the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 148 , what is the difference between the ages of patrick and monica ?

Explanation: "ages of p and mi = 3 x + 5 x ages of mi and mo = 3 x : 5 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 25 x sum = 47 x = 148 x = 3 difference if ages of pa and mo = 25 x - 9 x = 16 x = 16 * 3 = 48 answer b"

subtract(multiply(multiply(5, 5), divide(148, add(add(multiply(3, 3), multiply(3, 5)), multiply(5, 5)))), multiply(multiply(3, 3), divide(148, add(add(multiply(3, 3), multiply(3, 5)), multiply(5, 5)))))

<gadget id="calculator">5 * 5</gadget>
<output>25</output>
<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">3 * 5</gadget>
<output>15</output>
<gadget id="calculator">9 + 15</gadget>
<output>24</output>
<gadget id="calculator">24 + 25</gadget>
<output>49</output>
<gadget id="calculator">148 / 49</gadget>
<output>148/49 = around 3.020408</output>
<gadget id="calculator">25 * (148/49)</gadget>
<output>3_700/49 = around 75.510204</output>
<gadget id="calculator">9 * (148/49)</gadget>
<output>1_332/49 = around 27.183673</output>
<gadget id="calculator">(3_700/49) - (1_332/49)</gadget>
<output>2_368/49 = around 48.326531</output>
<result>2_368/49 = around 48.326531</result>


you collect baseball cards . suppose you start out with 15 . maria takes half of one more than the number of baseball cards you have . since you ' re nice , you give peter 1 baseball card . since his father makes baseball cards , paul decides to triple your baseball cards . how many baseball cards do you have at the end ?

Explanation: solution start with 15 baseball cards . maria takes half of one more than the number of baseball cards you have . so maria takes half of 15 + 1 which is 8 , so you ' re left with 15 - 8 = 7 . peter takes 1 baseball card from you : 7 - 1 = 6 baseball cards . paul triples the number of baseball cards you have : 6 × 3 = 18 baseball cards . so you have 18 at the end . correct answer : b

multiply(subtract(subtract(subtract(15, const_4), const_4), 1), const_3)

<gadget id="calculator">15 - 4</gadget>
<output>11</output>
<gadget id="calculator">11 - 4</gadget>
<output>7</output>
<gadget id="calculator">7 - 1</gadget>
<output>6</output>
<gadget id="calculator">6 * 3</gadget>
<output>18</output>
<result>18</result>


xavier , yvonne , and zelda each try independently to solve a problem . if their individual probabilities for success are 1 / 4 , 2 / 3 and 5 / 8 , respectively , what is the probability that xavier and yvonne , but not zelda , will solve the problem ?

Explanation: p ( xavier will solve ) = 1 / 4 p ( yvonne will solve ) = 2 / 3 p ( zelda will not solve ) = 1 - 5 / 8 = 3 / 8 . now , we need to multiply all this ps to find an answer : p = ( 1 / 4 ) * ( 2 / 3 ) * ( 3 / 8 ) = 1 / 16 . ans . a .

multiply(multiply(divide(1, 4), divide(2, 3)), subtract(const_1, divide(5, 8)))

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(1/4) * (2/3)</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">5 / 8</gadget>
<output>5/8 = around 0.625</output>
<gadget id="calculator">1 - (5/8)</gadget>
<output>3/8 = around 0.375</output>
<gadget id="calculator">(1/6) * (3/8)</gadget>
<output>1/16 = around 0.0625</output>
<result>1/16 = around 0.0625</result>


in a certain lottery , the probability that a number between 1 and 15 , inclusive , is drawn is 1 / 3 . if the probability that a number 1 or larger is drawn is 2 / 3 , what is the probability that a number less than or equal to 15 is drawn ?

Explanation: you can simply use sets concept in this question . the formula total = n ( a ) + n ( b ) - n ( a and b ) is applicable here too . set 1 : number 1 or larger set 2 : number 15 or smaller 1 = p ( set 1 ) + p ( set 2 ) - p ( set 1 and set 2 ) ( combined probability is 1 because every number will be either 12 or moreor 20 or less or both ) 2 / 3 + p ( set 2 ) - 1 / 3 = 1 p ( set 2 ) = 2 / 3 answer a

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

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 + (1/3)</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(4/3) - (2/3)</gadget>
<output>2/3 = around 0.666667</output>
<result>2/3 = around 0.666667</result>


if x is less than y by 25 % then y exceed x by :

Explanation: "using formula ( x / ( 100 - x ) * 100 ) where x is percentage decrease ( here it is 25 % ) = > 25 ( 100 - 25 ) * 100 = 33.33 % answer : a"

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

<gadget id="calculator">100 - 25</gadget>
<output>75</output>
<gadget id="calculator">100 / 75</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">(4/3) - 1</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/3) * 100</gadget>
<output>100/3 = around 33.333333</output>
<result>100/3 = around 33.333333</result>


a pharmaceutical company received $ 8 million in royalties on the first $ 20 million in sales of the generic equivalent of one of its products and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percent did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ?

Explanation: "solution : this is a percent decrease problem . we will use the formula : percent change = ( new – old ) / old x 100 to calculate the final answer . we first set up the ratios of royalties to sales . the first ratio will be for the first 20 million in sales , and the second ratio will be for the next 108 million in sales . because all of the sales are in millions , we do not have to express all the trailing zeros in our ratios . first 20 million royalties / sales = 8 / 20 next 108 million royalties / sales = 9 / 108 = 1 / 12 because each ratio is not an easy number to use , we can simplify each one by multiplying each by the lcm of the two denominators , which is 60 . keep in mind that we are able to do this only because our answer choices are expressed in percents . first 20 million royalties / sales = ( 8 / 20 ) x 60 = 24 next 108 million royalties / sales = 9 / 108 = ( 1 / 12 ) x 60 = 5 we can plug 24 and 5 into our percent change formula : ( new – old ) / old x 100 [ ( 5 – 24 ) / 24 ] x 100 - 475 / 6 x 100 at this point we can stop and consider the answer choices . since we know that 475 / 6 is just a bit less than ½ , we know that - 475 / 6 x 100 is about a 79 % decrease . answer e ."

multiply(divide(subtract(multiply(divide(8, 20), const_100), multiply(divide(9, 108), const_100)), multiply(divide(8, 20), const_100)), const_100)

<gadget id="calculator">8 / 20</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) * 100</gadget>
<output>40</output>
<gadget id="calculator">9 / 108</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">(1/12) * 100</gadget>
<output>25/3 = around 8.333333</output>
<gadget id="calculator">40 - (25/3)</gadget>
<output>95/3 = around 31.666667</output>
<gadget id="calculator">(95/3) / 40</gadget>
<output>19/24 = around 0.791667</output>
<gadget id="calculator">(19/24) * 100</gadget>
<output>475/6 = around 79.166667</output>
<result>475/6 = around 79.166667</result>


a square with sides of 15 units each . what would be the area of the square . consider a square as a combination of two right angled triangles .

Explanation: a square can be considered as a set of two right angled triangles joined from the hypotenuse . since the sides are 10 units each . the height and base of both the triangles is 10 each . area of a right angled triangle is 1 / 2 * base * height area of both the triangles is 2 * 1 / 2 * base * height . since both triangles are similar . = base * height = 15 * 15 = 225 ans : c

<gadget id="calculator">(15 * 15) / 2</gadget>
<output>225/2 = around 112.5</output>
<gadget id="calculator">(225/2) * 2</gadget>
<output>225</output>
<result>225</result>


how many digits are required to number a book containing 240 pages ?

Explanation: 9 pages from 1 to 9 will require 9 digits . 90 pages from 10 to 99 will require 90 * 2 = 180 digits . 240 - ( 90 + 9 ) = 141 pages will require 141 * 3 = 423 digits . the total number of digits is 9 + 180 + 423 = 612 . the answer is b .

add(add(subtract(const_10, const_1), multiply(multiply(subtract(const_10, const_1), const_10), const_2)), multiply(add(subtract(240, const_100), const_1), const_3))

<gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">9 * 10</gadget>
<output>90</output>
<gadget id="calculator">90 * 2</gadget>
<output>180</output>
<gadget id="calculator">9 + 180</gadget>
<output>189</output>
<gadget id="calculator">240 - 100</gadget>
<output>140</output>
<gadget id="calculator">140 + 1</gadget>
<output>141</output>
<gadget id="calculator">141 * 3</gadget>
<output>423</output>
<gadget id="calculator">189 + 423</gadget>
<output>612</output>
<result>612</result>


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

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

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


george does 3 / 5 th of a piece of work in 9 days . he then calls in paul and they finish the work in 4 days . how long would paul take to do the work by himself ?

Explanation: "9 day 3 / 5 1 day 1 / 15 remaing 1 - 3 / 5 = 2 / 5 both can do 2 / 5 work in 4 day one day work of both = 1 / 10 therfor paul would take 1 / 10 - 1 / 15 = 1 / 30 or 30 days answer : c"

inverse(divide(subtract(subtract(const_1, divide(3, 5)), multiply(4, divide(const_1, multiply(5, 3)))), 4))

<gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">1 - (3/5)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">5 * 3</gadget>
<output>15</output>
<gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">4 * (1/15)</gadget>
<output>4/15 = around 0.266667</output>
<gadget id="calculator">(2/5) - (4/15)</gadget>
<output>2/15 = around 0.133333</output>
<gadget id="calculator">(2/15) / 4</gadget>
<output>1/30 = around 0.033333</output>
<gadget id="calculator">1 / (1/30)</gadget>
<output>30</output>
<result>30</result>


in august , a cricket team that played 120 matches won 24 % of the games it played . after a continuous winning streak , this team raised its average to 52 % . how many matches did the team win to attain this average ?

Explanation: let the no of matches played more = x so , ( 120 + x ) * 52 / 100 = 28.8 + x by solving we get x = 70 answer : d

divide(subtract(multiply(divide(52, const_100), 120), multiply(divide(24, const_100), 120)), subtract(const_1, divide(52, const_100)))

<gadget id="calculator">52 / 100</gadget>
<output>13/25 = around 0.52</output>
<gadget id="calculator">(13/25) * 120</gadget>
<output>312/5 = around 62.4</output>
<gadget id="calculator">24 / 100</gadget>
<output>6/25 = around 0.24</output>
<gadget id="calculator">(6/25) * 120</gadget>
<output>144/5 = around 28.8</output>
<gadget id="calculator">(312/5) - (144/5)</gadget>
<output>168/5 = around 33.6</output>
<gadget id="calculator">1 - (13/25)</gadget>
<output>12/25 = around 0.48</output>
<gadget id="calculator">(168/5) / (12/25)</gadget>
<output>70</output>
<result>70</result>


in a survey of 340 employees , 104 of them are uninsured , 54 work part time , and 12.5 percent of employees who are uninsured work part time . if a person is to be randomly selected from those surveyed , what is the probability that the person will neither work part time nor be uninsured ?

Explanation: - - - - - - - - - ui - - - - - - - - - - - - - - - - nui - - - - - - - total pt - - - - ( 12.5 / 100 ) * 104 = 13 - - - - - - - - - - - - - 54 npt - - - 104 - 13 - - - - - - - - - - - - - - x - - - - - - - - 286 total - - 104 - - - - - - - - - - - - - - - - - - - - - - - - - - - - 340 we have to find not part time and not uninsured . in other words not part time and insured = x / 340 = ( 286 - 104 + 13 ) / 340 = 39 / 68 answer is c .

divide(subtract(340, add(subtract(54, divide(multiply(12.5, 104), multiply(const_1, const_100))), 104)), 340)

<gadget id="calculator">12.5 * 104</gadget>
<output>1_300</output>
<gadget id="calculator">1 * 100</gadget>
<output>100</output>
<gadget id="calculator">1_300 / 100</gadget>
<output>13</output>
<gadget id="calculator">54 - 13</gadget>
<output>41</output>
<gadget id="calculator">41 + 104</gadget>
<output>145</output>
<gadget id="calculator">340 - 145</gadget>
<output>195</output>
<gadget id="calculator">195 / 340</gadget>
<output>39/68 = around 0.573529</output>
<result>39/68 = around 0.573529</result>


a ( 3 , w ^ 3 ) is the ( x , y ) coordinate of point located on the parabola y = x ^ 2 - 1 . what is the value of w ?

