = > p = 1000 answer : d"

multiply(multiply(divide(10, multiply(10, 2)), const_100), multiply(10, 2))

<gadget id="calculator">10 * 2</gadget>
<output>20</output>
<gadget id="calculator">10 / 20</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * 100</gadget>
<output>50</output>
<gadget id="calculator">50 * 20</gadget>
<output>1_000</output>
<result>1_000</result>


a room is 7 meters 68 centimeters in length and 4 meters 32 centimeters in width . find the least number of square tiles of equal size required to cover the entire floor of the room .

Explanation: "let us calculate both the length and width of the room in centimeters . length = 7 meters and 68 centimeters = 768 cm width = 4 meters and 32 centimeters = 432 cm as we want the least number of square tiles required , it means the length of each square tile should be as large as possible . further , the length of each square tile should be a factor of both the length and width of the room . hence , the length of each square tile will be equal to the hcf of the length and width of the room = hcf of 768 and 432 = 48 thus , the number of square tiles required = ( 768 x 432 ) / ( 48 x 48 ) = 16 x 9 = 144 answer : b"

divide(multiply(add(multiply(7, const_100), 68), add(multiply(4, const_100), 32)), multiply(gcd(add(multiply(7, const_100), 68), add(multiply(4, const_100), 32)), gcd(add(multiply(7, const_100), 68), add(multiply(4, const_100), 32))))

<gadget id="calculator">7 * 100</gadget>
<output>700</output>
<gadget id="calculator">700 + 68</gadget>
<output>768</output>
<gadget id="calculator">4 * 100</gadget>
<output>400</output>
<gadget id="calculator">400 + 32</gadget>
<output>432</output>
<gadget id="calculator">768 * 432</gadget>
<output>331_776</output>
<gadget id="calculator">gcd(768, 432)</gadget>
<output>48</output>
<gadget id="calculator">48 * 48</gadget>
<output>2_304</output>
<gadget id="calculator">331_776 / 2_304</gadget>
<output>144</output>
<result>144</result>


there is enough provisions for 600 men in an army camp for 25 days . if there were 300 men less , how long will the provision last ?

Explanation: "exp : we have , m 1 d 1 = m 2 d 2 600 * 25 = 300 * d 2 d 2 = 600 * 25 / 300 = 50 days . answer : d"

<gadget id="calculator">600 * 25</gadget>
<output>15_000</output>
<gadget id="calculator">15_000 / 300</gadget>
<output>50</output>
<result>50</result>


two cars start from the opposite places of a main road , 140 km apart . first car runs for 25 km and takes a right turn and then runs 15 km . it then turns left and then runs for another 25 km and then takes the direction back to reach the main road . in the mean time , due to minor break down the other car has run only 35 km along the main road . what would be the distance between two cars at this point ?

Explanation: answer : d ) 55 km

subtract(subtract(140, 35), add(25, 25))

<gadget id="calculator">140 - 35</gadget>
<output>105</output>
<gadget id="calculator">25 + 25</gadget>
<output>50</output>
<gadget id="calculator">105 - 50</gadget>
<output>55</output>
<result>55</result>


Explanation: explanation : 1 ÷ [ 1 + 1 ÷ { 1 + 1 ÷ ( 1 ÷ 1 ) } ] = 1 ÷ [ 1 + 1 ÷ { 1 + 1 ÷ 1 } ] = 1 ÷ [ 1 + 1 ÷ { 1 + 1 } ] = 1 ÷ [ 1 + 1 ÷ 2 ] = 1 ÷ [ 1 + ( 1 / 2 ) ] = 1 ÷ 3 / 2 = 1 × 3 / 2 = 1 × 2 / 3 = 2 / 3 answer : option c

divide(1, add(1, divide(1, add(1, divide(1, 1)))))

<gadget id="calculator">1 / 1</gadget>
<output>1</output>
<gadget id="calculator">1 + 1</gadget>
<output>2</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">1 / (3/2)</gadget>
<output>2/3 = around 0.666667</output>
<result>2/3 = around 0.666667</result>


john had a stock of 1000 books in his bookshop . he sold 75 on monday , 50 on tuesday , 64 on wednesday , 78 on thursday and 135 on friday . what percentage of the books were not sold ?

Explanation: "let n be the total number of books sold . hence n = 75 + 50 + 64 + 78 + 135 = 402 let m be the books not sold m = 1000 - n = 1000 - 402 = 598 percentage books not sold / total number of books = 598 / 1000 = 59.8 = 59.8 % correct answer a"

<gadget id="calculator">75 + 50</gadget>
<output>125</output>
<gadget id="calculator">64 + 78</gadget>
<output>142</output>
<gadget id="calculator">125 + 142</gadget>
<output>267</output>
<gadget id="calculator">267 + 135</gadget>
<output>402</output>
<gadget id="calculator">1_000 - 402</gadget>
<output>598</output>
<gadget id="calculator">598 / 1_000</gadget>
<output>299/500 = around 0.598</output>
<gadget id="calculator">(299/500) * 100</gadget>
<output>299/5 = around 59.8</output>
<result>299/5 = around 59.8</result>


a line that passes through ( – 1 , – 4 ) and ( 2 , k ) has a slope = k . what is the value of k ?

Explanation: "slope = ( y 2 - y 1 ) / ( x 2 - x 1 ) = > k = ( k + 4 ) / ( 2 + 1 ) = > 3 k = k + 4 = > k = 2 ans d it is !"

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


p , q and r have $ 8000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?

Explanation: "c 3200 let the amount with r be $ r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 8000 - r ) = > 3 r = 16000 - 2 r = > 5 r = 16000 = > r = 3200 ."

divide(multiply(8000, multiply(const_2, const_2)), add(add(multiply(divide(multiply(const_2, const_2), const_3), const_3), multiply(const_1, const_3)), multiply(const_1, const_3)))

<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">8_000 * 4</gadget>
<output>32_000</output>
<gadget id="calculator">4 / 3</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">(4/3) * 3</gadget>
<output>4</output>
<gadget id="calculator">1 * 3</gadget>
<output>3</output>
<gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">7 + 3</gadget>
<output>10</output>
<gadget id="calculator">32_000 / 10</gadget>
<output>3_200</output>
<result>3_200</result>


a recipe requires 2 1 / 2 ( mixed number ) cups of flour 2 3 / 4 ( mixed number ) cups of sugar and 1 1 / 3 ( mixed number ) cups of milk to make one cake . victor has 15 cups if flour , 16 cups of sugar and 8 cups of milk . what is the greatest number of cakes bil can make using this recipe ?

