two numbers a and b are such that the sum of 5 % of a and 2 % of b is two - third of the sum of 6 % of a and 8 % of b . find the ratio of a : b .

Explanation: explanation : 5 % of a + 2 % of b = 2 / 3 ( 6 % of a + 8 % of b ) 5 a / 100 + 2 b / 100 = 2 / 3 ( 6 a / 100 + 8 b / 100 ) ⇒ 5 a + 2 b = 2 / 3 ( 6 a + 8 b ) ⇒ 15 a + 6 b = 12 a + 16 b ⇒ 3 a = 10 b ⇒ ab = 10 / 3 ⇒ a : b = 10 : 3 answer : option d

divide(subtract(divide(multiply(divide(8, const_100), const_2), const_3), divide(2, const_100)), subtract(divide(5, const_100), divide(multiply(divide(6, const_100), const_2), const_3)))

<gadget id="calculator">8 / 100</gadget>
<output>2/25 = around 0.08</output>
<gadget id="calculator">(2/25) * 2</gadget>
<output>4/25 = around 0.16</output>
<gadget id="calculator">(4/25) / 3</gadget>
<output>4/75 = around 0.053333</output>
<gadget id="calculator">2 / 100</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">(4/75) - (1/50)</gadget>
<output>1/30 = around 0.033333</output>
<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">6 / 100</gadget>
<output>3/50 = around 0.06</output>
<gadget id="calculator">(3/50) * 2</gadget>
<output>3/25 = around 0.12</output>
<gadget id="calculator">(3/25) / 3</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">(1/20) - (1/25)</gadget>
<output>1/100 = around 0.01</output>
<gadget id="calculator">(1/30) / (1/100)</gadget>
<output>10/3 = around 3.333333</output>
<result>10/3 = around 3.333333</result>


20 men do a work in 20 days . how many men are needed to finish the work in 10 days ?

Explanation: "men required to finish the work in 10 days = 20 * 20 / 10 = 40 answer is e"

<gadget id="calculator">20 * 20</gadget>
<output>400</output>
<gadget id="calculator">400 / 10</gadget>
<output>40</output>
<result>40</result>


if 5 a = 6 b and ab ≠ 0 , what is the ratio of a / 6 to b / 5 ?

Explanation: "a nice fast approach is the first find a pair of numbers that satisfy the given equation : 5 a = 6 b here ' s one pair : a = 6 and b = 5 what is the ratio of a / 6 to b / 5 ? in other words , what is the value of ( a / 6 ) / ( b / 5 ) ? plug in values to get : ( a / 6 ) / ( b / 5 ) = ( 6 / 6 ) / ( 5 / 5 ) = 1 / 1 = 1 c"

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


x does a work in 20 days . y does the same work in 30 days . in how many days they together will do the same work ?

Explanation: "x ' s 1 day ' s work = 1 / 20 y ' s 1 day ' s work = 1 / 30 ( x + y ) ' s 1 day ' s work = ( 1 / 20 + 1 / 30 ) = 1 / 12 both together will finish the work in 12 days . correct option is b"

inverse(add(divide(const_1, 20), divide(const_1, 30)))

<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">1 / 30</gadget>
<output>1/30 = around 0.033333</output>
<gadget id="calculator">(1/20) + (1/30)</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">1 / (1/12)</gadget>
<output>12</output>
<result>12</result>


jack and jill are marathon runners . jack can finish a marathon ( 42 km ) in 3.5 hours and jill can run a marathon in 4.2 hours . what is the ratio of their average running speed ? ( jack : jill )

Explanation: average speed of jack = distance / time = 42 / ( 7 / 2 ) = 84 / 7 average speed of jill = 42 / ( 4.2 ) = 10 ratio of average speed of jack to jill = ( 84 / 7 ) / 10 = 84 / 70 = 6 / 5 answer d

<gadget id="calculator">42 / 3.5</gadget>
<output>12</output>
<gadget id="calculator">42 / 4.2</gadget>
<output>10</output>
<gadget id="calculator">12 / 10</gadget>
<output>6/5 = around 1.2</output>
<result>6/5 = around 1.2</result>


a container contains 1000 liters of milk , from this container 10 liters of milk was taken out and replaced by water . this process was repeated further 2 times . how much milk is now contained by the container ?