Explanation: y = x ^ 2 - 1 w ^ 3 = 3 ^ 2 - 1 w ^ 3 = 8 w = 2 answer a

power(subtract(power(3, 2), 1), divide(1, 3))

<gadget id="calculator">3 ** 2</gadget>
<output>9</output>
<gadget id="calculator">9 - 1</gadget>
<output>8</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">8 ** (1/3)</gadget>
<output>2</output>
<result>2</result>


in x game of billiards , x can give y 20 points in 60 and he can give z 30 points in 60 . how many points can y give z in x game of 120 ?

Explanation: x scores 60 while y score 40 and z scores 30 . the number of points that z scores when y scores 120 = ( 120 * 30 ) / 40 = 90 . in x game of 100 points , y gives ( 120 - 90 ) = 30 points to c . a

subtract(multiply(subtract(60, 20), const_3), multiply(subtract(60, 30), const_3))

<gadget id="calculator">60 - 20</gadget>
<output>40</output>
<gadget id="calculator">40 * 3</gadget>
<output>120</output>
<gadget id="calculator">60 - 30</gadget>
<output>30</output>
<gadget id="calculator">30 * 3</gadget>
<output>90</output>
<gadget id="calculator">120 - 90</gadget>
<output>30</output>
<result>30</result>


a house wife saved $ 2.50 in buying an item on sale . if she spent $ 25 for the item , approximately how much percent she saved in the transaction ?

Explanation: actual price = 25 + 2.50 = $ 27.50 saving = 2.50 / 27.50 * 100 = 100 / 11 = 9 % approximately answer is b

multiply(divide(2.5, add(25, 2.5)), const_100)

<gadget id="calculator">25 + 2.5</gadget>
<output>27.5</output>
<gadget id="calculator">2.5 / 27.5</gadget>
<output>0.090909</output>
<gadget id="calculator">0.090909 * 100</gadget>
<output>9.0909</output>
<result>9.0909</result>


after successive discounts of 20 % , 10 % and 5 % a certain good is sold for rs . 6700 . find the actual price of the good .

Explanation: let actual price was 100 . after three successive discount this will become , 100 = = 20 % discount = > 80 = = 10 % discount = > 72 = = 5 % discount = 68.4 now compare , 68.4 = 6700 1 = 6700 / 68.4 100 = ( 6700 * 100 ) / 68.4 = rs . 9795 . answer : option d

divide(multiply(6700, const_100), subtract(subtract(subtract(const_100, 20), divide(multiply(subtract(const_100, 20), 10), const_100)), divide(multiply(subtract(subtract(const_100, 20), divide(multiply(subtract(const_100, 20), 10), const_100)), 5), const_100)))

<gadget id="calculator">6_700 * 100</gadget>
<output>670_000</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">80 * 10</gadget>
<output>800</output>
<gadget id="calculator">800 / 100</gadget>
<output>8</output>
<gadget id="calculator">80 - 8</gadget>
<output>72</output>
<gadget id="calculator">72 * 5</gadget>
<output>360</output>
<gadget id="calculator">360 / 100</gadget>
<output>18/5 = around 3.6</output>
<gadget id="calculator">72 - (18/5)</gadget>
<output>342/5 = around 68.4</output>
<gadget id="calculator">670_000 / (342/5)</gadget>
<output>1_675_000/171 = around 9_795.321637</output>
<result>1_675_000/171 = around 9_795.321637</result>


in a factory , an average of 60 tv ' s are produced per day for the fist 25 days of the months . a few workers fell ill for the next 5 days reducing the daily avg for the month to 58 sets / day . the average production per day for day last 5 days is ?

Explanation: production during these 5 days = total production in a month - production in first 25 days . = 30 x 58 - 25 x 60 = 240 ∴ average for last 5 days = 240 / 5 = 48 c

divide(subtract(multiply(add(25, 5), 58), multiply(25, 60)), 5)

<gadget id="calculator">25 + 5</gadget>
<output>30</output>
<gadget id="calculator">30 * 58</gadget>
<output>1_740</output>
<gadget id="calculator">25 * 60</gadget>
<output>1_500</output>
<gadget id="calculator">1_740 - 1_500</gadget>
<output>240</output>
<gadget id="calculator">240 / 5</gadget>
<output>48</output>
<result>48</result>


the ratio between the present ages of a and b is 5 : 3 respectively . the ratio between a ' s age 4 years ago and b ' s age 4 years hence is 1 : 1 . what is the ratio between a ' s age 4 years hence and b ' s age 4 years ago ?

Explanation: "let the present ages of a and b be 5 x and 3 x years respectively . then , ( 5 x - 4 ) / ( 3 x + 4 ) = 1 / 1 2 x = 8 = > x = 4 required ratio = ( 5 x + 4 ) : ( 3 x - 4 ) = 24 : 8 = 3 : 1 answer : c"

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

<gadget id="calculator">5 + 5</gadget>
<output>10</output>
<gadget id="calculator">5 - 3</gadget>
<output>2</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">5 * 5</gadget>
<output>25</output>
<gadget id="calculator">25 + 5</gadget>
<output>30</output>
<gadget id="calculator">3 * 5</gadget>
<output>15</output>
<gadget id="calculator">15 - 5</gadget>
<output>10</output>
<gadget id="calculator">30 / 10</gadget>
<output>3</output>
<result>3</result>


in n is a positive integer less than 200 , and 14 n / 60 is an integer , then n has how many different positive prime factors s ?

Explanation: "i like to put the numbers in prime factors so it is easier and faster to visualize . 14 * n / 60 if we write the factors of 14 - - > 2 , 7 , and the factors of 60 - - > 2 , 2 , 3 , 5 , we have ( 2 * 7 * n ) / ( 2 ^ 2 * 3 * 5 ) simplifying 7 * n / ( 2 * 3 * 5 ) the only way the equation above has an integer value is if n has at least the factors 2 , 3 and 5 , so we can simplify again and we have the number 7 . the number could be 2 * 3 * 5 , or 2 * 3 * 5 * 2 , or 2 * 3 * 5 * . . . . . however to be less than 200 we can not add any prime number . 2 * 3 * 5 = 120 if we added the next prime factor 7 , we would have s = 2 * 3 * 5 * 7 = 840 thus , answer b"

add(divide(add(const_1, const_4), divide(divide(divide(60, const_2), const_2), const_3)), const_2)

<gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">60 / 2</gadget>
<output>30</output>
<gadget id="calculator">30 / 2</gadget>
<output>15</output>
<gadget id="calculator">15 / 3</gadget>
<output>5</output>
<gadget id="calculator">5 / 5</gadget>
<output>1</output>
<gadget id="calculator">1 + 2</gadget>
<output>3</output>
<result>3</result>


an equilateral triangle t 2 is formed by joining the mid points of the sides of another equilateral triangle t 1 . a third equilateral triangle t 3 is formed by joining the mid - points of t 2 and this process is continued indefinitely . if each side of t 1 is 40 cm , find the sum of the perimeters of all the triangles .

Explanation: we have 40 for first triangle , when we join mid - points of first triangle we get the second equilateral traingle then the length of second one is 20 and continues . so we have 40 , 20,10 , . . . we have ratio = 1 / 2 , and it is gp type . sum of infinite triangle is a / 1 - r = 40 / 1 - ( 1 / 2 ) = 80 equilateral triangle perimeter is 3 a = 3 * 80 = 240 . so option c .

add(triangle_perimeter(40, 40, 40), triangle_perimeter(40, 40, 40))

<gadget id="calculator">40 + 40 + 40</gadget>
<output>120</output>
<gadget id="calculator">120 + 120</gadget>
<output>240</output>
<result>240</result>


two pipes a and b can fill a tank in 10 hours and 20 hours respectively . if both the pipes are opened simultaneously , how much time will be taken to fill the tank ?

Explanation: "part filled by a in 1 hour = 1 / 10 part filled by b in 1 hour = 1 / 20 part filled by ( a + b ) in 1 hour = 1 / 10 + 1 / 20 = 3 / 20 both the pipes together fill the tank in 20 / 3 hours answer is b"

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

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


the number obtained by interchanging the digits of a two - digit number is less than the original number by 36 . the sum of the digits of the number is 8 . what is the original number ?

Explanation: explanation : let the number be 10 x + y . ∴ x + y = 8 . . . . . ( i ) 10 x + y - ( 10 y + x ) = 36 ∴ 9 ( x - y ) = 3 ∴ x - y = 4 . . . . . . . ( ii ) from equation ( i ) and ( ii ) : x = 6 , y = 2 ∴ number = 62 answer : option b

add(multiply(subtract(8, divide(36, add(const_10, 8))), const_10), divide(36, add(const_10, 8)))

<gadget id="calculator">10 + 8</gadget>
<output>18</output>
<gadget id="calculator">36 / 18</gadget>
<output>2</output>
<gadget id="calculator">8 - 2</gadget>
<output>6</output>
<gadget id="calculator">6 * 10</gadget>
<output>60</output>
<gadget id="calculator">60 + 2</gadget>
<output>62</output>
<result>62</result>


in one alloy there is 10 % chromium while in another alloy it is 6 % . 15 kg of the first alloy was melted together with 35 kg of the second one to form a third alloy . find the percentage of chromium in the new alloy .

Explanation: "the amount of chromium in the new 15 + 35 = 50 kg alloy is 0.10 * 15 + 0.06 * 35 = 3.6 kg , so the percentage is 3.6 / 50 * 100 = 7.2 % . answer : a ."

multiply(divide(add(divide(multiply(10, 15), const_100), divide(multiply(6, 35), const_100)), add(15, 35)), const_100)

<gadget id="calculator">10 * 15</gadget>
<output>150</output>
<gadget id="calculator">150 / 100</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">6 * 35</gadget>
<output>210</output>
<gadget id="calculator">210 / 100</gadget>
<output>21/10 = around 2.1</output>
<gadget id="calculator">(3/2) + (21/10)</gadget>
<output>18/5 = around 3.6</output>
<gadget id="calculator">15 + 35</gadget>
<output>50</output>
<gadget id="calculator">(18/5) / 50</gadget>
<output>9/125 = around 0.072</output>
<gadget id="calculator">(9/125) * 100</gadget>
<output>36/5 = around 7.2</output>
<result>36/5 = around 7.2</result>


the food in a camp lasts for 10 men for 20 days . if 30 more men join , how many days will the food last ?

Explanation: "one man can consume the same food in 10 * 20 = 200 days . 30 more men join , the total number of men = 40 the number of days the food will last = 200 / 40 = 5 days . answer : c"

<gadget id="calculator">10 * 20</gadget>
<output>200</output>
<gadget id="calculator">10 + 30</gadget>
<output>40</output>
<gadget id="calculator">200 / 40</gadget>
<output>5</output>
<result>5</result>


surface area of a sphere is 2464 cm 2 . if its radius is doubled , then the surface area of the new sphere will be

Explanation: sol . let the original radius be r . then , original surface area = 4 π r 2 = 2464 cm 2 ( given ) . new radius = 2 r . ∴ new surface area = 4 π ( 2 r ) 2 = 4 x 4 π r 2 = ( 4 x 2464 ) cm 2 = 9856 cm 2 answer c

surface_sphere(multiply(sqrt(divide(2464, multiply(const_4, const_pi))), const_2))

<gadget id="calculator">4 * pi</gadget>
<output>4*pi = around 12.566371</output>
<gadget id="calculator">2_464 / (4*pi)</gadget>
<output>616/pi = around 196.07889</output>
<gadget id="calculator">(616/pi) ** (1/2)</gadget>
<output>2*sqrt(154)/sqrt(pi) = around 14.002817</output>
<gadget id="calculator">(2*sqrt(154)/sqrt(pi)) * 2</gadget>
<output>4*sqrt(154)/sqrt(pi) = around 28.005634</output>
<gadget id="calculator">4 * pi * ((4*sqrt(154)/sqrt(pi)) ** 2)</gadget>
<output>9_856</output>
<result>9_856</result>


how long does a train 100 m long travelling at 60 kmph takes to cross a bridge of 80 m in length ?