Explanation: "less work up front : go through each item and see what the greatest number of cakes you can make with each . the lowest of these will be the right answer . flour : 15 cups , we need 2.5 cups each . just keep going up the line to see how many cakes we can make : that means i can make 2 cakes with 5 cups , so 6 cakes overall with 15 cups . i ' ve already got the answer narrowed to either a or b . sugar : 16 cups , we need 2.75 cups each . same principle . i can make 2 cups with 5.5 cups , so to make 6 cakes i ' d need 16.5 cups . i do n ' t have that much sugar , so we ' re limited to 5 cakes . no need to even do milk because we ' re already at 5 . sugar will be the limiting factor . answer is a"

min(min(divide(15, add(2, divide(1, 2))), floor(divide(16, add(divide(3, 4), 2)))), divide(8, add(divide(1, 3), 1)))

<gadget id="calculator">1 / 2</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">15 / (5/2)</gadget>
<output>6</output>
<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(3/4) + 2</gadget>
<output>11/4 = around 2.75</output>
<gadget id="calculator">16 / (11/4)</gadget>
<output>64/11 = around 5.818182</output>
<gadget id="calculator">floor(64/11)</gadget>
<output>5</output>
<gadget id="calculator">min(6, 5)</gadget>
<output>5</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/3) + 1</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">8 / (4/3)</gadget>
<output>6</output>
<gadget id="calculator">min(5, 6)</gadget>
<output>5</output>
<result>5</result>


of the 3,600 employees of company x , 16 / 25 are clerical . if the clerical staff were to be reduced by 1 / 4 , what percent of the total number of the remaining employees would then be clerical ?

Explanation: "let ' s see , the way i did it was 16 / 25 are clerical out of 3600 so 2304 are clerical 2304 reduced by 1 / 4 is 2304 * 1 / 4 so it reduced 576 people , so there is 1728 clerical people left but since 576 people left , it also reduced from the total of 3600 so there are 3024 people total since 1728 clerical left / 3024 people total you get ( a ) 57 %"

multiply(divide(multiply(divide(16, 25), subtract(1, divide(1, 4))), add(multiply(divide(16, 25), subtract(1, divide(1, 4))), subtract(1, divide(16, 25)))), const_100)

<gadget id="calculator">16 / 25</gadget>
<output>16/25 = around 0.64</output>
<gadget id="calculator">1 / 4</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">(16/25) * (3/4)</gadget>
<output>12/25 = around 0.48</output>
<gadget id="calculator">1 - (16/25)</gadget>
<output>9/25 = around 0.36</output>
<gadget id="calculator">(12/25) + (9/25)</gadget>
<output>21/25 = around 0.84</output>
<gadget id="calculator">(12/25) / (21/25)</gadget>
<output>4/7 = around 0.571429</output>
<gadget id="calculator">(4/7) * 100</gadget>
<output>400/7 = around 57.142857</output>
<result>400/7 = around 57.142857</result>


the difference between two numbers is 1365 . when the larger number is divided by the smaller one , the quotient is 6 and the remainder is 15 . the smaller number is

Explanation: "solution let the numbers be x and x ( x + 1365 ) . then , x + 1365 = 6 x + 15 ‹ = › 5 x = 1350 . ‹ = › x = 270 . answer d"

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

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


the sum of present age of abe and the age before 7 years is 33 . find the present age of abe . what will be his age after 7 years ?

Explanation: "present age = x before 7 yrs , y = x - 7 after 7 yrs , z = x + 7 by the qn , x + ( x - 7 ) = 33 2 x - 7 = 33 2 x = 33 + 7 x = 40 / 2 x = 20 z = x + 7 = 20 + 7 = 27 answer : c"

<gadget id="calculator">33 + 7</gadget>
<output>40</output>
<gadget id="calculator">40 / 2</gadget>
<output>20</output>
<gadget id="calculator">20 + 7</gadget>
<output>27</output>
<result>27</result>


a train running at a speed of 60 kmph crosses a pole in 18 seconds . what is the length of the train ?

Explanation: 60 kmph = 50 / 3 m / sec 50 / 3 * 18 = 300 m answer : b

multiply(divide(multiply(60, const_1000), const_3600), 18)

<gadget id="calculator">60 * 1_000</gadget>
<output>60_000</output>
<gadget id="calculator">60_000 / 3_600</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">(50/3) * 18</gadget>
<output>300</output>
<result>300</result>


a company conducted a survey about its two brands , a and b . x percent of respondents liked product a , ( x – 20 ) percent liked product b , 23 percent liked both products , and 23 percent liked neither product . what is the minimum number w of people surveyed by the company ?

Explanation: "100 = x + x - 20 + 23 - 23 x = 60 , so , product a = 60 % , product b = 40 % , both = 23 % , neither = 23 % 23 % of the total no . of people should be an integer . so , a , bc are out . 60 % of d and 40 % of d are both integers . so , d satisfies all conditions . so , answer is d ."

add(subtract(divide(add(add(subtract(const_100, 23), 23), 20), const_2), 20), divide(add(add(subtract(const_100, 23), 23), 20), const_2))

<gadget id="calculator">100 - 23</gadget>
<output>77</output>
<gadget id="calculator">77 + 23</gadget>
<output>100</output>
<gadget id="calculator">100 + 20</gadget>
<output>120</output>
<gadget id="calculator">120 / 2</gadget>
<output>60</output>
<gadget id="calculator">60 - 20</gadget>
<output>40</output>
<gadget id="calculator">40 + 60</gadget>
<output>100</output>
<result>100</result>


when a person aged 39 is added to a group of n people , the average age increases by 2 . when a person aged 15 is added instead , the average age decreases by 1 . what is the value of t ?

Explanation: "a simple and elegant solution . as addition of 39 , shifts mean by 2 , and addition of 15 , shifts mean by 1 to the other side , we have the mean lying between 3915 , and in a ratio of 2 : 1 39 - 15 = 24 24 divide by 3 is 8 . meaning mean of the n terms is 15 + 8 = 39 - 16 = 23 now , from first statement , when a person aged 39 is added to a group of n people , the average age increases by 2 . t * 23 + 39 = 25 * ( t + 1 ) t = 7 ans . ( a )"

subtract(divide(subtract(39, 15), add(2, 1)), 1)

<gadget id="calculator">39 - 15</gadget>
<output>24</output>
<gadget id="calculator">2 + 1</gadget>
<output>3</output>
<gadget id="calculator">24 / 3</gadget>
<output>8</output>
<gadget id="calculator">8 - 1</gadget>
<output>7</output>
<result>7</result>


the average earning of a person for the first 4 days of a week is rs 18 and for the last 4 days is rs 22 . if he earns rs 20 on the fourth day , his average earning for the whole week is ?