Explanation: amount of milk left after 3 operations = 1000 ( 1 - 10 / 1000 ) ^ 3 = 1000 * 99 / 100 * 99 / 100 * 99 / 100 = 970.3 liters answer is a

subtract(subtract(subtract(1000, 10), 10), 10)

<gadget id="calculator">1_000 - 10</gadget>
<output>990</output>
<gadget id="calculator">990 - 10</gadget>
<output>980</output>
<gadget id="calculator">980 - 10</gadget>
<output>970</output>
<result>970</result>


a squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 3 feet . how many feet does the squirrel travels if the post is 18 feet tall and 3 feet in circumference ?

Explanation: "total circuit = 18 / 3 = 6 total feet squirrel travels = 6 * 3 = 18 feet answer : e"

<gadget id="calculator">18 / 3</gadget>
<output>6</output>
<gadget id="calculator">6 * 3</gadget>
<output>18</output>
<result>18</result>


in an electric circuit , two resistors with resistances 3 ohm and 5 ohm are connected in parallel . in this case , if r is the combined resistance of these two resistors , then the reciprocal of r is equal to the sum of the reciprocals of two resistors . what is the value ?

Explanation: the wording is a bit confusing , though basically we are told that 1 / r = 1 / 3 + 1 / 5 , from which it follows that r = 15 / 8 ohms . answer : b .

<gadget id="calculator">3 * 5</gadget>
<output>15</output>
<gadget id="calculator">3 + 5</gadget>
<output>8</output>
<gadget id="calculator">15 / 8</gadget>
<output>15/8 = around 1.875</output>
<result>15/8 = around 1.875</result>


a and b enterd into a partnership investing rs . 16000 and rs . 12000 respectively . after 3 months , a withdrew rs . 5000 while b invested rs . 5000 more . after 3 more months . c joins the business with a capital of rs . 21000 . the share of b exceeds that of c , out of a total profit of rs . 26400 after one year by

Explanation: solution a : b : c = ( 16000 x 3 + 11000 x 9 ) : ( 12000 x 3 + 17000 x 9 ) : ( 21000 x 6 ) = 147 : 180 : 126 = 7 : 9 : 6 . ∴ difference of b and c ’ s shares = rs . ( 26400 x 9 / 22 - 26400 x 6 / 22 ) = rs . 3600 . answer c

subtract(multiply(26400, divide(add(multiply(12000, 3), multiply(add(12000, 5000), subtract(const_12, 3))), add(add(add(multiply(16000, 3), multiply(subtract(16000, 5000), subtract(const_12, 3))), add(multiply(12000, 3), multiply(add(12000, 5000), subtract(const_12, 3)))), multiply(21000, subtract(subtract(const_12, 3), 3))))), multiply(26400, divide(multiply(21000, subtract(subtract(const_12, 3), 3)), add(add(add(multiply(16000, 3), multiply(subtract(16000, 5000), subtract(const_12, 3))), add(multiply(12000, 3), multiply(add(12000, 5000), subtract(const_12, 3)))), multiply(21000, subtract(subtract(const_12, 3), 3))))))

<gadget id="calculator">12_000 * 3</gadget>
<output>36_000</output>
<gadget id="calculator">12_000 + 5_000</gadget>
<output>17_000</output>
<gadget id="calculator">12 - 3</gadget>
<output>9</output>
<gadget id="calculator">17_000 * 9</gadget>
<output>153_000</output>
<gadget id="calculator">36_000 + 153_000</gadget>
<output>189_000</output>
<gadget id="calculator">16_000 * 3</gadget>
<output>48_000</output>
<gadget id="calculator">16_000 - 5_000</gadget>
<output>11_000</output>
<gadget id="calculator">11_000 * 9</gadget>
<output>99_000</output>
<gadget id="calculator">48_000 + 99_000</gadget>
<output>147_000</output>
<gadget id="calculator">147_000 + 189_000</gadget>
<output>336_000</output>
<gadget id="calculator">9 - 3</gadget>
<output>6</output>
<gadget id="calculator">21_000 * 6</gadget>
<output>126_000</output>
<gadget id="calculator">336_000 + 126_000</gadget>
<output>462_000</output>
<gadget id="calculator">189_000 / 462_000</gadget>
<output>9/22 = around 0.409091</output>
<gadget id="calculator">26_400 * (9/22)</gadget>
<output>10_800</output>
<gadget id="calculator">126_000 / 462_000</gadget>
<output>3/11 = around 0.272727</output>
<gadget id="calculator">26_400 * (3/11)</gadget>
<output>7_200</output>
<gadget id="calculator">10_800 - 7_200</gadget>
<output>3_600</output>
<result>3_600</result>


in a 500 m race , the ratio of the speeds of two contestants a and b is 3 : 4 . a has a start of 155 m . then , a wins by :