Explanation: "d 16.8 sec d = 100 + 80 = 180 m s = 60 * 5 / 18 = 50 / 3 t = 180 * 3 / 50 = 10.8 sec"

<gadget id="calculator">100 + 80</gadget>
<output>180</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">60 * (5/18)</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">180 / (50/3)</gadget>
<output>54/5 = around 10.8</output>
<result>54/5 = around 10.8</result>


Explanation: "given exp . = - 74 x ( 30 - 1 ) + 265 = - ( 74 x 30 ) + 74 + 265 = - 2220 + 339 = - 1881 answer is b"

multiply(subtract(const_1, const_2), subtract(multiply(74, 29), 265))

<gadget id="calculator">1 - 2</gadget>
<output>-1</output>
<gadget id="calculator">74 * 29</gadget>
<output>2_146</output>
<gadget id="calculator">2_146 - 265</gadget>
<output>1_881</output>
<gadget id="calculator">(-1) * 1_881</gadget>
<output>-1_881</output>
<result>-1_881</result>


the population of 6 villages is 803 , 9001100 , 1023945 and 980 . what is the population of the seventh village if the average population of the 7 villages is 1000 ?

Explanation: population of seventh village = 7 * 1000 - ( 803 + 900 + 1100 + 1023 + 945 + 980 ) = 1249 answer is e

subtract(multiply(1000, 7), add(add(const_10, const_10), subtract(subtract(multiply(980, 6), multiply(7, 7)), const_100)))

<gadget id="calculator">1_000 * 7</gadget>
<output>7_000</output>
<gadget id="calculator">10 + 10</gadget>
<output>20</output>
<gadget id="calculator">980 * 6</gadget>
<output>5_880</output>
<gadget id="calculator">7 * 7</gadget>
<output>49</output>
<gadget id="calculator">5_880 - 49</gadget>
<output>5_831</output>
<gadget id="calculator">5_831 - 100</gadget>
<output>5_731</output>
<gadget id="calculator">20 + 5_731</gadget>
<output>5_751</output>
<gadget id="calculator">7_000 - 5_751</gadget>
<output>1_249</output>
<result>1_249</result>


Explanation: "we ' re told that 625 ^ ( - x ) + 25 ^ ( - 2 x ) + 5 ^ ( - 4 x ) = 15 . we ' re asked for the value of x . since each of the calculated terms must be positive ( regardless of what the exponent is ) , we can use thebasesto our advantage . . . . . with answer a , we ' d have 625 ^ 4 , which is much bigger than 15 ( and we ' d be adding to that big number ) . eliminate a . with answer e , we ' d have 625 ^ ( - 4 ) , which would create a tiny fraction ( and we ' d add some other fractions to it , so the total would be much too small ) . eliminate e . with answer d , we ' d have 625 ^ ( - 1 / 4 ) , which will also be a fraction ( just not as tiny as the one in answer e ) , but the total would still be too small . eliminate d . with answer c , anything to the ' 0 power ' is 1 , so we ' d have 1 + 1 + 1 = 3 . this is not 15 . eliminate c . d"

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<result>1/4 = around 0.25</result>


the radius of the wheel of a bus is 70 cms and the speed of the bus is 66 km / h , then the r . p . m . ( revolutions per minutes ) of the wheel is

Explanation: "radius of the wheel of bus = 70 cm . then , circumference of wheel = 2 π r = 140 π = 440 cm distance covered by bus in 1 minute = 66 ⁄ 60 × 1000 × 100 cms distance covered by one revolution of wheel = circumference of wheel = 440 cm ∴ revolutions per minute = 6600000 / 60 × 440 = 250 answer b"

divide(divide(multiply(const_100, multiply(const_1000, 66)), multiply(const_60, const_1)), multiply(multiply(const_2, 70), add(const_3, divide(add(const_2, multiply(const_3, const_4)), power(add(const_2, multiply(const_4, const_2)), const_2)))))

<gadget id="calculator">1_000 * 66</gadget>
<output>66_000</output>
<gadget id="calculator">100 * 66_000</gadget>
<output>6_600_000</output>
<gadget id="calculator">60 * 1</gadget>
<output>60</output>
<gadget id="calculator">6_600_000 / 60</gadget>
<output>110_000</output>
<gadget id="calculator">2 * 70</gadget>
<output>140</output>
<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">2 + 12</gadget>
<output>14</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">2 + 8</gadget>
<output>10</output>
<gadget id="calculator">10 ** 2</gadget>
<output>100</output>
<gadget id="calculator">14 / 100</gadget>
<output>7/50 = around 0.14</output>
<gadget id="calculator">3 + (7/50)</gadget>
<output>157/50 = around 3.14</output>
<gadget id="calculator">140 * (157/50)</gadget>
<output>2_198/5 = around 439.6</output>
<gadget id="calculator">110_000 / (2_198/5)</gadget>
<output>275_000/1_099 = around 250.22748</output>
<result>275_000/1_099 = around 250.22748</result>


harry started a 4 - mile hike with a full 6 - cup canteen of water and finished the hike in 2 hours with 1 cup of water remaining in the canteen . if the canteen leaked at the rate of 1 cup per hour and harry drank 1 cups of water during the last mile , how many cups did he drink per mile during the first 3 miles of the hike ?

Explanation: no of cups leaked during the trip = 2 cups . no of cups harry drank = 3 cups . no of cups harry drank during the first 3 miles = 2 . drink / mile = 2 / 3 answer : b

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

<gadget id="calculator">6 - 2</gadget>
<output>4</output>
<gadget id="calculator">4 - 1</gadget>
<output>3</output>
<gadget id="calculator">3 - 1</gadget>
<output>2</output>
<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<result>2/3 = around 0.666667</result>


two taps a and b can fill a cistern in 12 minutes and 18 minutes respectively . they are turned on at the same time . if the tap a is turned off after 4 minutes , how long will tap b take to fill the rest of the cistern ?

Explanation: in one min , ( a + b ) fill the cistern = 1 ⁄ 12 + 1 ⁄ 18 = 5 ⁄ 36 th in 4 min , ( a + b ) fill the cistern = 5 ⁄ 36 × 4 = 5 ⁄ 9 th rest part = 1 - 5 ⁄ 9 = 4 ⁄ 9 th ∵ 1 ⁄ 18 th part is filled by b in one min . ∴ 4 ⁄ 9 th part is filled by b in 18 × 4 ⁄ 9 = 8 min answer a

divide(subtract(const_1, multiply(add(divide(const_1, 12), divide(const_1, 18)), 4)), divide(const_1, 18))

<gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">1 / 18</gadget>
<output>1/18 = around 0.055556</output>
<gadget id="calculator">(1/12) + (1/18)</gadget>
<output>5/36 = around 0.138889</output>
<gadget id="calculator">(5/36) * 4</gadget>
<output>5/9 = around 0.555556</output>
<gadget id="calculator">1 - (5/9)</gadget>
<output>4/9 = around 0.444444</output>
<gadget id="calculator">(4/9) / (1/18)</gadget>
<output>8</output>
<result>8</result>


jack and christina are standing 240 feet apart on a level surface . their dog , lindy , is standing next to christina . at the same time , they all begin moving toward each other . jack walks in a straight line toward christina at a constant speed of 3 feet per second and christina walks in a straight line toward jack at a constant speed of 3 feet per second . lindy runs at a constant speed of 10 feet per second from christina to jack , back to christina , back to jack , and so forth . what is the total distance , in feet , that lindy has traveled when the three meet at one place ?

Explanation: "the relative speed of jack and christina is 3 + 3 = 6 feet per second . the distance between them is 210 feet , hence they will meet in ( time ) = ( distance ) / ( relative speed ) = 240 / 6 = 40 seconds . for all this time lindy was running back and forth , so it covered ( distance ) = ( speed ) * ( time ) = 10 * 40 = 400 feet . answer : d ."

<gadget id="calculator">3 + 3</gadget>
<output>6</output>
<gadget id="calculator">240 / 6</gadget>
<output>40</output>
<gadget id="calculator">40 * 10</gadget>
<output>400</output>
<result>400</result>


a solution of 70 litres contains oil and water in the ratio 9 : x . if 6 litres of water is added to the solution , the ratio becomes 6 : 4 , find the value of x ?

Explanation: exp . total new quantity = original sol + water = 70 + 6 = 76 new ratio = 6 : 4 , new quantity of oil = 6 / 10 * 76 = 45.6 lit , new quantity of water = 4 / 10 * 76 = 30.4 lit water present initially = ( 30.4 - 6 ) = 24.4 lit ratio = 45.6 / 24.4 = 9 / x there for x = 4.81 approx 5 answer : e

divide(9, divide(subtract(70, subtract(multiply(4, divide(add(70, 6), add(6, 4))), 6)), subtract(multiply(4, divide(add(70, 6), add(6, 4))), 6)))

<gadget id="calculator">70 + 6</gadget>
<output>76</output>
<gadget id="calculator">6 + 4</gadget>
<output>10</output>
<gadget id="calculator">76 / 10</gadget>
<output>38/5 = around 7.6</output>
<gadget id="calculator">4 * (38/5)</gadget>
<output>152/5 = around 30.4</output>
<gadget id="calculator">(152/5) - 6</gadget>
<output>122/5 = around 24.4</output>
<gadget id="calculator">70 - (122/5)</gadget>
<output>228/5 = around 45.6</output>
<gadget id="calculator">(228/5) / (122/5)</gadget>
<output>114/61 = around 1.868852</output>
<gadget id="calculator">9 / (114/61)</gadget>
<output>183/38 = around 4.815789</output>
<result>183/38 = around 4.815789</result>


if a , b , c , d , e and f are integers and ( ab + cdef ) < 0 , then what is the maximum number d of integers that can be negative ?

Explanation: "minimuum should be 1 maximum should be 4 : 1 out of a or b to make the multiplication negative 3 out of c , d , e or f to make the multiplication negative . negative + negative < 0 answer : c maximum will be 5 . . you dont require both the multiplicatin to be negative for entire equation to be negative . . . any one a or b can be negative to make ab negative and it can still be more ( away from 0 ) than the multiplication of 4 other - ve numbers . . . actually by writing minimum required as 1 out of 6 , you are actually meaning 5 out of 6 also possible as you will see d = 5 or 1 will give you same equation . . ans d"

<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">5 + 0</gadget>
<output>5</output>
<result>5</result>


the length of the rectangular field is double its width . inside the field there is square shaped pond 6 m long . if the area of the pond is 1 / 8 of the area of the field . what is the length of the field ?

Explanation: "a / 8 = 6 * 6 = > a = 6 * 6 * 8 x * 2 x = 6 * 6 * 8 x = 12 = > 2 x = 24 answer : a"

<gadget id="calculator">6 ** 2</gadget>
<output>36</output>
<gadget id="calculator">36 * 8</gadget>
<output>288</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">288 / (1/2)</gadget>
<output>576</output>
<gadget id="calculator">576 ** (1/2)</gadget>
<output>24</output>
<result>24</result>


the area of a triangle is with base 2 m and height 3 m ?

Explanation: "1 / 2 * 2 * 3 = 3 m 2 answer : d"

<gadget id="calculator">(2 * 3) / 2</gadget>
<output>3</output>
<result>3</result>


if the price of a certain computer increased 30 percent from c dollars to 351 dollars , then 2 c =

Explanation: "before price increase price = c after 30 % price increase price = c + ( 30 / 100 ) * c = 1.3 c = 351 ( given ) i . e . c = 351 / 1.3 = $ 270 i . e . 2 c = 2 * 270 = 540 answer : option a"

multiply(divide(351, divide(add(const_100, 30), const_100)), 2)

<gadget id="calculator">100 + 30</gadget>
<output>130</output>
<gadget id="calculator">130 / 100</gadget>
<output>13/10 = around 1.3</output>
<gadget id="calculator">351 / (13/10)</gadget>
<output>270</output>
<gadget id="calculator">270 * 2</gadget>
<output>540</output>
<result>540</result>


the purchase price of an article is $ 48 . in order to include 5 % of cost for overhead and to provide $ 12 of net profit , the markup should be

Explanation: "cost price of article = 48 $ % of overhead cost = 5 net profit = 12 $ we need to calculate % markup net profit as % of cost price = ( 12 / 48 ) * 100 = 25 % total markup should be = 25 + 5 = 30 % answer c"

add(multiply(divide(12, 48), const_100), 5)

<gadget id="calculator">12 / 48</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<gadget id="calculator">25 + 5</gadget>
<output>30</output>
<result>30</result>


a store reduced the price of all items in the store by 12 % on the first day and by another 10 % on the second day . the price of items on the second day was what percent of the price before the first reduction took place ?