Explanation: total earning for the week = rs ( 4 × 18 + 4 × 22 - 20 ) = rs 140 average earning = rs 140 / 7 = rs 20 . answer : c

divide(subtract(add(multiply(4, 18), multiply(4, 22)), 20), add(const_4, const_3))

<gadget id="calculator">4 * 18</gadget>
<output>72</output>
<gadget id="calculator">4 * 22</gadget>
<output>88</output>
<gadget id="calculator">72 + 88</gadget>
<output>160</output>
<gadget id="calculator">160 - 20</gadget>
<output>140</output>
<gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">140 / 7</gadget>
<output>20</output>
<result>20</result>


mary can do a piece of work in 12 days . rosy is 50 % more efficient than mary . the number of days taken by rosy to do the same piece of work is ?

Explanation: ratio of times taken by mary and rosy = 150 : 100 = 3 : 2 suppose rosy takes x days to do the work . 3 : 2 : : 12 : x = > x = 8 days . hence , rosy takes 8 days to complete the work . answer : b

divide(12, add(const_1, divide(50, const_100)))

<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 + (1/2)</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">12 / (3/2)</gadget>
<output>8</output>
<result>8</result>


points a , b , and , c have xy - coordinates ( 20 ) , ( 812 ) , and ( 140 ) , respectively . points x , y , and z have xy - coordinates ( 60 ) , ( 84 ) , and ( 100 ) , respectively . what fraction c of the area of triangle abc is the area of triangle xyz ?

Explanation: if you notice , both triangles abc and xyz have a side on x axis . we can take these sides as bases for each triangle , therefore area of abc is 1 / 2 * 12 * 12 ( height of abc is the y coordinate of the third point ( 812 ) ) similarly area of xyz is 1 / 2 * 4 * 4 dividing area of xyz with that of abc gives c = 1 / 9 . a

divide(divide(multiply(const_4, const_4), const_2), multiply(subtract(20, multiply(const_4, const_2)), divide(subtract(20, multiply(const_4, const_2)), const_2)))

<gadget id="calculator">4 * 4</gadget>
<output>16</output>
<gadget id="calculator">16 / 2</gadget>
<output>8</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">20 - 8</gadget>
<output>12</output>
<gadget id="calculator">12 / 2</gadget>
<output>6</output>
<gadget id="calculator">12 * 6</gadget>
<output>72</output>
<gadget id="calculator">8 / 72</gadget>
<output>1/9 = around 0.111111</output>
<result>1/9 = around 0.111111</result>


a man ' s regular pay is $ 3 per hour up to 40 hours . overtime is twice the payment for regular time . if he was paid $ 174 , how many hours overtime did he work ?

Explanation: "at $ 3 per hour up to 40 hours , regular pay = $ 3 x 40 = $ 120 if total pay = $ 168 , overtime pay = $ 174 - $ 120 = $ 54 overtime rate ( twice regular ) = 2 x $ 3 = $ 6 per hour = > number of overtime hours = $ 54 / $ 6 = 9 ans is c"

divide(subtract(174, multiply(3, 40)), multiply(3, const_2))

<gadget id="calculator">3 * 40</gadget>
<output>120</output>
<gadget id="calculator">174 - 120</gadget>
<output>54</output>
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">54 / 6</gadget>
<output>9</output>
<result>9</result>


the price of rice falls by 25 % . how much rice can be bought now with the money that was sufficient to buy 20 kg of rice previously ?

Explanation: solution : let rs . 100 be spend on rice initially for 20 kg . as the price falls by 20 % , new price for 20 kg rice , = ( 100 - 25 % of 100 ) = 75 new price of rice = 75 / 20 = rs . 3.75 per kg . rice can bought now at = 100 / 3.75 = 26.67 kg . answer : option c

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

<gadget id="calculator">100 - 25</gadget>
<output>75</output>
<gadget id="calculator">75 / 20</gadget>
<output>15/4 = around 3.75</output>
<gadget id="calculator">100 / (15/4)</gadget>
<output>80/3 = around 26.666667</output>
<result>80/3 = around 26.666667</result>


john purchased 1370 large bottles at $ 1.99 per bottle and 690 small bottles at $ 1.50 per bottle . what was the approximate average price paid per bottle ?

Explanation: "( 1370 * 1.99 + 690 * 1.50 ) / ( 1370 + 690 ) = ~ 1.83 - option ( e )"

<gadget id="calculator">1_370 * 1.99</gadget>
<output>2_726.3</output>
<gadget id="calculator">690 * 1.5</gadget>
<output>1_035</output>
<gadget id="calculator">2_726.3 + 1_035</gadget>
<output>3_761.3</output>
<gadget id="calculator">1_370 + 690</gadget>
<output>2_060</output>
<gadget id="calculator">3_761.3 / 2_060</gadget>
<output>1.825874</output>
<result>1.825874</result>


find the ratio in which rice at rs . 7.30 a kg be mixed with rice at rs . 5.70 a kg to produce a mixture worth rs . 6.30 a kg

Explanation: "by the rule of alligation : cost of 1 kg rice of 1 st kind cost of 1 kg rice of 2 nd kind required ratio = 60 : 100 = 3 : 5 answer : c"

<gadget id="calculator">6.3 - 5.7</gadget>
<output>0.6</output>
<gadget id="calculator">7.3 - 6.3</gadget>
<output>1</output>
<gadget id="calculator">0.6 / 1</gadget>
<output>0.6</output>
<result>0.6</result>


3 different containers contain 50 litres , 100 litres and 150 litres of mixture of milk and water respectively . what is the biggest measure can measure all the different quantities exactly ?

Explanation: m 1 = 50 litres m 2 = 100 litres m 3 = 150 litres required measurement = h . c . f . of m 1 , m 2 , m 3 = 50 litres answer is d

<gadget id="calculator">gcd(50, 100)</gadget>
<output>50</output>
<gadget id="calculator">gcd(50, 150)</gadget>
<output>50</output>
<result>50</result>


Explanation: 2034 - 50 = 1984 answer : e

<gadget id="calculator">1_002 / 20.04</gadget>
<output>50</output>
<gadget id="calculator">2_034 - 50</gadget>
<output>1_984</output>
<result>1_984</result>


x , y , and z are all unique numbers . if x is chosen randomly from the set { 10 , 11 } and y and z are chosen randomly from the set { 20 , 21 , 22 , 23 } , what is the probability that x and y are prime and z is not ?

Explanation: p ( x is prime ) = 1 / 2 p ( y is prime ) = 1 / 4 if y is prime , then z is not prime since y and z are unique . then the probability is 1 / 2 * 1 / 4 = 1 / 8 the answer is c .