Explanation: "to reach the winning post a will have to cover a distance of ( 500 - 155 ) m , i . e . , 345 m . while a covers 3 m , b covers 4 m . while a covers 345 m , b covers 4 x 345 / 3 m = 460 m . thus , when a reaches the winning post , b covers 460 m and therefore remains 40 m behind . a wins by 40 m . answer : c"

subtract(500, divide(multiply(subtract(500, 155), 4), 3))

<gadget id="calculator">500 - 155</gadget>
<output>345</output>
<gadget id="calculator">345 * 4</gadget>
<output>1_380</output>
<gadget id="calculator">1_380 / 3</gadget>
<output>460</output>
<gadget id="calculator">500 - 460</gadget>
<output>40</output>
<result>40</result>


dan ' s age after 16 years will be 6 times his age 4 years ago . what is the present age of dan ?

Explanation: "let dan ' s present age be x . x + 16 = 6 ( x - 4 ) 5 x = 40 x = 8 the answer is a ."

divide(add(16, multiply(4, 6)), subtract(6, const_1))

<gadget id="calculator">4 * 6</gadget>
<output>24</output>
<gadget id="calculator">16 + 24</gadget>
<output>40</output>
<gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">40 / 5</gadget>
<output>8</output>
<result>8</result>


by selling 20 pencils for a rupee a man loses 60 % . how many for a rupee should he sell in order to gain 60 % ?

Explanation: "40 % - - - 20 160 % - - - ? 40 / 160 * 20 = 5 answer : e"

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

<gadget id="calculator">100 + 60</gadget>
<output>160</output>
<gadget id="calculator">100 - 60</gadget>
<output>40</output>
<gadget id="calculator">1 / 40</gadget>
<output>1/40 = around 0.025</output>
<gadget id="calculator">160 * (1/40)</gadget>
<output>4</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 20</gadget>
<output>5</output>
<result>5</result>


after decreasing 24 % in the price of an article costs rs . 1216 . find the actual cost of an article ?

Explanation: "cp * ( 76 / 100 ) = 1216 cp = 16 * 100 = > cp = 1600 answer : d"

divide(1216, subtract(const_1, divide(24, const_100)))

<gadget id="calculator">24 / 100</gadget>
<output>6/25 = around 0.24</output>
<gadget id="calculator">1 - (6/25)</gadget>
<output>19/25 = around 0.76</output>
<gadget id="calculator">1_216 / (19/25)</gadget>
<output>1_600</output>
<result>1_600</result>


if ( 18 ^ a ) * 9 ^ ( 3 a – 1 ) = ( 2 ^ 3 ) ( 3 ^ b ) and a and b are positive integers , what is the value of a ?

Explanation: 18 ^ a ) * 9 ^ ( 3 a – 1 ) = ( 2 ^ 3 ) ( 3 ^ b ) = 2 ^ a . 9 ^ a . 9 ^ ( 3 a – 1 ) = ( 2 ^ 3 ) ( 3 ^ b ) just compare powers of 2 from both sides ( no need to calculate powers of 3 , 9 as value of b is not asked ) answer = 3 answer : e

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


a student traveled 10 percent of the distance of the trip alone , continued another 30 miles with a friend , and then finished the last half of the trip alone . how many miles long was the trip ?

Explanation: let x be the total length of the trip . 0.1 x + 30 miles + 0.5 x = x 30 miles = 0.4 x x = 75 miles the answer is a .

divide(30, subtract(subtract(const_1, inverse(10)), divide(const_1, const_2)))

<gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 - (1/10)</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(9/10) - (1/2)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">30 / (2/5)</gadget>
<output>75</output>
<result>75</result>


a bag marked at $ 250 is sold for $ 120 . the rate of discount is ?

Explanation: "rate of discount = 130 / 250 * 100 = 52 % answer is d"

multiply(divide(subtract(250, 120), 250), const_100)

<gadget id="calculator">250 - 120</gadget>
<output>130</output>
<gadget id="calculator">130 / 250</gadget>
<output>13/25 = around 0.52</output>
<gadget id="calculator">(13/25) * 100</gadget>
<output>52</output>
<result>52</result>


a can do a piece of work 30 days . b can do work in 45 days . in how many days they will complete the work together ?

Explanation: "lcm = 90 , ratio = 30 : 45 = 2 : 3 no of days = 90 / ( 2 + 3 ) = 90 / 5 = 18 days answer : e"

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

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


average between two sets of numbers is closer to the set with morenumbers ?