Explanation: "consider price of the all items as $ 100 after a initial reduction of 12 % price becomes = 0.88 * 100 = $ 88 after the final reduction of 10 % price becomes = 0.9 * 88 = $ 79.2 price of all items on second day is 79.2 % of price on first day correct answer option b"

multiply(multiply(divide(subtract(const_100, 12), const_100), divide(subtract(const_100, 10), const_100)), const_100)

<gadget id="calculator">100 - 12</gadget>
<output>88</output>
<gadget id="calculator">88 / 100</gadget>
<output>22/25 = around 0.88</output>
<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">90 / 100</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">(22/25) * (9/10)</gadget>
<output>99/125 = around 0.792</output>
<gadget id="calculator">(99/125) * 100</gadget>
<output>396/5 = around 79.2</output>
<result>396/5 = around 79.2</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 10 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 + 10 x = 15.5 minutes answer : c"

subtract(subtract(divide(const_60, const_2), 10), divide(const_60, divide(20, 1.5)))

<gadget id="calculator">60 / 2</gadget>
<output>30</output>
<gadget id="calculator">30 - 10</gadget>
<output>20</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">20 - 4.5</gadget>
<output>15.5</output>
<result>15.5</result>


when the smallest of 3 consecutive odd integers is added to 4 times the largest , it produces a result 732 more than 4 times the middle integer . find the numbers ?

Explanation: x + 4 ( x + 4 ) = 732 + 4 ( x + 2 ) solve for x and find all three numbers x + 4 x + 16 = 732 + 4 x + 8 x = 724 x + 2 = 726 x + 4 = 728 check : the smallest is added to four times the largest 724 + 4 * 728 = 3636 four times the middle 4 * 726 = 2904 3636 is more than 2904 by 3636 - 2904 = 732 a

divide(subtract(add(732, multiply(4, const_2)), multiply(4, const_4)), subtract(add(const_1, 4), 4))

<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">732 + 8</gadget>
<output>740</output>
<gadget id="calculator">4 * 4</gadget>
<output>16</output>
<gadget id="calculator">740 - 16</gadget>
<output>724</output>
<gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">5 - 4</gadget>
<output>1</output>
<gadget id="calculator">724 / 1</gadget>
<output>724</output>
<result>724</result>


in a particular city there are 100 homes numbered from 1 , 23 , . . , 100 . the city was build by a builder from chennai . there was 4 to 5 shops in the town which was build by a builder from mumbai . the 2 nd builder can build in 1 ½ times as compared to time by 1 st builder . the 2 nd builder builds in 15 days , then how many 2 ' s are used by the builder from chennai in numbering the 100 homes ?

Explanation: in the last line it should be given the builder from chennai in numbering the 100 homes ? then ans is 20 answer : d

<gadget id="calculator">15 - 5</gadget>
<output>10</output>
<gadget id="calculator">10 * 2</gadget>
<output>20</output>
<result>20</result>


p and q can complete a work in 40 days and 24 days respectively . p alone started the work and q joined him after 8 days till the completion of the work . how long did the work last ?

Explanation: "explanation : work done by p in 1 day = 1 / 40 work done by q in 1 day = 1 / 24 work done by p in 8 days = 8 ã — ( 1 / 40 ) = 1 / 5 remaining work = 1 â € “ 1 / 5 = 4 / 5 work done by p and q in 1 day = 1 / 40 + 1 / 24 = 1 / 15 number of days p and q take to complete the remaining work = ( 4 / 5 ) / ( 1 / 15 ) = 12 total days = 8 + 12 = 20 answer : option d"

add(8, divide(subtract(const_1, divide(8, 40)), add(inverse(40), inverse(24))))

<gadget id="calculator">8 / 40</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 / 40</gadget>
<output>1/40 = around 0.025</output>
<gadget id="calculator">1 / 24</gadget>
<output>1/24 = around 0.041667</output>
<gadget id="calculator">(1/40) + (1/24)</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">(4/5) / (1/15)</gadget>
<output>12</output>
<gadget id="calculator">8 + 12</gadget>
<output>20</output>
<result>20</result>


joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 4 of all the paint . during the second week , he uses 1 / 2 of the remaining paint . how many gallons of paint has joe used ?

Explanation: "total paint initially = 360 gallons paint used in the first week = ( 1 / 4 ) * 360 = 90 gallons . remaning paint = 270 gallons paint used in the second week = ( 1 / 2 ) * 270 = 135 gallons total paint used = 225 gallons . option b"

add(multiply(divide(360, 4), 1), divide(subtract(360, multiply(divide(360, 4), 1)), 2))

<gadget id="calculator">360 / 4</gadget>
<output>90</output>
<gadget id="calculator">90 * 1</gadget>
<output>90</output>
<gadget id="calculator">360 - 90</gadget>
<output>270</output>
<gadget id="calculator">270 / 2</gadget>
<output>135</output>
<gadget id="calculator">90 + 135</gadget>
<output>225</output>
<result>225</result>


a computer manufacturer produces a certain electronic component at a cost of $ 80 per component . shipping costs for delivering the components are $ 5 per unit . further , the manufacturer has costs of $ 16500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 150 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?

Explanation: by the question , the equation would be 150 p - 85 * 150 - 16500 = 0 p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component . solving the equation , we get p = $ 195 . answer e for me .

<gadget id="calculator">80 + 5</gadget>
<output>85</output>
<gadget id="calculator">85 * 150</gadget>
<output>12_750</output>
<gadget id="calculator">12_750 + 16_500</gadget>
<output>29_250</output>
<gadget id="calculator">29_250 / 150</gadget>
<output>195</output>
<result>195</result>


the average runs scored by a batsman in 30 matches is 50 . in the next 15 matches the batsman scored an average of 26 runs . find his average in all the 45 matches ?

Explanation: total score of the batsman in 30 matches = 1500 . total score of the batsman in the next 15 matches = 390 . total score of the batsman in the 30 matches = 1890 . average score of the batsman = 1890 / 45 = 42 . answer : b

divide(add(multiply(50, 30), multiply(26, 15)), add(30, 15))

<gadget id="calculator">50 * 30</gadget>
<output>1_500</output>
<gadget id="calculator">26 * 15</gadget>
<output>390</output>
<gadget id="calculator">1_500 + 390</gadget>
<output>1_890</output>
<gadget id="calculator">30 + 15</gadget>
<output>45</output>
<gadget id="calculator">1_890 / 45</gadget>
<output>42</output>
<result>42</result>


the owner of a furniture shop charges his customer 60 % more than the cost price . if a customer paid rs . 2000 for a computer table , then what was the cost price of the computer table ?

Explanation: "cp = sp * ( 100 / ( 100 + profit % ) ) = 1250 ( 100 / 160 ) = rs . 1250 . answer : c"

divide(2000, add(const_1, divide(60, const_100)))

<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">1 + (3/5)</gadget>
<output>8/5 = around 1.6</output>
<gadget id="calculator">2_000 / (8/5)</gadget>
<output>1_250</output>
<result>1_250</result>


a shipment of 240 smartphones contains 84 that are defective . if a customer buys two smartphones at random from the shipment , what is the approximate probability that both phones are defective ?

Explanation: "probability of chosing one defective phone from a lot of 240 which ontains 84 defective phones is = ( 84 / 240 ) probability of chosing one defective phone from a lot of 239 ( we already picked one ) which ontains 83 ( we already picked one ) defective phones is = ( 83 / 239 ) combined probability of series of events = product of the probabilities = ( 84 / 240 ) * ( 83 / 239 ) 84 / 240 is close to ( 7 / 20 ) and ( 83 / 239 ) = ( 25 / 72 ) so answer is ( 7 / 20 ) * ( 25 / 72 ) ( 9 / 74 ) so , answer will be b"

divide(multiply(84, subtract(84, const_1)), multiply(240, subtract(240, const_1)))

<gadget id="calculator">84 - 1</gadget>
<output>83</output>
<gadget id="calculator">84 * 83</gadget>
<output>6_972</output>
<gadget id="calculator">240 - 1</gadget>
<output>239</output>
<gadget id="calculator">240 * 239</gadget>
<output>57_360</output>
<gadget id="calculator">6_972 / 57_360</gadget>
<output>581/4_780 = around 0.121548</output>
<result>581/4_780 = around 0.121548</result>


set a { 3 , 3,3 , 4,5 , 5,5 } has a standard deviation of 1 . what will the standard deviation be if every number in the set is multiplied by 8 ?

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

<gadget id="calculator">8 * 1</gadget>
<output>8</output>
<result>8</result>


the length of a room is 5.5 m and width is 3.75 m . what is the cost of paying the floor by slabs at the rate of $ 600 per sq . metre .

Explanation: "a area = 5.5 × 3.75 sq . metre . cost for 1 sq . metre . = $ 600 hence , total cost = 5.5 × 3.75 × 600 = $ 12375 a"

<gadget id="calculator">5.5 * 3.75</gadget>
<output>20.625</output>
<gadget id="calculator">600 * 20.625</gadget>
<output>12_375</output>
<result>12_375</result>


what is the sum of the multiples of 4 between 63 and 151 inclusive ?

Explanation: "the fastest way in an ap is to find the average and multiply with total integers . . between 63 and 151 , the smallest multiple of 4 is 64 and largest = 148 . . average = ( 64 + 148 ) / 2 = 106 . . total numbers = ( 148 - 64 ) / 4 + 1 = 21 + 1 = 22 . . sum = 22 * 106 = 2332 ans e"

multiply(divide(add(subtract(151, const_3), add(63, const_2)), const_2), add(divide(subtract(subtract(151, const_3), add(63, const_2)), 4), const_1))

<gadget id="calculator">151 - 3</gadget>
<output>148</output>
<gadget id="calculator">63 + 2</gadget>
<output>65</output>
<gadget id="calculator">148 + 65</gadget>
<output>213</output>
<gadget id="calculator">213 / 2</gadget>
<output>213/2 = around 106.5</output>
<gadget id="calculator">148 - 65</gadget>
<output>83</output>
<gadget id="calculator">83 / 4</gadget>
<output>83/4 = around 20.75</output>
<gadget id="calculator">(83/4) + 1</gadget>
<output>87/4 = around 21.75</output>
<gadget id="calculator">(213/2) * (87/4)</gadget>
<output>18_531/8 = around 2_316.375</output>
<result>18_531/8 = around 2_316.375</result>


if the ratio of apples to bananas is 4 to 3 and the ratio of bananas to cucumbers is 1 to 3 , what is the ratio of apples to cucumbers ?

Explanation: "the ratio of bananas to cucumbers is 1 to 3 which equals 3 to 9 . the ratio of apples to bananas to cucumbers is 4 to 3 to 9 . the answer is a ."

<gadget id="calculator">4 / 3</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">(4/3) / 3</gadget>
<output>4/9 = around 0.444444</output>
<result>4/9 = around 0.444444</result>


a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 46.24 , the number of the member is the group is :

Explanation: "explanation : money collected = ( 46.24 x 100 ) paise = 4624 paise . ∴ number of members = √ ( 4624 ) = 68 . answer : b"

<gadget id="calculator">46.24 * 100</gadget>
<output>4_624</output>
<gadget id="calculator">4_624 ** (1/2)</gadget>
<output>68</output>
<result>68</result>


arnold and danny are two twin brothers that are celebrating their birthday . the product of their ages today is smaller by 15 from the product of their ages a year from today . what is their age today ?

Explanation: "ad = ( a + 1 ) ( d + 1 ) - 15 0 = a + d - 14 a + d = 14 a = d ( as they are twin brothers ) a = d = 7 d is the answer"

<gadget id="calculator">15 - 1</gadget>
<output>14</output>
<gadget id="calculator">14 / 2</gadget>
<output>7</output>
<result>7</result>


for how many unique pairs of nonnegative integers { a , b } is the equation a ^ 2 - b ^ 2 = 99 true ?