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

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


marty ' s pizza shop guarantees that their pizzas all have at least 75 % of the surface area covered with toppings , with a crust of uniform width surrounding them . if you order their best seller – a circular pizza with a diameter of 16 inches – what is the maximum width you can expect to see for the crust ?

Explanation: total area = 8 * 8 * pi radius = 64 pi surface = . 75 * 64 * pi = 48 pi radius of surface = 4 sqrt ( 3 ) ~ 6.8 radius width = 8 - 6.8 = 1.2 answer : b

divide(subtract(16, multiply(sqrt(divide(divide(multiply(circle_area(divide(16, const_2)), 75), const_100), const_pi)), const_2)), const_2)

<gadget id="calculator">16 / 2</gadget>
<output>8</output>
<gadget id="calculator">pi * (8 ** 2)</gadget>
<output>64*pi = around 201.06193</output>
<gadget id="calculator">(64*pi) * 75</gadget>
<output>4800*pi = around 15_079.644737</output>
<gadget id="calculator">(4800*pi) / 100</gadget>
<output>48*pi = around 150.796447</output>
<gadget id="calculator">(48*pi) / pi</gadget>
<output>48</output>
<gadget id="calculator">48 ** (1/2)</gadget>
<output>4*sqrt(3) = around 6.928203</output>
<gadget id="calculator">(4*sqrt(3)) * 2</gadget>
<output>8*sqrt(3) = around 13.856406</output>
<gadget id="calculator">16 - (8*sqrt(3))</gadget>
<output>16 - 8*sqrt(3) = around 2.143594</output>
<gadget id="calculator">(16 - 8*sqrt(3)) / 2</gadget>
<output>8 - 4*sqrt(3) = around 1.071797</output>
<result>8 - 4*sqrt(3) = around 1.071797</result>


compute all real solutions to 16 x + 4 x + 1 - 96 = 0

Explanation: if we substitute y = 4 x , we have y 2 + 4 y - 96 = 0 , so y = - 4 or y = 8 . the first does not map to a real solution , while the second maps to x = 3 / 2 correct answer a

divide(subtract(4, 1), subtract(subtract(4, 1), 1))

<gadget id="calculator">4 - 1</gadget>
<output>3</output>
<gadget id="calculator">3 - 1</gadget>
<output>2</output>
<gadget id="calculator">3 / 2</gadget>
<output>3/2 = around 1.5</output>
<result>3/2 = around 1.5</result>


virginia , adrienne , and dennis have taught history for a combined total of 87 years . if virginia has taught for 9 more years than adrienne and for 9 fewer years than dennis , for how many years has dennis taught ?

Explanation: "let number of years taught by virginia = v number of years taught by adrienne = a number of years taught by dennis = d v + a + d = 96 v = a + 9 = > a = v - 9 v = d - 9 = > a = ( d - 9 ) - 9 = d - 18 d - 9 + d - 18 + d = 87 = > 3 d = 87 + 27 = 114 = > d = 38 answer c"

add(divide(subtract(87, add(add(9, 9), 9)), const_3), add(9, 9))

<gadget id="calculator">9 + 9</gadget>
<output>18</output>
<gadget id="calculator">18 + 9</gadget>
<output>27</output>
<gadget id="calculator">87 - 27</gadget>
<output>60</output>
<gadget id="calculator">60 / 3</gadget>
<output>20</output>
<gadget id="calculator">20 + 18</gadget>
<output>38</output>
<result>38</result>


the edges of a cuboid are 4 cm , 5 cm and 7 cm . find the volume of the cuboid ?

Explanation: "4 * 5 * 7 = 120 answer : a"

<gadget id="calculator">4 * 5 * 7</gadget>
<output>140</output>
<result>140</result>


what is the number of integers from 1 to 1000 ( inclusive ) that are divisible by neither 20 nor by 35 ?

Explanation: "in 1000 consecutive numbers , number of multiples of 20 = 1000 / 20 = 50 ( ignore decimals ) in 1000 consecutive numbers , number of multiples of 35 = 1000 / 35 = 28 number of multiples of 20 * 35 i . e . 700 = 1000 / 700 = 1 number of integers from 1 to 1000 that are divisible by neither 20 nor by 35 = 1000 - ( 50 + 28 - 1 ) { using the concept of sets here ) = 923 answer is d"

subtract(1000, subtract(add(divide(1000, 20), divide(1000, 35)), divide(1000, multiply(20, 35))))

<gadget id="calculator">1_000 / 20</gadget>
<output>50</output>
<gadget id="calculator">1_000 / 35</gadget>
<output>200/7 = around 28.571429</output>
<gadget id="calculator">50 + (200/7)</gadget>
<output>550/7 = around 78.571429</output>
<gadget id="calculator">20 * 35</gadget>
<output>700</output>
<gadget id="calculator">1_000 / 700</gadget>
<output>10/7 = around 1.428571</output>
<gadget id="calculator">(550/7) - (10/7)</gadget>
<output>540/7 = around 77.142857</output>
<gadget id="calculator">1_000 - (540/7)</gadget>
<output>6_460/7 = around 922.857143</output>
<result>6_460/7 = around 922.857143</result>


the population of a town is 10000 . it decreases annually at the rate of 20 % p . a . what will be its population after 2 years ?

Explanation: "10000 × 80 / 100 × 80 / 100 = 6400 answer : a"

subtract(subtract(10000, multiply(10000, divide(20, const_100))), multiply(subtract(10000, multiply(10000, divide(20, const_100))), divide(20, const_100)))

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">10_000 * (1/5)</gadget>
<output>2_000</output>
<gadget id="calculator">10_000 - 2_000</gadget>
<output>8_000</output>
<gadget id="calculator">8_000 * (1/5)</gadget>
<output>1_600</output>
<gadget id="calculator">8_000 - 1_600</gadget>
<output>6_400</output>
<result>6_400</result>


in a rectangular coordinate system , what is the area of a rectangle whose vertices have the coordinates ( - 4 , 1 ) , ( 1 , 1 ) , ( 1 , - 3 ) and ( - 4 , - 3 ) ?

Explanation: "length of side 1 = 4 + 1 = 5 length of side 2 = 3 + 1 = 4 area of rectangle = 5 * 4 = 20 b is the answer"

<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">1 + 3</gadget>
<output>4</output>
<gadget id="calculator">5 * 4</gadget>
<output>20</output>
<result>20</result>


each person in a group of 110 investors has investments in either equities or securities or both . exactly 25 of the investors in equities have investments in securities , and exactly 40 of the investors in securities have investments in equities . how many have investments in equities ?