Explanation: "if on a test three people answered 90 % of the questions correctly and two people answered 80 % correctly , then the average for the group is not 85 % but rather 3 × 90 + 2 × 805 = 4305 = 86.3 × 90 + 2 × 805 = 4305 = 86 . here , 90 has a weight of 3 = > it occurs 3 times . whereas 80 has a weight of 2 = > it occurs 2 times . so the average is closer to 90 than to 80 as we have just calculated . b"

<gadget id="calculator">2 * 4</gadget>
<output>8</output>
<gadget id="calculator">8 * 10</gadget>
<output>80</output>
<result>80</result>


what is the probability that the sum of two dice will yield a 6 , and then when both are thrown again , their sum will again yield a 6 ? assume that each die has 5 sides with faces numbered 1 to 5 .

Explanation: solution - rolling dices is an independent event . the combinations to get 6 are ( 1,5 ) , ( 5,1 ) , ( 2,4 ) , ( 4,2 ) , ( 3,3 ) and total combinations of both dices is 25 . the probability of getting 6 in first attempt is 5 / 25 = 1 / 5 . probability of getting 6 again in second attempt = ( 1 / 5 ) * ( 1 / 5 ) = 1 / 25 . ans b

multiply(divide(5, power(5, const_2)), divide(5, power(5, const_2)))

<gadget id="calculator">5 ** 2</gadget>
<output>25</output>
<gadget id="calculator">5 / 25</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * (1/5)</gadget>
<output>1/25 = around 0.04</output>
<result>1/25 = around 0.04</result>


the average of runs of a cricket player of 10 innings was 34 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?

Explanation: "explanation : average = total runs / no . of innings = 34 so , total = average x no . of innings = 34 x 10 = 340 . now increase in avg = 4 runs . so , new avg = 34 + 4 = 38 runs total runs = new avg x new no . of innings = 38 x 11 = 418 runs made in the 11 th inning = 418 - 340 = 78 answer : a"

subtract(multiply(add(10, const_1), add(4, 34)), multiply(10, 34))

<gadget id="calculator">10 + 1</gadget>
<output>11</output>
<gadget id="calculator">4 + 34</gadget>
<output>38</output>
<gadget id="calculator">11 * 38</gadget>
<output>418</output>
<gadget id="calculator">10 * 34</gadget>
<output>340</output>
<gadget id="calculator">418 - 340</gadget>
<output>78</output>
<result>78</result>


a truck covers a distance of 288 km at a certain speed in 8 hours . how much time would a car take at an average speed which is 18 kmph more than that of the speed of the truck to cover a distance which is 90 km more than that travelled by the truck ?

Explanation: "explanation : speed of the truck = distance / time = 288 / 8 = 36 kmph now , speed of car = ( speed of truck + 18 ) kmph = ( 36 + 18 ) = 54 kmph distance travelled by car = 288 + 90 = 378 km time taken by car = distance / speed = 378 / 54 = 7 hours . answer – c"

<gadget id="calculator">288 + 90</gadget>
<output>378</output>
<gadget id="calculator">288 / 8</gadget>
<output>36</output>
<gadget id="calculator">36 + 18</gadget>
<output>54</output>
<gadget id="calculator">378 / 54</gadget>
<output>7</output>
<result>7</result>


a , b and c play a cricket match . the ratio of the runs scored by them in the match is a : b = 2 : 3 and b : c = 2 : 5 . if the total runs scored by all of them are 75 , the runs scored by b are ? a . 15 b . 18

Explanation: a : b = 2 : 3 b : c = 2 : 5 a : b : c = 4 : 6 : 15 6 / 25 * 75 = 18 answer : b

multiply(divide(75, add(add(multiply(divide(2, 3), divide(2, 5)), divide(2, 5)), const_1)), divide(2, 5))

<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/3) * (2/5)</gadget>
<output>4/15 = around 0.266667</output>
<gadget id="calculator">(4/15) + (2/5)</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) + 1</gadget>
<output>5/3 = around 1.666667</output>
<gadget id="calculator">75 / (5/3)</gadget>
<output>45</output>
<gadget id="calculator">45 * (2/5)</gadget>
<output>18</output>
<result>18</result>


if 65 percent of a class answered the first question on a certain test correctly , 50 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?