Explanation: "answer c ( a + b ) ( a - b ) = 99 3 cases for ( a + b ) , ( a - b ) 99 , 1 33 , 3 11 , 9 answer b"

<gadget id="calculator">log(99)</gadget>
<output>log(99) = around 4.59512</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">log(5)</gadget>
<output>log(5) = around 1.609438</output>
<gadget id="calculator">log(99) / log(5)</gadget>
<output>log(99)/log(5) = around 2.855108</output>
<result>log(99)/log(5) = around 2.855108</result>


when x is multiplied by 2 , the result is 19 more than the result of subtracting x from 26 . what is the value of x ?

Explanation: "the equation that can be formed is : 2 x - 19 = 26 - x or , 3 x = 45 or , x = 15 . c answer ."

<gadget id="calculator">26 + 19</gadget>
<output>45</output>
<gadget id="calculator">2 + 1</gadget>
<output>3</output>
<gadget id="calculator">45 / 3</gadget>
<output>15</output>
<result>15</result>


a can give b 60 meters start and c 200 meters start in a kilometer race . how much start can b give c in a kilometer race ?

Explanation: "a runs 1000 m while b runs 940 m and c runs 800 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 800 ) / 940 = 851.06 m . b can give c = 1000 - 851.06 = 148.94 m . answer : a"

subtract(multiply(const_100, const_10), divide(multiply(multiply(const_100, const_10), subtract(multiply(const_100, const_10), 200)), subtract(multiply(const_100, const_10), 60)))

<gadget id="calculator">100 * 10</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 - 200</gadget>
<output>800</output>
<gadget id="calculator">1_000 * 800</gadget>
<output>800_000</output>
<gadget id="calculator">1_000 - 60</gadget>
<output>940</output>
<gadget id="calculator">800_000 / 940</gadget>
<output>40_000/47 = around 851.06383</output>
<gadget id="calculator">1_000 - (40_000/47)</gadget>
<output>7_000/47 = around 148.93617</output>
<result>7_000/47 = around 148.93617</result>


the average of marks obtained by 120 boys was 38 . if the average of marks of passed boys was 39 and that of failed boys was 15 , the number of boys who passed the examination is ?

Explanation: "let the number of boys who passed = x . then , 39 x x + 15 x ( 120 - x ) = 120 x 38 24 x = 4560 - 1800 = > x = 2760 / 24 x = 115 . hence , the number of boys passed = 115 . answer : c"

divide(subtract(multiply(38, 120), multiply(120, 15)), subtract(39, 15))

<gadget id="calculator">38 * 120</gadget>
<output>4_560</output>
<gadget id="calculator">120 * 15</gadget>
<output>1_800</output>
<gadget id="calculator">4_560 - 1_800</gadget>
<output>2_760</output>
<gadget id="calculator">39 - 15</gadget>
<output>24</output>
<gadget id="calculator">2_760 / 24</gadget>
<output>115</output>
<result>115</result>


if x , y , and z are positive integers , and 2 x = 5 y = 8 z , then the least possible value of x + y + z is

Explanation: "take lcm of 2,5 and 8 = 40 now 2 x = 40 = > x = 20 5 y = 40 = > y = 8 8 z = 40 = > z = 5 20 + 8 + 5 = 33 . option c ."

add(add(divide(divide(multiply(multiply(2, 5), 8), const_2), 2), divide(divide(multiply(multiply(2, 5), 8), const_2), 5)), divide(divide(multiply(multiply(2, 5), 8), const_2), 8))

<gadget id="calculator">2 * 5</gadget>
<output>10</output>
<gadget id="calculator">10 * 8</gadget>
<output>80</output>
<gadget id="calculator">80 / 2</gadget>
<output>40</output>
<gadget id="calculator">40 / 2</gadget>
<output>20</output>
<gadget id="calculator">40 / 5</gadget>
<output>8</output>
<gadget id="calculator">20 + 8</gadget>
<output>28</output>
<gadget id="calculator">40 / 8</gadget>
<output>5</output>
<gadget id="calculator">28 + 5</gadget>
<output>33</output>
<result>33</result>


john and beth each drove from smallville to crown city by different routes . john drove an an average speed of 40 miles per hour and completed the trip in 30 minutes . beth ' s route was 5 miles longer , and it took her 20 minutes more than john to complete the trip . how many miles per hour was beth ' s average speed on this trip ?

Explanation: speed = distance / time distance for john = speed * time = 40 * 1 / 2 = 20 miles distance for beth = distance for john + 5 = 20 + 5 = 25 miles time taken by beth = time taken by john + ( 1 / 3 hour ) = 1 / 2 + 1 / 3 = 5 / 6 speed of beth = d / t = 25 / ( 5 / 6 ) = 25 * 6 / 5 = 30 miles per hour hence , b is the answer .

divide(add(multiply(40, divide(30, const_60)), 5), divide(add(30, 20), const_60))

<gadget id="calculator">30 / 60</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">40 * (1/2)</gadget>
<output>20</output>
<gadget id="calculator">20 + 5</gadget>
<output>25</output>
<gadget id="calculator">30 + 20</gadget>
<output>50</output>
<gadget id="calculator">50 / 60</gadget>
<output>5/6 = around 0.833333</output>
<gadget id="calculator">25 / (5/6)</gadget>
<output>30</output>
<result>30</result>


5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 180 only . men â € ™ s wages are ?

Explanation: "5 m = xw = 8 b 5 m + xw + 8 b - - - - - 180 rs . 5 m + 5 m + 5 m - - - - - 180 rs . 15 m - - - - - - 180 rs . = > 1 m = 12 rs . answer : e"

<gadget id="calculator">3 * 5</gadget>
<output>15</output>
<gadget id="calculator">180 / 15</gadget>
<output>12</output>
<result>12</result>


a train is 250 meter long is running at a speed of 36 km / hour . in what time will it pass a station of 200 meter length ?

Explanation: "speed = 36 km / hr = 36 * ( 5 / 18 ) m / sec = 10 m / sec total distance = 250 + 200 = 450 meter time = distance / speed = 450 * ( 10 ) = 45 seconds answer : c"

divide(add(250, 200), divide(multiply(36, const_1000), const_3600))

<gadget id="calculator">250 + 200</gadget>
<output>450</output>
<gadget id="calculator">36 * 1_000</gadget>
<output>36_000</output>
<gadget id="calculator">36_000 / 3_600</gadget>
<output>10</output>
<gadget id="calculator">450 / 10</gadget>
<output>45</output>
<result>45</result>


a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 72.25 , the number of the member is the group is :

Explanation: "explanation : money collected = ( 72.25 x 100 ) paise = 7225 paise . ∴ number of members = √ ( 7225 ) = 85 . answer : d"

<gadget id="calculator">72.25 * 100</gadget>
<output>7_225</output>
<gadget id="calculator">7_225 ** (1/2)</gadget>
<output>85</output>
<result>85</result>


triangle atriangle b are similar triangles with areas 2023 units square and 1792 units square respectively . the ratio of there corresponding height would be

Explanation: "let x be the height of triangle a and y be the height of triangle of b . since triangles are similar , ratio of area of a and b is in the ratio of x ^ 2 / y ^ 2 therefore , ( x ^ 2 / y ^ 2 ) = 2023 / 1792 ( x ^ 2 / y ^ 2 ) = ( 17 * 17 * 7 ) / ( 16 * 16 * 7 ) ( x ^ 2 / y ^ 2 ) = 17 ^ 2 / 16 ^ 2 x / y = 17 / 16 ans = b you need to take a hint from given options to find factors of 2013 and 2527 ."

<gadget id="calculator">2_023 / 1_792</gadget>
<output>289/256 = around 1.128906</output>
<gadget id="calculator">(289/256) ** (1/2)</gadget>
<output>17/16 = around 1.0625</output>
<result>17/16 = around 1.0625</result>


the length of a rectangle is reduced by 20 % . by what % would the width have to be increased to maintainthe original area ?

Explanation: "sol . required change = ( 20 * 100 ) / ( 100 - 20 ) = 25 % c"

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

<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">1 - (4/5)</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) / (4/5)</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<result>25</result>


find the area of a parallelogram with base 10 cm and height 20 cm .

Explanation: "area of a parallelogram = base * height = 10 * 20 = 200 cm 2 answer : option c"

<gadget id="calculator">10 * 20</gadget>
<output>200</output>
<result>200</result>


a train covers a distance in 50 min , if it runs at a speed of 48 kmph on an average . the speed at which the train must run to reduce the time of journey to 40 min will be .

Explanation: time = 50 / 60 hr = 5 / 6 hr speed = 48 mph distance = s * t = 48 * 5 / 6 = 40 km time = 40 / 60 hr = 2 / 3 hr new speed = 40 * 3 / 2 kmph = 60 kmph answer is a .

divide(multiply(48, divide(50, const_60)), divide(40, const_60))

<gadget id="calculator">50 / 60</gadget>
<output>5/6 = around 0.833333</output>
<gadget id="calculator">48 * (5/6)</gadget>
<output>40</output>
<gadget id="calculator">40 / 60</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">40 / (2/3)</gadget>
<output>60</output>
<result>60</result>


if y > 0 , ( 2 y ) / 10 + ( 3 y ) / 10 is what percent of y ?

Explanation: "can be reduced to y / 5 + 3 y / 10 = 2 y / 5 = 50 % b"

multiply(const_100, add(divide(2, 10), divide(3, 10)))

<gadget id="calculator">2 / 10</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">3 / 10</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(1/5) + (3/10)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">100 * (1/2)</gadget>
<output>50</output>
<result>50</result>


200 pupil total , out of 125 like pizza , 115 like burger , then how many like both ?

Explanation: n ( a u b ) = n ( a ) + n ( b ) - n ( a intersection b ) 200 = 125 + 115 - both both = 240 - 200 = 40 . answer : a

<gadget id="calculator">125 + 115</gadget>
<output>240</output>
<gadget id="calculator">240 - 200</gadget>
<output>40</output>
<result>40</result>


the area of a rectangular plot is 15 times its breadth . if the difference between the length and the breadth is 10 metres , what is its breadth ?

Explanation: "l × b = 15 × b ∴ l = 15 m and l – b = 10 ∴ b = 15 – 10 = 5 m answer b"

<gadget id="calculator">15 - 10</gadget>
<output>5</output>
<result>5</result>


the compound interest earned by sunil on a certain amount at the end of two years at the rate of 10 % p . a . was rs . 420 . find the total amount that sunil got back at the end of two years in the form of principal plus interest earned .

Explanation: "let the sum be rs . p p { [ 1 + 10 / 100 ] 2 - 1 } = 420 p ( 10 / 100 ) ( 2 + 10 / 100 ) = 420 [ a 2 - b 2 = ( a - b ) ( a + b ) ] p = 420 / ( 0.1 ) ( 2.1 ) = 2000 . amount = 2000 + 420 = rs . 2420 answer : c"

add(divide(420, subtract(power(add(const_1, divide(10, const_100)), const_2), const_1)), 420)

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 + (1/10)</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">(11/10) ** 2</gadget>
<output>121/100 = around 1.21</output>
<gadget id="calculator">(121/100) - 1</gadget>
<output>21/100 = around 0.21</output>
<gadget id="calculator">420 / (21/100)</gadget>
<output>2_000</output>
<gadget id="calculator">2_000 + 420</gadget>
<output>2_420</output>
<result>2_420</result>


sandy walked 20 meters towards south . then sandy turned to her left and walked 20 meters . she then turned to her left and walked 20 meters . she then turned to her right and walked 25 meters . what distance is she from the starting point and in which direction ?

Explanation: the net distance is 20 + 25 = 45 meters to the east . the answer is e .

<gadget id="calculator">20 + 25</gadget>
<output>45</output>
<result>45</result>


the weight of every type a widget is the same , the weight of every type b widget is the same , and the weight of every type c widget is the same . if the weight of 7 type a widgets is equal to the weight of 4 type b widgets , and the weight of 3 type b widgets is equal to the weight of 7 type c widgets . what is the ratio of the total weight of 1 type a widget and 1 type b widget , to the total weight of 1 type b widget and 1 type c widget ?