Explanation: explanation : the investors can be categorized into three groups : ( 1 ) those who have investments in equities only . ( 2 ) those who have investments in securities only . ( 3 ) those who have investments in both equities and securities . let x , y , and z denote the number of people in the respective categories . since the total number of investors is 110 , we have : - = > x + y + z = 110 - - - - - - - - - - - - - ( 1 ) . also , the number of people with investments in equities is x + z and the number of people with investments in securities is y + z . since exactly 25 % of the investors in equities have investments in securities , we have the equation = > ( 25 / 100 ) × ( x + z ) = z . = > ( 25 / 100 ) × x = 75 z / 100 . = > x = 3 z . - - - - - - - - - - - - - - ( 2 ) since exactly 40 % of the investors in securities have investments in equities , we have the equation = > ( 40 / 100 ) × ( y + z ) = z . = > ( y + z ) = 5 z / 2 . = > y = 3 z / 2 . - - - - - - - - - - - - - - - - - ( 3 ) substituting equations ( 2 ) and ( 3 ) into equation ( 1 ) gives : - = > 3 z + ( 3 z / 2 ) + z = 110 . = > 11 z / 2 = 110 . = > z = 110 × 2 / 11 = 20 . hence , the number of people with investments in equities is : = > x + z = 3 z + z = 3 × 20 + 20 = 60 + 20 = 80 . answer : b

multiply(divide(110, add(add(multiply(divide(divide(40, const_100), divide(25, const_100)), divide(25, const_100)), subtract(const_1, multiply(divide(divide(40, const_100), divide(25, const_100)), divide(25, const_100)))), subtract(divide(divide(40, const_100), divide(25, const_100)), multiply(divide(divide(40, const_100), divide(25, const_100)), divide(25, const_100))))), divide(divide(40, const_100), divide(25, const_100)))

<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(2/5) / (1/4)</gadget>
<output>8/5 = around 1.6</output>
<gadget id="calculator">(8/5) * (1/4)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">1 - (2/5)</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(2/5) + (3/5)</gadget>
<output>1</output>
<gadget id="calculator">(8/5) - (2/5)</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">1 + (6/5)</gadget>
<output>11/5 = around 2.2</output>
<gadget id="calculator">110 / (11/5)</gadget>
<output>50</output>
<gadget id="calculator">50 * (8/5)</gadget>
<output>80</output>
<result>80</result>


a certain number of two digits is 3 times the sum of its digits and if 45 be added to it , the degits are reversed . the number is .

Explanation: let the ten ' s digit be x and unit ' s digit be y . then 10 x + y = 3 ( x + y ) = = > 7 x - 2 y = 0 = = > 7 x - 2 y = 0 - - - - > ( i ) 10 + y + 45 = 10 y + x = = > y - x = 5 = = = > - 2 x + 2 y = 10 - - - - - - ( ii ) by adding ( i ) and ( ii ) we get 5 x = 10 so x = 2 and y = 7 so the required number is 27 . so the correct option is b ) 27 .

add(multiply(subtract(divide(subtract(45, const_10), subtract(subtract(const_10, 3), const_2)), subtract(subtract(const_10, 3), const_2)), const_10), divide(subtract(45, const_10), subtract(subtract(const_10, 3), const_2)))

<gadget id="calculator">45 - 10</gadget>
<output>35</output>
<gadget id="calculator">10 - 3</gadget>
<output>7</output>
<gadget id="calculator">7 - 2</gadget>
<output>5</output>
<gadget id="calculator">35 / 5</gadget>
<output>7</output>
<gadget id="calculator">7 - 5</gadget>
<output>2</output>
<gadget id="calculator">2 * 10</gadget>
<output>20</output>
<gadget id="calculator">20 + 7</gadget>
<output>27</output>
<result>27</result>


tom , working alone , can paint a room in 16 hours . peter and john , working independently , can paint the same room in 8 hours and 4 hours , respectively . tom starts painting the room and works on his own for two hour . he is then joined by peter and they work together for two hour . finally , john joins them and the three of them work together to finish the room , each one working at his respective rate . what fraction of the whole job was done by peter ?

Explanation: "let the time when all three were working together be t hours . then : tom worked for t + 4 hour and has done 1 / 16 * ( t + 4 ) part of the job ; peter worked for t + 2 hour and has done 1 / 8 * ( t + 2 ) part of the job ; john worked for t hours and has done 1 / 4 * t part of the job : 1 / 16 * ( t + 4 ) + 1 / 8 * ( t + 2 ) + 1 / 4 * t = 1 - - > multiply by 16 - - > ( t + 4 ) + ( 2 t + 2 ) + 4 t = 16 - - > t = 10 / 7 ; hence peter has done 1 / 8 * ( 10 / 7 + 2 ) = 1 / 8 * 24 / 7 = 3 / 7 answer : e"

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

<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">8 + 1</gadget>
<output>9</output>
<gadget id="calculator">4 / 9</gadget>
<output>4/9 = around 0.444444</output>
<result>4/9 = around 0.444444</result>


an angry arjun carried some arrows for fighting with bheeshm . with half the arrows , he cut down the arrows thrown by bheeshm on him and with 6 other arrows he killed the chariot driver of bheeshm . with one arrow each he knocked down respectively the chariot , the flag and the bow of bheeshm . finally , with one more than 4 times the square root of arrows he laid bheeshm unconscious on an arrow bed . find the total number of arrows arjun had .

Explanation: x / 2 + 6 + 3 + 1 + 4 sqrt ( x ) = x x / 2 + 10 + 4 sqrt ( x ) = x 4 sqrt ( x ) = x / 2 - 10 squaring on both sides 16 x = x ² / 4 + 100 - 10 x simplifying x ² - 104 x + 400 = 0 x = 100 , 4 x = 4 is not possible therefore x = 100 answer : b

<gadget id="calculator">6 + 4</gadget>
<output>10</output>
<gadget id="calculator">10 ** 2</gadget>
<output>100</output>
<result>100</result>


find the distance covered by a man walking for 10 min at a speed of 6 km / hr ?

Explanation: "distance = 6 * 10 / 60 = 1 km answer is a"

divide(multiply(10, divide(multiply(6, const_1000), const_60)), const_1000)

<gadget id="calculator">6 * 1_000</gadget>
<output>6_000</output>
<gadget id="calculator">6_000 / 60</gadget>
<output>100</output>
<gadget id="calculator">10 * 100</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 / 1_000</gadget>
<output>1</output>
<result>1</result>


in the above number , a and b represent the tens and units digits , respectively . if the above number is divisible by 15 , what is the greatest possible value of b x a ?