Explanation: "65 % answered the first question correctly and 20 % answered neither correctly . then 15 % missed the first question but answered the second question correctly . then the percent who answered both correctly is 50 % - 15 % = 35 % . the answer is c ."

subtract(add(add(65, 50), 20), const_100)

<gadget id="calculator">65 + 50</gadget>
<output>115</output>
<gadget id="calculator">115 + 20</gadget>
<output>135</output>
<gadget id="calculator">135 - 100</gadget>
<output>35</output>
<result>35</result>


john and ingrid pay 30 % and 40 % tax annually , respectively . if john makes $ 56000 and ingrid makes $ 73000 , what is their combined tax rate ?

Explanation: "( 1 ) when 30 and 40 has equal weight or weight = 1 / 2 , the answer would be 35 . ( 2 ) when 40 has larger weight than 30 , the answer would be in between 35 and 40 . unfortunately , we have 2 answer choices d and e that fit that condition so we need to narrow down our range . ( 3 ) get 73000 / 129000 = 73 / 129 is a little above 1 / 2 . thus , our answer is just a little above 35 . answer : d"

multiply(divide(add(multiply(divide(30, const_100), 56000), multiply(divide(40, const_100), 73000)), add(73000, 56000)), const_100)

<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(3/10) * 56_000</gadget>
<output>16_800</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) * 73_000</gadget>
<output>29_200</output>
<gadget id="calculator">16_800 + 29_200</gadget>
<output>46_000</output>
<gadget id="calculator">73_000 + 56_000</gadget>
<output>129_000</output>
<gadget id="calculator">46_000 / 129_000</gadget>
<output>46/129 = around 0.356589</output>
<gadget id="calculator">(46/129) * 100</gadget>
<output>4_600/129 = around 35.658915</output>
<result>4_600/129 = around 35.658915</result>


the average ( arithmetic mean ) of 20 , 40 , and 60 is 6 more than the average of 10 , 70 , and what number ?

Explanation: "a 1 = 120 / 3 = 40 a 2 = a 1 - 6 = 34 sum of second list = 34 * 3 = 102 therefore the number = 102 - 80 = 22 answer : d"

subtract(add(add(20, 40), 60), add(add(multiply(6, const_3), 10), 70))

<gadget id="calculator">20 + 40</gadget>
<output>60</output>
<gadget id="calculator">60 + 60</gadget>
<output>120</output>
<gadget id="calculator">6 * 3</gadget>
<output>18</output>
<gadget id="calculator">18 + 10</gadget>
<output>28</output>
<gadget id="calculator">28 + 70</gadget>
<output>98</output>
<gadget id="calculator">120 - 98</gadget>
<output>22</output>
<result>22</result>


if 150 ! / 10 ^ n is an integer , what is the largest possible value of n ?

Explanation: the question actually asks the highest power of 10 which divides 150 ! ( for a number to be an integer - without any remainder all the trailing zeroe ' s must be divided by the denominator ) 10 = 2 x 5 150 factorial will have 37 as - 150 / 5 = 30 30 / 5 = 6 6 / 5 = 1 so answer will be ( e ) 37

add(divide(divide(150, add(const_4, const_1)), add(const_4, const_1)), divide(150, add(const_4, const_1)))

<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">150 / 5</gadget>
<output>30</output>
<gadget id="calculator">30 / 5</gadget>
<output>6</output>
<gadget id="calculator">6 + 30</gadget>
<output>36</output>
<result>36</result>


the average height of 20 students in a class was calculated as 175 cm . it has later found that the height of one of the students in the class was incorrectly written as 151 cm whereas the actual height was 131 cm . what was the actual average height of the students in the class ?

Explanation: "the total height was 20 cm too much . the average height should be reduced by 20 cm / 20 = 1 cm the answer is a ."

divide(subtract(multiply(20, 175), subtract(151, 131)), 20)

<gadget id="calculator">20 * 175</gadget>
<output>3_500</output>
<gadget id="calculator">151 - 131</gadget>
<output>20</output>
<gadget id="calculator">3_500 - 20</gadget>
<output>3_480</output>
<gadget id="calculator">3_480 / 20</gadget>
<output>174</output>
<result>174</result>


a certain number of workers can do a work in 85 days . if there were 10 workers more it could be finished in 10 days less . how many workers are there ?

Explanation: "number of workers = 10 * ( 85 - 10 ) / 10 = 75 answer is a"

divide(multiply(subtract(85, 10), 10), subtract(85, subtract(85, 10)))

<gadget id="calculator">85 - 10</gadget>
<output>75</output>
<gadget id="calculator">75 * 10</gadget>
<output>750</output>
<gadget id="calculator">85 - 75</gadget>
<output>10</output>
<gadget id="calculator">750 / 10</gadget>
<output>75</output>
<result>75</result>


car z travels 48 miles per gallon of gasoline when driven at a constant rate of 45 miles per hour , but travels 20 percent fewer miles per gallon of gasoline when driven at a constant rate of 60 miles per hour . how many miles does car z travel on 10 gallons of gasoline when driven at a constant rate of 60 miles per hour ?