Explanation: "3 b = 7 c and so b = 7 c / 3 7 a = 4 b and so a = 4 b / 7 = 4 c / 3 a + b = 4 c / 3 + 7 c / 3 = 11 c / 3 b + c = 7 c / 3 + c = 10 c / 3 the ratio of a + b : b + c = 11 : 10 the answer is d ."

divide(add(1, divide(7, 4)), add(divide(7, 4), divide(3, 4)))

<gadget id="calculator">7 / 4</gadget>
<output>7/4 = around 1.75</output>
<gadget id="calculator">1 + (7/4)</gadget>
<output>11/4 = around 2.75</output>
<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(7/4) + (3/4)</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">(11/4) / (5/2)</gadget>
<output>11/10 = around 1.1</output>
<result>11/10 = around 1.1</result>


a man can swim in still water at 3 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?

Explanation: "m = 3 s = x ds = 3 + x us = 3 + x 3 + x = ( 3 - x ) 2 3 + x = 6 - 2 x 3 x = 3 x = 1 answer : e"

<gadget id="calculator">3 / 3</gadget>
<output>1</output>
<result>1</result>


a man gains 30 % by selling an article for a certain price . if he sells it at double the price , the percentage of profit will be .

Explanation: "explanation : let the c . p . = x , then s . p . = ( 130 / 100 ) x = 13 x / 10 new s . p . = 2 ( 13 x / 10 ) = 26 x / 10 profit = 26 x / 10 - x = 26 x / 10 profit % = ( profit / c . p . ) * 100 = > ( 26 x / 10 ) * ( 1 / x ) * 100 = 260 % option d"

add(multiply(subtract(multiply(add(const_1, divide(30, const_100)), const_2), const_1), const_100), const_100)

<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">1 + (3/10)</gadget>
<output>13/10 = around 1.3</output>
<gadget id="calculator">(13/10) * 2</gadget>
<output>13/5 = around 2.6</output>
<gadget id="calculator">(13/5) - 1</gadget>
<output>8/5 = around 1.6</output>
<gadget id="calculator">(8/5) * 100</gadget>
<output>160</output>
<gadget id="calculator">160 + 100</gadget>
<output>260</output>
<result>260</result>


2 persons can finish a job in 8 days . first person alone can finish the work in 24 days . how many days does the second person take to finish the job ?

Explanation: 2 persons can do work in 1 day = 1 / 8 first person can do work in 1 day = 1 / 24 second person can do work in 1 day = 1 / 8 - 1 / 24 = 1 / 12 so second person can finish work in 12 days answer : b

inverse(subtract(divide(const_1, 8), divide(const_1, 24)))

<gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">1 / 24</gadget>
<output>1/24 = around 0.041667</output>
<gadget id="calculator">(1/8) - (1/24)</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">1 / (1/12)</gadget>
<output>12</output>
<result>12</result>


a cistern is filled by pipe a in 12 hours and the full cistern can be leaked out by an exhaust pipe b in 18 hours . if both the pipes are opened , in what time the cistern is full ?

Explanation: "time taken to full the cistern = ( 1 / 12 - 1 / 18 ) hrs = 1 / 36 = 36 hrs answer : c"

divide(const_1, subtract(divide(const_1, 12), divide(const_1, 18)))

<gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">1 / 18</gadget>
<output>1/18 = around 0.055556</output>
<gadget id="calculator">(1/12) - (1/18)</gadget>
<output>1/36 = around 0.027778</output>
<gadget id="calculator">1 / (1/36)</gadget>
<output>36</output>
<result>36</result>


a number x is multiplied by 3 , and this product is then divided by 7 . if the positive square root of the result of these two operations equals x , what is the value of x if x ≠ 0 ?

Explanation: "sqrt ( 3 x / 7 ) to be perfect square x has to 3 / 7 ans : b"

<gadget id="calculator">3 / 7</gadget>
<output>3/7 = around 0.428571</output>
<result>3/7 = around 0.428571</result>


the list price of an article is rs . 70 . a customer pays rs . 56.16 for it . he was given two successive discounts , one of them being 10 % . the other discount is ?

Explanation: "70 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 56.16 x = 10.85 % answer : a"

multiply(divide(subtract(subtract(70, multiply(70, divide(10, const_100))), 56.16), subtract(70, multiply(70, divide(10, const_100)))), const_100)

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">70 * (1/10)</gadget>
<output>7</output>
<gadget id="calculator">70 - 7</gadget>
<output>63</output>
<gadget id="calculator">63 - 56.16</gadget>
<output>6.84</output>
<gadget id="calculator">6.84 / 63</gadget>
<output>0.108571</output>
<gadget id="calculator">0.108571 * 100</gadget>
<output>10.8571</output>
<result>10.8571</result>


a man swims downstream 42 km and upstream 18 km taking 3 hours each time , what is the speed of the man in still water ?

Explanation: "42 - - - 3 ds = 14 ? - - - - 1 18 - - - - 3 us = 6 ? - - - - 1 m = ? m = ( 14 + 6 ) / 2 = 10 answer : e"

divide(add(divide(18, 3), divide(42, 3)), const_2)

<gadget id="calculator">18 / 3</gadget>
<output>6</output>
<gadget id="calculator">42 / 3</gadget>
<output>14</output>
<gadget id="calculator">6 + 14</gadget>
<output>20</output>
<gadget id="calculator">20 / 2</gadget>
<output>10</output>
<result>10</result>


a starts business with rs . 3500 and after 8 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b â € ™ s contribution in the capital ?

Explanation: "explanation : a invested rs . 3500 for 12 months . let b joined with investment x . and he invested for 12 - 8 = 4 months . so there profit ratio = ( 3500 ã — 12 ) : ( 4 x ) = 2 : 3 â ‡ ’ x = 15750 answer : d"

divide(multiply(multiply(3500, const_12), 3), multiply(subtract(const_12, 8), 2))

<gadget id="calculator">3_500 * 12</gadget>
<output>42_000</output>
<gadget id="calculator">42_000 * 3</gadget>
<output>126_000</output>
<gadget id="calculator">12 - 8</gadget>
<output>4</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">126_000 / 8</gadget>
<output>15_750</output>
<result>15_750</result>


joan took out a mortgage from hel local bank . each monthly mortgage payment she makes must be triple the amount of the previous month ' s payment . if her first payment is $ 100 , and the total amount she must pay back is $ 914800 , how many months will it take joan to pay back her mortgage ?

Explanation: joan starts off with 100 $ . . which is to be tripled every month her monthly payments look like this : 100 , 300 , 900 , 2700 . . . . . . . . . upto 914800 this can be re written as : 100 x 1 , 100 x 3 , 100 x 9 , 100 x 27 . . . . . . 100 x 9148 so we have 1 , 3 , 9 , 27 . . . . . 914800 in gp we know that a = 1 , and r = 3 ( its easy to figure it out by looking at the question , but regardless of it being mentioned in the question we can still compute the value of r using the formula tn = a 3 ^ n - 1 . . . ) therefore to find the sum of n terms of a gp we use this formula : sn = a ( 1 - r ^ n ) / 1 - r using this and plugging in the information we get . . . 9148 = 1 - 3 ^ n / 1 - 3 ; 1 - 3 ^ n / - 2 cross multiplying we get 9148 x - 2 = 1 - 3 ^ n - 19682 = 1 - 3 ^ n - 19682 = - 3 ^ n 19683 = 3 ^ n ( negatives cancel out ) 19863 can also be re written as 3 ^ 9 therefore ; 3 ^ 9 = 3 ^ n thus n = 9 ( d )

divide(log(add(divide(multiply(914800, const_2), 100), const_1)), log(const_3))

<gadget id="calculator">914_800 * 2</gadget>
<output>1_829_600</output>
<gadget id="calculator">1_829_600 / 100</gadget>
<output>18_296</output>
<gadget id="calculator">18_296 + 1</gadget>
<output>18_297</output>
<gadget id="calculator">log(18_297)</gadget>
<output>log(18297) = around 9.814492</output>
<gadget id="calculator">log(3)</gadget>
<output>log(3) = around 1.098612</output>
<gadget id="calculator">log(18297) / log(3)</gadget>
<output>log(18297)/log(3) = around 8.933536</output>
<result>log(18297)/log(3) = around 8.933536</result>


the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 7 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ?

Explanation: "area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 7 = rs . 6342 answer : b"

multiply(subtract(subtract(multiply(multiply(const_2, 12), add(15, 25)), multiply(6, 3)), multiply(3, multiply(4, 3))), 7)

<gadget id="calculator">2 * 12</gadget>
<output>24</output>
<gadget id="calculator">15 + 25</gadget>
<output>40</output>
<gadget id="calculator">24 * 40</gadget>
<output>960</output>
<gadget id="calculator">6 * 3</gadget>
<output>18</output>
<gadget id="calculator">960 - 18</gadget>
<output>942</output>
<gadget id="calculator">4 * 3</gadget>
<output>12</output>
<gadget id="calculator">3 * 12</gadget>
<output>36</output>
<gadget id="calculator">942 - 36</gadget>
<output>906</output>
<gadget id="calculator">906 * 7</gadget>
<output>6_342</output>
<result>6_342</result>


the grade point average of the entire class is 80 . if the average of one fourth of the class is 92 , what is the average of the rest of the class ?

Explanation: let x be the number of students in the class . let p be the average of the rest of the class . 80 x = ( 1 / 4 ) 92 x + ( 3 / 4 ) ( p ) x 320 = 92 + 3 p 3 p = 228 p = 76 . the answer is d .

divide(subtract(multiply(80, const_4), 92), subtract(const_4, const_1))

<gadget id="calculator">80 * 4</gadget>
<output>320</output>
<gadget id="calculator">320 - 92</gadget>
<output>228</output>
<gadget id="calculator">4 - 1</gadget>
<output>3</output>
<gadget id="calculator">228 / 3</gadget>
<output>76</output>
<result>76</result>


the compound interest earned on a sum for the second and the third years are $ 1200 and $ 1260 respectively . what is the rate of interest ?

Explanation: "1260 - 1200 = 60 is the rate of interest on $ 1200 for one year . the rate of interest = ( 100 * 60 ) / ( 1200 ) = 5 % the answer is a ."

divide(multiply(subtract(1260, 1200), const_100), 1200)

<gadget id="calculator">1_260 - 1_200</gadget>
<output>60</output>
<gadget id="calculator">60 * 100</gadget>
<output>6_000</output>
<gadget id="calculator">6_000 / 1_200</gadget>
<output>5</output>
<result>5</result>


a fair 2 sided coin is flipped 7 times . what is the probability that tails will be the result at least twice , but not more than 7 times ?

Explanation: "at least twice , but not more than 7 timesmeans exactly 2 times , 3 times , 4 times , 5 times , 6 times , 7 times the probability of getting exactly k results out of n flips is nck / 2 ^ n 7 c 2 / 2 ^ 7 + 7 c 3 / 2 ^ 7 + 7 c 4 / 2 ^ 7 + 7 c 5 / 2 ^ 7 + 7 c 6 / 2 ^ 7 = 119 / 128 option : a"

subtract(const_1, add(multiply(inverse(power(2, 7)), 7), add(inverse(power(2, 7)), inverse(power(2, 7)))))

<gadget id="calculator">2 ** 7</gadget>
<output>128</output>
<gadget id="calculator">1 / 128</gadget>
<output>1/128 = around 0.007812</output>
<gadget id="calculator">(1/128) * 7</gadget>
<output>7/128 = around 0.054688</output>
<gadget id="calculator">(1/128) + (1/128)</gadget>
<output>1/64 = around 0.015625</output>
<gadget id="calculator">(7/128) + (1/64)</gadget>
<output>9/128 = around 0.070312</output>
<gadget id="calculator">1 - (9/128)</gadget>
<output>119/128 = around 0.929688</output>
<result>119/128 = around 0.929688</result>


in february wilson ’ s earnings were 40 percent of his family ’ s total income . in march wilson earned 25 percent less than in february . if the rest of his family ’ s income was the same in both months , then , in march , wilson ’ s earnings were approximately what percent q of his family ’ s total income ?