Explanation: "i also was confused when i was looking forabove number : d as far as i understood , 15 is a factor of ab . in other words , the values of b ( units digits can be 5 or 0 . better to have option for 5 in this case to havebigger result ) . now let ' s try 15 x 1 ( a = 1 , b = 5 respectively we have = 5 ) . to ensure , let ' s check ( avoid even multiples of 2,4 , 6,8 etc ( we will have 0 in units thus making our result 0 ) 15 x 3 = 45 ( a = 4 b = 5 respectively . hey ! that ' s 20 . but we do n ' t have this number in answer choices , move on ) . 15 x 5 = 75 ( a = 7 , b = 5 respectively . increasing trend , we have 35 now ) 15 x 7 = 105 ( a = 0 , b = 5 . have 0 now . can create a pattern ) imo e ."

multiply(add(const_3, const_4), add(const_2, const_3))

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


let s be the set of all positive integers that , when divided by 8 , have a remainder of 5 . what is the 79 th number in this set ?

Explanation: "the set s = { 5 , 13 , 21 , 29 , . . . . . . . . . . . . . . . . . . . . . } 1 st number = 8 * 0 + 5 = 5 2 nd number = 8 * 1 + 5 = 13 3 rd number = 8 * 2 + 5 = 21 79 th number = 8 * ( 79 - 1 ) + 5 = 629 answer = e"

add(multiply(subtract(79, const_1), 8), 5)

<gadget id="calculator">79 - 1</gadget>
<output>78</output>
<gadget id="calculator">78 * 8</gadget>
<output>624</output>
<gadget id="calculator">624 + 5</gadget>
<output>629</output>
<result>629</result>


the area of a sector of a circle of radius 4 cm formed by an arc of length 4.5 cm is ?

Explanation: "( 4 * 4.5 ) / 2 = 9 answer : e"

multiply(divide(const_1, const_2), multiply(4, 4.5))

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">4 * 4.5</gadget>
<output>18</output>
<gadget id="calculator">(1/2) * 18</gadget>
<output>9</output>
<result>9</result>


the speed at which a man can row a boat in still water is 21 kmph . if he rows downstream , where the speed of current is 5 kmph , what time will he take to cover 90 metres ?

Explanation: speed of the boat downstream = 21 + 5 = 26 kmph = 26 * 5 / 18 = 7.22 m / s hence time taken to cover 90 m = 90 / 7.22 = 12.46 seconds . answer : d

divide(90, multiply(add(21, 5), const_0_2778))

<gadget id="calculator">21 + 5</gadget>
<output>26</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">26 * (5/18)</gadget>
<output>65/9 = around 7.222222</output>
<gadget id="calculator">90 / (65/9)</gadget>
<output>162/13 = around 12.461538</output>
<result>162/13 = around 12.461538</result>


if a man lost 4 % by selling oranges at the rate of 48 a rupee at how many a rupee must he sell them to gain 44 % ?

Explanation: "96 % - - - - 48 144 % - - - - ? 96 / 144 * 48 = 32 answer : e"

divide(multiply(subtract(const_100, 4), 48), add(const_100, 44))

<gadget id="calculator">100 - 4</gadget>
<output>96</output>
<gadget id="calculator">96 * 48</gadget>
<output>4_608</output>
<gadget id="calculator">100 + 44</gadget>
<output>144</output>
<gadget id="calculator">4_608 / 144</gadget>
<output>32</output>
<result>32</result>


an industrial loom weaves 0.128 metres of cloth every second . approximately , how many seconds will it take for the loom to weave 28 metre of cloth ?

Explanation: "explanation : let the time required by x seconds . then , more cloth means more time ( direct proportion ) so , 0.128 : 1 : : 28 : x = > x = { \ color { blue } \ frac { 28 \ times 1 } { 0.128 } } = > x = 218.75 so time will be approx 219 seconds answer : b"

<gadget id="calculator">28 / 0.128</gadget>
<output>218.75</output>
<result>218.75</result>


the radius of a circular wheel is 1.75 m , how many revolutions will it make in traveling 1 km ?

Explanation: 2 * 22 / 7 * 1.75 * x = 11000 x = 1000 answer : a

divide(multiply(multiply(multiply(const_pi, const_2), 1.75), const_1000), add(1, const_10))

<gadget id="calculator">pi * 2</gadget>
<output>2*pi = around 6.283185</output>
<gadget id="calculator">(2*pi) * 1.75</gadget>
<output>3.5*pi = around 10.995574</output>
<gadget id="calculator">(3.5*pi) * 1_000</gadget>
<output>3500.0*pi = around 10_995.574288</output>
<gadget id="calculator">1 + 10</gadget>
<output>11</output>
<gadget id="calculator">(3500.0*pi) / 11</gadget>
<output>318.181818181818*pi = around 999.597663</output>
<result>318.181818181818*pi = around 999.597663</result>


a 340 - liter solution of kola is made from 88 % water , 5 % concentrated kola and the rest is made from sugar . if 4.2 liters of sugar , 10 liter of water and 6.8 liters of concentrated kola were added to the solution , what percent of the solution is made from sugar ?

Explanation: "denominator : 340 + 10 + 4.2 + 6.8 = 361 numerator : 340 ( 1 - . 88 - . 05 ) + 4.2 340 ( 0.07 ) + 4.2 23.8 + 4.2 28 ratio : 28 / 361 = 0.077 answer : b"

multiply(divide(add(subtract(subtract(340, multiply(340, divide(88, const_100))), multiply(340, divide(5, const_100))), 4.2), add(add(add(340, 4.2), 10), 6.8)), const_100)

<gadget id="calculator">88 / 100</gadget>
<output>22/25 = around 0.88</output>
<gadget id="calculator">340 * (22/25)</gadget>
<output>1_496/5 = around 299.2</output>
<gadget id="calculator">340 - (1_496/5)</gadget>
<output>204/5 = around 40.8</output>
<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">340 * (1/20)</gadget>
<output>17</output>
<gadget id="calculator">(204/5) - 17</gadget>
<output>119/5 = around 23.8</output>
<gadget id="calculator">(119/5) + 4.2</gadget>
<output>28</output>
<gadget id="calculator">340 + 4.2</gadget>
<output>344.2</output>
<gadget id="calculator">344.2 + 10</gadget>
<output>354.2</output>
<gadget id="calculator">354.2 + 6.8</gadget>
<output>361</output>
<gadget id="calculator">28 / 361</gadget>
<output>28/361 = around 0.077562</output>
<gadget id="calculator">(28/361) * 100</gadget>
<output>2_800/361 = around 7.756233</output>
<result>2_800/361 = around 7.756233</result>


if the radius of a cylinder is doubled and so is the height , what is the new volume of the cylinder divided by the old one ?