Explanation: "the question stem asks us for the distance possible with 10 gallons of fuel at a constant speed of 60 miles per hour . we therefore first calculate the fuel efficiency at that speed . the stem tells us that at 45 miles / hour , the car will run 48 miles / gallon and at 60 miles / hour , that distance decreases by 20 % . we can therefore conclude that the car will travel 38.4 miles / gallon at a constant speed of 60 miles / gallon . with 10 gallons of fuel , the car can therefore travel 38.4 miles / gallon * 10 gallons = 384 miles . answer b ."

multiply(multiply(subtract(const_1, divide(20, const_100)), 48), 10)

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(4/5) * 48</gadget>
<output>192/5 = around 38.4</output>
<gadget id="calculator">(192/5) * 10</gadget>
<output>384</output>
<result>384</result>


mr yadav spends 60 % of his monthly salary on consumable items and 50 % of the remaining on clothes and transport . he saves the remaining amount . if his savings at the end of the year were 24000 , how much amount per month would he have spent on clothes and transport ?

Explanation: "∵ amount , he have spent in 1 month on clothes transport = amount spent on saving per month ∵ amount , spent on clothes and transport = 24000 ⁄ 12 = 2000 answer a"

multiply(divide(divide(24000, divide(divide(multiply(subtract(const_100, 60), 50), const_100), const_100)), multiply(const_3, const_4)), divide(divide(multiply(subtract(const_100, 60), 50), const_100), const_100))

<gadget id="calculator">100 - 60</gadget>
<output>40</output>
<gadget id="calculator">40 * 50</gadget>
<output>2_000</output>
<gadget id="calculator">2_000 / 100</gadget>
<output>20</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">24_000 / (1/5)</gadget>
<output>120_000</output>
<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">120_000 / 12</gadget>
<output>10_000</output>
<gadget id="calculator">10_000 * (1/5)</gadget>
<output>2_000</output>
<result>2_000</result>


in the class of 50 students , 30 speak tamil and 40 speak telugu . what is the lowest possible number of students who speak both the languages ?

Explanation: let the student who speaks tamil - x let the student who speaks telugu - y as ( xuy ) - ( xny ) = total 30 + 40 - ( xny ) = 50 = 20 c )

<gadget id="calculator">40 + 30</gadget>
<output>70</output>
<gadget id="calculator">70 - 50</gadget>
<output>20</output>
<result>20</result>


two trains start simultaneously from opposite ends of a 175 - km route and travel toward each other on parallel tracks . train x , traveling at a constant rate , completes the 175 - km trip in 4 hours . train y , travelling at a constant rate , completes the 175 - km trip in 3 hours . how many kilometers had train x traveled when it met train y ?

Explanation: if the two trains cover a total distance d , then train x travels ( 3 / 7 ) * d while train y travels ( 4 / 7 ) * d . if the trains travel 175 km to the meeting point , then train x travels ( 3 / 7 ) * 175 = 75 km . the answer is d .

multiply(divide(175, 4), divide(175, add(divide(175, 4), divide(175, 3))))

<gadget id="calculator">175 / 4</gadget>
<output>175/4 = around 43.75</output>
<gadget id="calculator">175 / 3</gadget>
<output>175/3 = around 58.333333</output>
<gadget id="calculator">(175/4) + (175/3)</gadget>
<output>1_225/12 = around 102.083333</output>
<gadget id="calculator">175 / (1_225/12)</gadget>
<output>12/7 = around 1.714286</output>
<gadget id="calculator">(175/4) * (12/7)</gadget>
<output>75</output>
<result>75</result>


what is the rate percent when the simple interest on rs . 2000 amount to rs . 320 in 4 years ?