Explanation: lets suppose the total family income in feb = 100 x wilson ' s earning in feb = 40 % of 100 x = 40 x earnings of remaining family in feb = 100 x - 40 x = 60 x wilson ' s earning in march = 75 % of wilson ' s feb earnings = 75 % of 40 x = 30 x earnings of remaining family in march = earnings of remaining family in feb = 60 x thus wilson ' s earning as % of total family income in march q = 30 x / ( 30 + 60 ) x = 30 x / 90 x = 33.33 % thus answer is e

multiply(divide(subtract(divide(40, const_100), multiply(divide(25, const_100), divide(40, const_100))), subtract(const_1, multiply(divide(25, const_100), divide(40, const_100)))), 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">(1/4) * (2/5)</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(2/5) - (1/10)</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">1 - (1/10)</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">(3/10) / (9/10)</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/3) * 100</gadget>
<output>100/3 = around 33.333333</output>
<result>100/3 = around 33.333333</result>


the s . i . on a certain sum of money for 2 years at 4 % per annum is half the c . i . on rs . 4000 for 2 years at 10 % per annum . the sum placed on s . i . is ?

Explanation: "explanation : c . i . = [ 4000 * ( 1 + 10 / 100 ) 2 - 4000 ] = ( 4000 * 11 / 10 * 11 / 10 - 4000 ) = rs . 840 . sum = ( 420 * 100 ) / ( 3 * 8 ) = rs . 5250 answer : a"

divide(divide(subtract(multiply(4000, power(add(const_1, divide(10, const_100)), 2)), 4000), 2), multiply(2, divide(4, const_100)))

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 + (1/10)</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">(11/10) ** 2</gadget>
<output>121/100 = around 1.21</output>
<gadget id="calculator">4_000 * (121/100)</gadget>
<output>4_840</output>
<gadget id="calculator">4_840 - 4_000</gadget>
<output>840</output>
<gadget id="calculator">840 / 2</gadget>
<output>420</output>
<gadget id="calculator">4 / 100</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">2 * (1/25)</gadget>
<output>2/25 = around 0.08</output>
<gadget id="calculator">420 / (2/25)</gadget>
<output>5_250</output>
<result>5_250</result>


a gardener grows cabbages in her garden that is in the shape of a square . each cabbage takes 1 square feet of area in her garden . this year , she has increased her output by 181 cabbages as compared to last year . the shape of the area used for growing the cabbages has remained a square in both these years . how many cabbages did she produce this year ?

Explanation: let the side for growing cabbages this year be x ft . thus the area is x ^ 2 . let the side for growing cabbages last year be y ft . thus , the area was y ^ 2 . the area would have increased by 181 sq ft as each cabbage takes 1 sq ft space . x ^ 2 - y ^ 2 = 181 ( x + y ) ( x - y ) = 181 181 is a prime number and thus it will be ( 91 + 90 ) * ( 91 - 90 ) . thus x = 91 and y = 90 x ^ 2 = 91 ^ 2 = 8281 the answer is c .

power(add(divide(181, const_2), add(const_0_25, const_0_25)), const_2)

<gadget id="calculator">181 / 2</gadget>
<output>181/2 = around 90.5</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) + (1/4)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(181/2) + (1/2)</gadget>
<output>91</output>
<gadget id="calculator">91 ** 2</gadget>
<output>8_281</output>
<result>8_281</result>


a survey of employers found that during 1993 employment costs rose 3.5 percent , where employment costs consist of salary costs and fringe - benefit costs . if salary costs rose 3 percent and fringe - benefit costs rose 9.5 percent during 1993 , then fringe - benefit costs represented what percent of employment costs at the beginning of 1993 ?

Explanation: "the amount by which employment costs rose is equal to 0.035 ( salary costs + fringe benefit costs ) ; on the other hand the amount by which employment costs rose is equal to 0.03 * salary costs + 0.095 * fringe benefit costs ; so , 35 ( s + f ) = 30 s + 95 f - - > s = f - - > f / s = 1 / 12 - - > f / ( s + f ) = 1 / ( 1 + 12 ) = 1 / 13 = 0.08 . answer : b ."

multiply(divide(subtract(3.5, 3), subtract(9.5, 3)), const_100)

<gadget id="calculator">3.5 - 3</gadget>
<output>0.5</output>
<gadget id="calculator">9.5 - 3</gadget>
<output>6.5</output>
<gadget id="calculator">0.5 / 6.5</gadget>
<output>0.076923</output>
<gadget id="calculator">0.076923 * 100</gadget>
<output>7.6923</output>
<result>7.6923</result>


Explanation: let p / q = a , then ( a - 1 / a ) = 21 / 10 ⇒ a 2 − 1 = a . 2110 ⇒ a 2 − 1 = a . 2110 ⇒ 10 a 2 − 21 a − 10 ⇒ 10 a 2 − 21 a − 10 = 0 roots of the equation = − b ± b 2 − 4 ac − − − − − − − √ 2 a − b ± b 2 − 4 ac 2 a a = 21 ± 441 + 400 − − − − − − − − √ 2021 ± 441 + 40020 a = 21 ± 292021 ± 2920 = 5 / 2 or - 2 / 5 for a = 5 / 2 , 4 p / q + 4 q / p = 58 / 5 for a = - 2 / 5 , 4 p / q + 4 q / p = - 58 / 5 answer : b

divide(add(add(add(add(21, 10), multiply(4, 4)), const_1), const_10), add(4, const_1))

<gadget id="calculator">21 + 10</gadget>
<output>31</output>
<gadget id="calculator">4 * 4</gadget>
<output>16</output>
<gadget id="calculator">31 + 16</gadget>
<output>47</output>
<gadget id="calculator">47 + 1</gadget>
<output>48</output>
<gadget id="calculator">48 + 10</gadget>
<output>58</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">58 / 5</gadget>
<output>58/5 = around 11.6</output>
<result>58/5 = around 11.6</result>


a jar was full with honey . a person used to draw out 20 % of the honey from the jar and replaced it with sugar solution . he has repeated the same process 4 times and thus there was only 512 gm of honey left in the jar , the rest part of the jar was filled with the sugar solution . the initial amount of honey in the jar was filled with the sugar solution . the initial amount of honey in the jar was :

Explanation: answer : a ) 1.25 kg

divide(divide(512, power(divide(4, divide(20, 4)), 4)), const_1000)

<gadget id="calculator">20 / 4</gadget>
<output>5</output>
<gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(4/5) ** 4</gadget>
<output>256/625 = around 0.4096</output>
<gadget id="calculator">512 / (256/625)</gadget>
<output>1_250</output>
<gadget id="calculator">1_250 / 1_000</gadget>
<output>5/4 = around 1.25</output>
<result>5/4 = around 1.25</result>


a pupil ' s marks were wrongly entered as 85 instead of 45 . due to that the average marks for the class got increased by half . the number of pupils in the class is :

Explanation: "let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 85 - 45 ) = > x / 2 = 40 = > x = 80 . answer : b"

<gadget id="calculator">85 - 45</gadget>
<output>40</output>
<gadget id="calculator">40 * 2</gadget>
<output>80</output>
<result>80</result>


the h . c . f . of two numbers is 20 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is :

Explanation: "clearly , the numbers are ( 20 x 13 ) and ( 20 x 14 ) . larger number = ( 20 x 14 ) = 280 . answer : option b"

<gadget id="calculator">20 * 14</gadget>
<output>280</output>
<result>280</result>


two cubes of their volumes in the ratio 64 : 125 . the ratio of their surface area is :

Explanation: "the ratio of their surface area is 64 : 125 4 : 5 answer is e ."

divide(power(64, const_0_33), power(125, const_0_33))

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">64 ** (1/3)</gadget>
<output>4</output>
<gadget id="calculator">125 ** (1/3)</gadget>
<output>5</output>
<gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>
<result>4/5 = around 0.8</result>


if the arithmetic mean of p and q is 10 and the arithmetic mean of q and r is 22 , what is the value of r - p ?

Explanation: "arithmetic mean expression for p and q : ( p + q ) / 2 = 10 ; p + q = 20 - - - - eq 1 arithmetic mean expression for q and r : ( q + r ) / 2 = 20 ; q + r = 44 - - - - eq 2 subtracting eq 1 from eq 2 we get : r - p = 24 hence , the correct answer is d"

subtract(multiply(22, const_2), multiply(10, const_2))

<gadget id="calculator">22 * 2</gadget>
<output>44</output>
<gadget id="calculator">10 * 2</gadget>
<output>20</output>
<gadget id="calculator">44 - 20</gadget>
<output>24</output>
<result>24</result>


a man is 28 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ?

Explanation: "let the son ' s present age be x years . then , man ' s present age = ( x + 28 ) years . ( x + 28 ) + 2 = 2 ( x + 2 ) x + 30 = 2 x + 4 = > x = 26 . answer : d"

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

<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">4 - 2</gadget>
<output>2</output>
<gadget id="calculator">28 - 2</gadget>
<output>26</output>
<gadget id="calculator">2 - 1</gadget>
<output>1</output>
<gadget id="calculator">26 / 1</gadget>
<output>26</output>
<result>26</result>


in an examination , 30 % of total students failed in hindi , 42 % failed in english and 28 % in both . the percentage of these who passed in both the subjects is :

Explanation: "explanation : formula n ( a â ˆ ª b ) = n ( a ) + n ( b ) â ˆ ’ n ( a â ˆ © b ) fail in hindi or english = 30 + 42 â € “ 28 = 44 therefore students who passed = 100 â € “ 44 = 56 . answer : c"

subtract(const_100, subtract(add(30, 42), 28))

<gadget id="calculator">30 + 42</gadget>
<output>72</output>
<gadget id="calculator">72 - 28</gadget>
<output>44</output>
<gadget id="calculator">100 - 44</gadget>
<output>56</output>
<result>56</result>


a person purchases 90 clocks and sells 40 clocks at a gain of 10 % and 50 clocks at a gain of 20 % . if he sold all of them at a uniform profit of 15 % , then he would have got rs . 40 less . the cost price of each clock is : ?

Explanation: "let c . p . of clock be rs . x . then , c . p . of 90 clocks = rs . 90 x . [ ( 110 % of 40 x ) + ( 120 % of 50 x ) ] - ( 115 % of 90 x ) = 40 44 x + 60 x - 103.5 x = 40 0.5 x = 40 = > x = 80 answer : c"

divide(40, subtract(add(multiply(40, add(const_1, divide(10, const_100))), multiply(50, add(const_1, divide(20, const_100)))), multiply(90, add(const_1, divide(15, const_100)))))

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 + (1/10)</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">40 * (11/10)</gadget>
<output>44</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 + (1/5)</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">50 * (6/5)</gadget>
<output>60</output>
<gadget id="calculator">44 + 60</gadget>
<output>104</output>
<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">1 + (3/20)</gadget>
<output>23/20 = around 1.15</output>
<gadget id="calculator">90 * (23/20)</gadget>
<output>207/2 = around 103.5</output>
<gadget id="calculator">104 - (207/2)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">40 / (1/2)</gadget>
<output>80</output>
<result>80</result>


two trains travelling in the same direction at 50 and 40 kmph completely pass off another in 1 1 / 2 minute . if the length of the first train is 125 m , what is the length of the second train ?

Explanation: rs = 50 â € “ 40 = 10 * 5 / 18 = 25 / 9 mps t = 90 sec d = 25 / 9 * 90 = 250 m 125 - - - - - - - - 125 m answer : c

subtract(multiply(add(multiply(1, const_60), divide(multiply(1, const_60), 2)), multiply(subtract(50, 40), const_0_2778)), 125)

<gadget id="calculator">1 * 60</gadget>
<output>60</output>
<gadget id="calculator">60 / 2</gadget>
<output>30</output>
<gadget id="calculator">60 + 30</gadget>
<output>90</output>
<gadget id="calculator">50 - 40</gadget>
<output>10</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">10 * (5/18)</gadget>
<output>25/9 = around 2.777778</output>
<gadget id="calculator">90 * (25/9)</gadget>
<output>250</output>
<gadget id="calculator">250 - 125</gadget>
<output>125</output>
<result>125</result>


a man can row upstream at 25 kmph and downstream at 31 kmph , and then find the speed of the man in still water ?