Explanation: let the radius be r and the the height be h . new radius = 2 r and height = 2 h . area ( new ) : area ( old ) = pi ∗ ( 2 r ) ^ 2 ∗ 2 h / pi ∗ r ^ 2 ∗ h = 8 : 1 . hence the answer is a .

divide(volume_cylinder(multiply(const_1, const_2), multiply(const_1, const_2)), volume_cylinder(const_1, const_1))

<gadget id="calculator">1 * 2</gadget>
<output>2</output>
<gadget id="calculator">pi * (2 ** 2) * 2</gadget>
<output>8*pi = around 25.132741</output>
<gadget id="calculator">pi * (1 ** 2) * 1</gadget>
<output>pi = around 3.141593</output>
<gadget id="calculator">(8*pi) / pi</gadget>
<output>8</output>
<result>8</result>


oil is poured into a tank so that the tank is being filled at the rate of 4 cubic feet per hour . if the empty rectangular tank is 9 feet long , 8 feet wide , and 5 feet deep , approximately how many hours does it take to fill the tank ?

Explanation: the volume the tank is : length * width * depth = 9 * 8 * 5 = 360 cubic feet . 360 cubic feet / 4 cubic feet per hour = 90 hours . it will take 90 hours to fill the tank . the answer is d .

divide(volume_rectangular_prism(9, 8, 5), 4)

<gadget id="calculator">9 * 8 * 5</gadget>
<output>360</output>
<gadget id="calculator">360 / 4</gadget>
<output>90</output>
<result>90</result>


the speed of a boat in still water in 37 km / hr and the rate of current is 13 km / hr . the distance travelled downstream in 10 minutes is :

Explanation: "explanation : speed downstream = ( 37 + 13 ) = 50 kmph time = 24 minutes = 10 / 60 hour = 1 / 6 hour distance travelled = time × speed = ( 1 / 6 ) × 50 = 8.33 km answer : option e"

multiply(add(37, 13), divide(10, const_60))

<gadget id="calculator">37 + 13</gadget>
<output>50</output>
<gadget id="calculator">10 / 60</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">50 * (1/6)</gadget>
<output>25/3 = around 8.333333</output>
<result>25/3 = around 8.333333</result>


a train 600 m long can cross an electric pole in 20 sec and then find the speed of the train ?

Explanation: "length = speed * time speed = l / t s = 600 / 20 s = 30 m / sec speed = 30 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 108 kmph answer : b"

divide(divide(600, const_1000), divide(20, const_3600))

<gadget id="calculator">600 / 1_000</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">20 / 3_600</gadget>
<output>1/180 = around 0.005556</output>
<gadget id="calculator">(3/5) / (1/180)</gadget>
<output>108</output>
<result>108</result>


the average of 30 numbers is 25 . if each number is multiplied by 5 , find the new average ?

Explanation: "sum of the 30 numbers = 30 * 25 = 750 if each number is multiplied by 5 , the sum also gets multiplied by 5 and the average also gets multiplied by 5 . thus , the new average = 25 * 5 = 125 . answer : b"

<gadget id="calculator">25 * 5</gadget>
<output>125</output>
<result>125</result>


Explanation: "explanation √ ( 21 ) ^ 2 = ? or , ? = 21 answer d"

<gadget id="calculator">21 ** 2</gadget>
<output>441</output>
<gadget id="calculator">441 ** (1/2)</gadget>
<output>21</output>
<result>21</result>


a and b began business with rs . 3000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000 more . at the end of the year , their profits amounted to rs . 798 find the share of a .

Explanation: "explanation : ( 3 * 8 + 2 * 4 ) : ( 4 * 8 + 5 * 4 ) 8 : 13 8 / 21 * 798 = 304 answer : d"

multiply(divide(798, add(add(multiply(3000, 8), multiply(subtract(3000, 1000), subtract(const_12, 8))), add(multiply(4000, 8), multiply(add(4000, 1000), subtract(const_12, 8))))), add(multiply(3000, 8), multiply(subtract(3000, 1000), subtract(const_12, 8))))

<gadget id="calculator">3_000 * 8</gadget>
<output>24_000</output>
<gadget id="calculator">3_000 - 1_000</gadget>
<output>2_000</output>
<gadget id="calculator">12 - 8</gadget>
<output>4</output>
<gadget id="calculator">2_000 * 4</gadget>
<output>8_000</output>
<gadget id="calculator">24_000 + 8_000</gadget>
<output>32_000</output>
<gadget id="calculator">4_000 * 8</gadget>
<output>32_000</output>
<gadget id="calculator">4_000 + 1_000</gadget>
<output>5_000</output>
<gadget id="calculator">5_000 * 4</gadget>
<output>20_000</output>
<gadget id="calculator">32_000 + 20_000</gadget>
<output>52_000</output>
<gadget id="calculator">32_000 + 52_000</gadget>
<output>84_000</output>
<gadget id="calculator">798 / 84_000</gadget>
<output>19/2_000 = around 0.0095</output>
<gadget id="calculator">(19/2_000) * 32_000</gadget>
<output>304</output>
<result>304</result>


the speed of a boat in still water is 15 km / hr and the rate of the current is 3 km / hr . the distance travelled downstream in 12 minutes is

Explanation: "speed downstream = ( 15 + 3 ) km / hr = 18 km / hr . distance travelled = ( 18 x 12 / 60 ) hours = 3.6 km . answer d"

multiply(divide(12, const_60), add(15, 3))

<gadget id="calculator">12 / 60</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">15 + 3</gadget>
<output>18</output>
<gadget id="calculator">(1/5) * 18</gadget>
<output>18/5 = around 3.6</output>
<result>18/5 = around 3.6</result>


a certain animal in the zoo has consumed 39 pounds of food in 6 days . if it continues to eat at the same rate , in how many more days will its total consumption be 117 pounds ?

Explanation: ans is c : 39 pounds - - > 6 days 117 pounds - - > x days x = 117 * 6 / 39 = 18 the animal has already consumed food in 6 days so the the number of days for it ' s total consumption be 117 pounds is 18 - 6 = 12

<gadget id="calculator">39 / 6</gadget>
<output>13/2 = around 6.5</output>
<gadget id="calculator">117 / (13/2)</gadget>
<output>18</output>
<gadget id="calculator">18 - 6</gadget>
<output>12</output>
<result>12</result>


the length of a rectangular floor is more than its breadth by 200 % . if rs . 441 is required to paint the floor at the rate of rs . 3 / sq m , what would be the length of the floor ?

Explanation: "let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 441 / 3 = 147 sq m l b = 147 i . e . , l * l / 3 = 147 l ^ 2 = 441 = > l = 21 . d"

multiply(sqrt(divide(divide(441, 3), const_3)), const_3)

<gadget id="calculator">441 / 3</gadget>
<output>147</output>
<gadget id="calculator">147 / 3</gadget>
<output>49</output>
<gadget id="calculator">49 ** (1/2)</gadget>
<output>7</output>
<gadget id="calculator">7 * 3</gadget>
<output>21</output>
<result>21</result>


in a class of 42 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 10 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?