Explanation: "interest for 1 year = 320 / 4 = 80 interest on rs 2000 p / a = 80 interest rate = 80 / 2000 * 100 = 4 % answer : c"

divide(multiply(const_100, 320), multiply(2000, 4))

<gadget id="calculator">100 * 320</gadget>
<output>32_000</output>
<gadget id="calculator">2_000 * 4</gadget>
<output>8_000</output>
<gadget id="calculator">32_000 / 8_000</gadget>
<output>4</output>
<result>4</result>


a ratio between two numbers is 4 : 5 and their l . c . m . is 200 . the first number is

Explanation: "sol . let the required numbers be 4 x and 5 x . then , their l . c . m . is 20 x . ∴ 20 x = 200 ⇔ x = 10 . hence , the first number is 40 . answer b"

multiply(divide(200, multiply(4, 5)), 4)

<gadget id="calculator">4 * 5</gadget>
<output>20</output>
<gadget id="calculator">200 / 20</gadget>
<output>10</output>
<gadget id="calculator">10 * 4</gadget>
<output>40</output>
<result>40</result>


10 camels cost as much as 24 horses , 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants . if the cost of 10 elephants is rs . 170000 , find the cost of a camel ?

Explanation: "cost of the camel = p 10 camels = 24 horses 16 horses = 4 oxen 6 oxen = 4 elephants 10 elephants = rs . 170000 p = rs . [ ( 24 * 4 * 4 * 170000 ) / ( 10 * 16 * 6 * 10 ) ] p = rs . ( 65280000 / 9600 ) = > p = rs . 6800 answer : d"

divide(multiply(multiply(multiply(24, 4), 4), 170000), multiply(multiply(multiply(10, 16), 6), 10))

<gadget id="calculator">24 * 4</gadget>
<output>96</output>
<gadget id="calculator">96 * 4</gadget>
<output>384</output>
<gadget id="calculator">384 * 170_000</gadget>
<output>65_280_000</output>
<gadget id="calculator">10 * 16</gadget>
<output>160</output>
<gadget id="calculator">160 * 6</gadget>
<output>960</output>
<gadget id="calculator">960 * 10</gadget>
<output>9_600</output>
<gadget id="calculator">65_280_000 / 9_600</gadget>
<output>6_800</output>
<result>6_800</result>


when the positive integer k is divided by the positive integer n , the remainder is 11 . if k / n = 81.1 , what is the value of n ?

Explanation: "here ' s an approach that ' s based on number properties and a bit ofbrute forcemath : we ' re told that k and n are both integers . since k / n = 81.2 , we can say that k = 81.2 ( n ) n has tomultiply outthe . 2 so that k becomes an integer . with the answers that we have to work with , n has to be a multiple of 5 . eliminate a and e . with the remaining answers , we can test the answers and find the one that fits the rest of the info ( k / n = 81.2 and k / n has a remainder of 11 ) answer b : if n = 20 , then k = 1624 ; 1624 / 20 has a remainder of 4 not a match answer c : if n = 55 , then k = 4466 ; 4466 / 55 has a remainder of 11 match . final answer : e"

divide(add(multiply(divide(subtract(multiply(81.1, const_10), const_2), const_10), divide(11, divide(const_2, const_10))), 11), divide(11, divide(const_2, const_10)))

<gadget id="calculator">81.1 * 10</gadget>
<output>811</output>
<gadget id="calculator">811 - 2</gadget>
<output>809</output>
<gadget id="calculator">809 / 10</gadget>
<output>809/10 = around 80.9</output>
<gadget id="calculator">2 / 10</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">11 / (1/5)</gadget>
<output>55</output>
<gadget id="calculator">(809/10) * 55</gadget>
<output>8_899/2 = around 4_449.5</output>
<gadget id="calculator">(8_899/2) + 11</gadget>
<output>8_921/2 = around 4_460.5</output>
<gadget id="calculator">(8_921/2) / 55</gadget>
<output>811/10 = around 81.1</output>
<result>811/10 = around 81.1</result>


if a person walks at 10 km / hr instead of 8 km / hr , he would have walked 14 km more . the actual distance traveled by him is ?

Explanation: "let the actual distance traveled be x km . then , x / 8 = ( x + 14 ) / 10 2 x - 112 = > x = 56 km . answer : c"

multiply(8, divide(14, subtract(10, 8)))

<gadget id="calculator">10 - 8</gadget>
<output>2</output>
<gadget id="calculator">14 / 2</gadget>
<output>7</output>
<gadget id="calculator">8 * 7</gadget>
<output>56</output>
<result>56</result>


if twice of a number divided by 3 d gives 20 as the remainder , and 5 times of the same number gives 32 as the remainder . what will be the value of d ?