Explanation: "us = 25 ds = 31 m = ( 31 + 25 ) / 2 = 28 answer : b"

<gadget id="calculator">25 + 31</gadget>
<output>56</output>
<gadget id="calculator">56 / 2</gadget>
<output>28</output>
<result>28</result>


a cricket player whose bowling average was 23.50 runs per wicket , takes 5 wicket for 52 runs in a match . due to this his average decreases by 0.50 . what will be the number of wickets taken by him till the last match ?

Explanation: "average = total runs / total wickets total runs after last match = 23.5 w + 52 total wickets after last match = w + 5 ( 23.5 w + 52 ) / ( w + 5 ) = 23.5 - 0.5 = 23 w = 126 so total wickets aftr last match = w + 5 = 131 answer : c"

divide(subtract(multiply(subtract(23.50, 0.50), 5), 52), 0.50)

<gadget id="calculator">23.5 - 0.5</gadget>
<output>23</output>
<gadget id="calculator">23 * 5</gadget>
<output>115</output>
<gadget id="calculator">115 - 52</gadget>
<output>63</output>
<gadget id="calculator">63 / 0.5</gadget>
<output>126</output>
<result>126</result>


on dividing 52 by a number , the quotient is 16 and the remainder is 4 . find the divisor ?

Explanation: "d = ( d - r ) / q = ( 52 - 4 ) / 16 = 48 / 16 = 3 b )"

<gadget id="calculator">52 / 16</gadget>
<output>13/4 = around 3.25</output>
<gadget id="calculator">floor(13/4)</gadget>
<output>3</output>
<result>3</result>


jim â € ™ s taxi service charges an initial fee of $ 2.5 at the beginning of a trip and an additional charge of $ 0.35 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?

Explanation: "let the fixed charge of jim â € ™ s taxi service = 2.5 $ and charge per 2 / 5 mile ( . 4 mile ) = . 35 $ total charge for a trip of 3.6 miles = 2.5 + ( 3.6 / . 4 ) * . 35 = 2.5 + 9 * . 35 = 5.65 $ answer d"

<gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">3.6 / (2/5)</gadget>
<output>9</output>
<gadget id="calculator">9 * 0.35</gadget>
<output>3.15</output>
<gadget id="calculator">3.15 + 2.5</gadget>
<output>5.65</output>
<result>5.65</result>


if the dimensions of a certain rectangular box are 5 inches by 2 inches by 3 inches , then the face of greatest area is of what area ?

Explanation: definitely ( d ) 5 * 3 = 15 sq inches the question asks to find the greatest area of the faces of a cuboid the possible area of the faces are - length * breadth , breadth * height & height * length the possible areas are - 6 , 10 & 15 thus 15 is the greatest possible area . . . . answer : d

<gadget id="calculator">5 * 3</gadget>
<output>15</output>
<result>15</result>


at a certain university , 66 % of the professors are women , and 70 % of the professors are tenured . if 90 % of the professors are women , tenured , or both , then what percent of the men are tenured ?

Explanation: "answer is 75 % total women = 66 % total men = 40 % total tenured = 70 % ( both men and women ) therefore , women tenured + women professors + men tenured = 90 % men tenured = 24 % but question wants to know the percent of men that are tenured 24 % / 40 % = 60 % c"

add(subtract(const_100, 66), subtract(90, 66))

<gadget id="calculator">100 - 66</gadget>
<output>34</output>
<gadget id="calculator">90 - 66</gadget>
<output>24</output>
<gadget id="calculator">34 + 24</gadget>
<output>58</output>
<result>58</result>


a farmer spent $ 35 on feed for chickens and goats . he spent 40 % money on chicken feed , which he bought at a 50 % discount off the full price , and spent the rest on goat feed , which he bought at full price . if the farmer had paid full price for both the chicken feed and the goat feed , what amount would he have spent on the chicken feed and goat feed combined ?

Explanation: a farmer spent 40 % money on chicken feed , so he spent 0.4 * $ 35 = $ 14 on chicken feed , thus he spent the remaining 35 - 14 = $ 21 on goat feed . now , since he bought chicken feed at a 20 % discount then the original price of it was x * 0.5 = $ 14 - - > x = $ 28 . therefore if the farmer had paid full price for both the chicken feed and the goat feed , then he would he have spent 28 + 21 = $ 49 . answer : b .

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

<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">35 * (2/5)</gadget>
<output>14</output>
<gadget id="calculator">14 + 35</gadget>
<output>49</output>
<result>49</result>


excluding stoppages , the speed of a bus is 58 kmph and including stoppages , it is 40 kmph . for how many minutes does the bus stop per hour ?

Explanation: "due to stoppages , it covers 18 km less . time taken to cover 18 km = ( ( 18 / 58 ) ã — 60 ) = 19 min . option ( a ) is correct"

multiply(const_60, divide(subtract(58, 40), 58))

<gadget id="calculator">58 - 40</gadget>
<output>18</output>
<gadget id="calculator">18 / 58</gadget>
<output>9/29 = around 0.310345</output>
<gadget id="calculator">60 * (9/29)</gadget>
<output>540/29 = around 18.62069</output>
<result>540/29 = around 18.62069</result>


the average salary of the employees in a office is rs . 120 / month . the avg salary of officers is rs . 430 and of non officers is rs 110 . if the no . of officers is 15 , then find the no of nonofficers in the office .

Explanation: "let no . of non - officers be x 15 * 430 + x * 110 = ( x + 15 ) 120 x = 465 b"

divide(subtract(multiply(15, 430), multiply(15, 120)), subtract(120, 110))

<gadget id="calculator">15 * 430</gadget>
<output>6_450</output>
<gadget id="calculator">15 * 120</gadget>
<output>1_800</output>
<gadget id="calculator">6_450 - 1_800</gadget>
<output>4_650</output>
<gadget id="calculator">120 - 110</gadget>
<output>10</output>
<gadget id="calculator">4_650 / 10</gadget>
<output>465</output>
<result>465</result>


the salary of a person was reduced by 14 % . by what percent should his reduced salary be raised so as to bring it at par with his original salary ?

Explanation: let the original salary be $ 100 new salary = $ 86 increase on 86 = 14 increase on 100 = 14 / 86 * 100 = 16.3 % answer is b

multiply(divide(multiply(const_100, divide(14, const_100)), subtract(const_100, multiply(const_100, divide(14, const_100)))), const_100)

<gadget id="calculator">14 / 100</gadget>
<output>7/50 = around 0.14</output>
<gadget id="calculator">100 * (7/50)</gadget>
<output>14</output>
<gadget id="calculator">100 - 14</gadget>
<output>86</output>
<gadget id="calculator">14 / 86</gadget>
<output>7/43 = around 0.162791</output>
<gadget id="calculator">(7/43) * 100</gadget>
<output>700/43 = around 16.27907</output>
<result>700/43 = around 16.27907</result>


a bullet train covers a distance in 50 min , if it runs at a speed of 48 kmph on an average . the speed at which the bullet train must run to reduce the time of journey to 40 min will be .

Explanation: c 60 kmph time = 50 / 60 hr = 5 / 6 hr speed = 48 mph distance = s * t = 48 * 5 / 6 = 40 km time = 40 / 60 hr = 2 / 3 hr new speed = 40 * 3 / 2 kmph = 60 kmph

<gadget id="calculator">50 * 48</gadget>
<output>2_400</output>
<gadget id="calculator">2_400 / 40</gadget>
<output>60</output>
<result>60</result>


the area of a triangle is with base 12 m and height 5 m ?

Explanation: "1 / 2 * 12 * 5 = 30 m 2 answer : b"

<gadget id="calculator">(12 * 5) / 2</gadget>
<output>30</output>
<result>30</result>


what is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular decagon ( 10 - sided polygon ) ?

Explanation: from any vertex , there are two vertices on sides , which do not make a diagonal but a side . so the remaining n - 3 vertices make diagonals . there are 2 of these diagonals which are the shortest . the probability of choosing one of the shortest diagonals is 2 / 7 . the answer is c .

divide(10, divide(multiply(10, subtract(10, const_3)), const_2))

<gadget id="calculator">10 - 3</gadget>
<output>7</output>
<gadget id="calculator">10 * 7</gadget>
<output>70</output>
<gadget id="calculator">70 / 2</gadget>
<output>35</output>
<gadget id="calculator">10 / 35</gadget>
<output>2/7 = around 0.285714</output>
<result>2/7 = around 0.285714</result>


sheila works 8 hours per day on monday , wednesday and friday , and 6 hours per day on tuesday and thursday . she does not work on saturday and sunday . she earns $ 360 per week . how much does she earn in dollars per hour ?

Explanation: "let sheila earn x dollars per hour so , on monday , wednesday and friday , she earns 8 x each and , on tuesday and thursday , she earns 6 x each in total , over the week she should earn , 3 ( 8 x ) + 2 ( 6 x ) = 36 x she earns $ 360 per week 36 x = 360 x = 10 correct option : b"

divide(360, add(multiply(8, const_3), multiply(6, const_2)))

<gadget id="calculator">8 * 3</gadget>
<output>24</output>
<gadget id="calculator">6 * 2</gadget>
<output>12</output>
<gadget id="calculator">24 + 12</gadget>
<output>36</output>
<gadget id="calculator">360 / 36</gadget>
<output>10</output>
<result>10</result>


dacid obtained 90 , 92 , 85 , 87 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?

Explanation: "average = ( 90 + 92 + 85 + 87 + 85 ) / 5 = 439 / 5 = 87.8 . answer : c"

divide(add(add(add(add(90, 92), 85), 87), 85), divide(const_10, const_2))

<gadget id="calculator">90 + 92</gadget>
<output>182</output>
<gadget id="calculator">182 + 85</gadget>
<output>267</output>
<gadget id="calculator">267 + 87</gadget>
<output>354</output>
<gadget id="calculator">354 + 85</gadget>
<output>439</output>
<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">439 / 5</gadget>
<output>439/5 = around 87.8</output>
<result>439/5 = around 87.8</result>


in a group of 6 boys and 4 girls , four children are to be selected . in how many different ways can they be selected ?

Explanation: "out of 10 students 4 children should to be selected . so the combination will be 10 c 4 . 10 c 4 = 10 ! / 6 ! * 4 ! = 10 * 9 * 8 * 7 * 6 ! / 6 ! * ( 4 * 3 * 2 * 1 ) 10 c 4 = 210 there are 210 differect possible ways to select 4 children out of 10 students ."

divide(factorial(add(6, 4)), multiply(factorial(4), factorial(6)))

<gadget id="calculator">6 + 4</gadget>
<output>10</output>
<gadget id="calculator">factorial(10)</gadget>
<output>3_628_800</output>
<gadget id="calculator">factorial(4)</gadget>
<output>24</output>
<gadget id="calculator">factorial(6)</gadget>
<output>720</output>
<gadget id="calculator">24 * 720</gadget>
<output>17_280</output>
<gadget id="calculator">3_628_800 / 17_280</gadget>
<output>210</output>
<result>210</result>


in a certain town , the ratio of ny yankees fans to ny mets fans is 3 : 2 , and the ratio of ny mets fans to boston red sox fans is 4 : 5 . if there are 360 baseball fans in the town , each of whom is a fan of exactly one of those three teams , how many ny mets fans are there in this town ?

Explanation: the ratio of yankees : mets : red sox = 6 : 4 : 5 the mets fans are 4 / 15 of the population . ( 4 / 15 ) * 360 = 96 the answer is a .

multiply(divide(360, add(add(multiply(3, 2), 4), 5)), 4)

<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">6 + 4</gadget>
<output>10</output>
<gadget id="calculator">10 + 5</gadget>
<output>15</output>
<gadget id="calculator">360 / 15</gadget>
<output>24</output>
<gadget id="calculator">24 * 4</gadget>
<output>96</output>
<result>96</result>


the sum of ages of 5 children born at the intervals of 3 years each is 55 years . what is the age of the youngest child ?

Explanation: "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 55 5 x = 25 x = 5 . age of the youngest child = x = 5 years . a )"

<gadget id="calculator">55 / 5</gadget>
<output>11</output>
<gadget id="calculator">11 - 3</gadget>
<output>8</output>
<gadget id="calculator">8 - 3</gadget>
<output>5</output>
<result>5</result>