Explanation: "total # of students = 42 avg # of books per student = 2 total # of books = 42 * 2 = 84 # of student borrowed at least 3 books = 42 - 2 - 12 - 10 = 18 # of books borrowed by above 18 students = 84 - ( 12 * 1 ) + ( 10 * 2 ) = 52 considering that 17 out of above 18 students borrowed only 3 books , # of books borrowed = 17 * 3 = 51 so maximum # of books borrowed by any single student = 52 - 51 = 1 option a"

subtract(multiply(42, 2), add(multiply(subtract(subtract(42, add(add(multiply(12, 1), 10), 2)), 1), 3), add(multiply(12, 1), multiply(10, 2))))

<gadget id="calculator">42 * 2</gadget>
<output>84</output>
<gadget id="calculator">12 * 1</gadget>
<output>12</output>
<gadget id="calculator">12 + 10</gadget>
<output>22</output>
<gadget id="calculator">22 + 2</gadget>
<output>24</output>
<gadget id="calculator">42 - 24</gadget>
<output>18</output>
<gadget id="calculator">18 - 1</gadget>
<output>17</output>
<gadget id="calculator">17 * 3</gadget>
<output>51</output>
<gadget id="calculator">10 * 2</gadget>
<output>20</output>
<gadget id="calculator">12 + 20</gadget>
<output>32</output>
<gadget id="calculator">51 + 32</gadget>
<output>83</output>
<gadget id="calculator">84 - 83</gadget>
<output>1</output>
<result>1</result>


a set of consecutive positive integers beginning with 1 is written on the blackboard . a student came along and erased one number . the average of the remaining numbers is 35 * 7 / 17 . what was the number erased ?

Explanation: explanation : let the higher number be n and x be the number erased . then ( ( n ( n + 1 ) / 2 ) + x ) / ( n + 1 ) = 35 * 7 / 17 = 602 / 17 hence , n = 69 and x = 7 satisfy the above conditions . answer : a

subtract(multiply(divide(floor(multiply(add(35, divide(7, 17)), const_2)), const_2), subtract(floor(multiply(add(35, divide(7, 17)), const_2)), const_1)), multiply(add(35, divide(7, 17)), subtract(subtract(floor(multiply(add(35, divide(7, 17)), const_2)), const_1), 1)))

<gadget id="calculator">7 / 17</gadget>
<output>7/17 = around 0.411765</output>
<gadget id="calculator">35 + (7/17)</gadget>
<output>602/17 = around 35.411765</output>
<gadget id="calculator">(602/17) * 2</gadget>
<output>1_204/17 = around 70.823529</output>
<gadget id="calculator">floor(1_204/17)</gadget>
<output>70</output>
<gadget id="calculator">70 / 2</gadget>
<output>35</output>
<gadget id="calculator">70 - 1</gadget>
<output>69</output>
<gadget id="calculator">35 * 69</gadget>
<output>2_415</output>
<gadget id="calculator">69 - 1</gadget>
<output>68</output>
<gadget id="calculator">(602/17) * 68</gadget>
<output>2_408</output>
<gadget id="calculator">2_415 - 2_408</gadget>
<output>7</output>
<result>7</result>


find the number which is nearest to 3105 and is exactly divisible by 21 ?

Explanation: on dividing 3105 by 21 , we get 18 as remainder . number to be added to 3105 = ( 21 - 18 ) - 3 . hence , required number = 3105 + 3 = 3108 . answer e

<gadget id="calculator">3_105 % 21</gadget>
<output>18</output>
<gadget id="calculator">21 - 18</gadget>
<output>3</output>
<gadget id="calculator">3_105 + 3</gadget>
<output>3_108</output>
<result>3_108</result>


the lengths of the diagonals of a rhombus are 20 and 48 meters . find the perimeter of the rhombus ?

Explanation: below is shown a rhombus with the given diagonals . consider the right triangle boc and apply pythagora ' s theorem as follows bc 2 = 10 ^ 2 + 24 ^ 2 and evaluate bc bc = 26 meters . we now evaluate the perimeter p as follows : p = 4 * 26 = 104 meters . answer is d

<gadget id="calculator">20 / 2</gadget>
<output>10</output>
<gadget id="calculator">10 ** 2</gadget>
<output>100</output>
<result>100</result>


a courtyard is 21 meter long and 14 meter board is to be paved with bricks of dimensions 14 cm by 8 cm . the total number of bricks required is :

Explanation: "explanation : number of bricks = courtyard area / 1 brick area = ( 2100 ã — 1400 / 14 ã — 8 ) = 26250 option d"

divide(multiply(multiply(21, const_100), multiply(14, const_100)), multiply(14, 8))

<gadget id="calculator">21 * 100</gadget>
<output>2_100</output>
<gadget id="calculator">14 * 100</gadget>
<output>1_400</output>
<gadget id="calculator">2_100 * 1_400</gadget>
<output>2_940_000</output>
<gadget id="calculator">14 * 8</gadget>
<output>112</output>
<gadget id="calculator">2_940_000 / 112</gadget>
<output>26_250</output>
<result>26_250</result>


the average age of students of a class is 15.8 years . the average age of boys in the class is 16.3 years and that of the girls is 15.4 years . the ration of the number of boys to the number of girls in the class is ?

Explanation: "let the ratio be k : 1 . then , k * 16.3 + 1 * 15.4 = ( k + 1 ) * 15.8 = ( 16.3 - 15.8 ) k = ( 15.8 - 15.4 ) = k = 0.4 / 0.5 = 4 / 5 required ratio = 4 / 5 : 1 = 4 : 5 . answer : c"

<gadget id="calculator">15.8 - 15.4</gadget>
<output>0.4</output>
<gadget id="calculator">16.3 - 15.8</gadget>
<output>0.5</output>
<gadget id="calculator">0.4 / 0.5</gadget>
<output>0.8</output>
<result>0.8</result>


during the first two weeks of june , the total rainfall in springdale was 40 inches . if the rainfall during the second week was 1.5 times the rainfall during the first week , what was the rainfall in inches during the second week of june ?

Explanation: let x be the rainfall in the first week . then 1.5 x was the rainfall in the second week . 2.5 x = 40 x = 16 the rainfall during the second week was 1.5 * 16 = 24 inches the answer is d .

multiply(divide(40, add(const_1, 1.5)), 1.5)

<gadget id="calculator">1 + 1.5</gadget>
<output>2.5</output>
<gadget id="calculator">40 / 2.5</gadget>
<output>16</output>
<gadget id="calculator">16 * 1.5</gadget>
<output>24</output>
<result>24</result>