Explanation: remainder in second case is , 32 . so , 3 d > = 33 . so , minimum value of d should 11 . if number = 28 . double of number = 56 and take d = 12 so 56 / 36 remainder = 20 . now 5 times of number = 140 . so 140 / 36 remainder = 32 . that is , 3 d = 36 satisfy the conditions . so d = 12 . answer : b

subtract(multiply(divide(32, 5), const_2), divide(const_1, const_4))

<gadget id="calculator">32 / 5</gadget>
<output>32/5 = around 6.4</output>
<gadget id="calculator">(32/5) * 2</gadget>
<output>64/5 = around 12.8</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(64/5) - (1/4)</gadget>
<output>251/20 = around 12.55</output>
<result>251/20 = around 12.55</result>


3 people candidates contested an election and they received 1136 , 7636 and 11628 votes respectively . what is the percentage of the total votes did the winning candidate get ?

Explanation: tot no of votes = ( 1136 + 7636 + 11628 ) = 20400 req = > ( 11628 / 20400 * 100 ) = > 57 % answer c

<gadget id="calculator">1_136 + 7_636</gadget>
<output>8_772</output>
<gadget id="calculator">8_772 + 11_628</gadget>
<output>20_400</output>
<gadget id="calculator">11_628 / 20_400</gadget>
<output>57/100 = around 0.57</output>
<gadget id="calculator">(57/100) * 100</gadget>
<output>57</output>
<result>57</result>


a spirit and water solution is sold in a market . the cost per liter of the solution is directly proportional to the part ( fraction ) of spirit ( by volume ) the solution has . a solution of 1 liter of spirit and 1 liter of water costs 40 cents . how many cents does a solution of 1 liter of spirit and 2 liters of water cost ?

Explanation: "yes , ensure that you understand the relation thoroughly ! cost per liter = k * fraction of spirit 40 cents is the cost of 2 liters of solution ( 1 part water , 1 part spirit ) . so cost per liter is 20 cents . fraction of spirit is 1 / 2 . 20 = k * ( 1 / 2 ) k = 40 cost per liter = 40 * ( 1 / 3 ) ( 1 part spirit , 2 parts water ) cost for 3 liters = 40 * ( 1 / 3 ) * 3 = 40 cents a . 40 cents"

multiply(multiply(40, divide(1, add(1, 2))), add(1, 2))

<gadget id="calculator">1 + 2</gadget>
<output>3</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">40 * (1/3)</gadget>
<output>40/3 = around 13.333333</output>
<gadget id="calculator">(40/3) * 3</gadget>
<output>40</output>
<result>40</result>


if 12 men or 20 women can do a piece of work in 54 days , then in how many days can 9 men and 12 women together do the work ?

Explanation: "e 40 days given that 12 m = 20 w = > 3 m = 5 w 9 men + 12 women = 15 women + 12 women = 27 women 20 women can do the work in 54 days . so , 27 women can do it in ( 20 * 54 ) / 27 = 40 days ."

inverse(add(divide(9, multiply(12, 54)), divide(12, multiply(20, 54))))

<gadget id="calculator">12 * 54</gadget>
<output>648</output>
<gadget id="calculator">9 / 648</gadget>
<output>1/72 = around 0.013889</output>
<gadget id="calculator">20 * 54</gadget>
<output>1_080</output>
<gadget id="calculator">12 / 1_080</gadget>
<output>1/90 = around 0.011111</output>
<gadget id="calculator">(1/72) + (1/90)</gadget>
<output>1/40 = around 0.025</output>
<gadget id="calculator">1 / (1/40)</gadget>
<output>40</output>
<result>40</result>


gold is 19 times as heavy as water and copper is 9 times as heavy as water . in what ratio should these be mixed to get an alloy 13 times as heavy as water ?

Explanation: "g = 19 w c = 9 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 19 w + 9 wx = x + 1 * 13 w 19 + 9 x = 13 ( x + 1 ) x = 3 / 2 ratio of gold with copper = 1 : 3 / 2 = 2 : 3 answer is b"

divide(subtract(13, 9), subtract(19, 13))

<gadget id="calculator">13 - 9</gadget>
<output>4</output>
<gadget id="calculator">19 - 13</gadget>
<output>6</output>
<gadget id="calculator">4 / 6</gadget>
<output>2/3 = around 0.666667</output>
<result>2/3 = around 0.666667</result>


a and b started a business jointly a ' s investment was thrice the investment of b and the period of his investment was two times the period of investment of b . if b received rs . 4000 as profit , then their total profit is

Explanation: "explanation : suppose b invested rs . x for y months . then , a invested rs . 3 x for 2 y months . so , a : b = ( 3 x * 2 y ) : ( x * y ) = 6 xy : xy = 6 : 1 . b ' s profit : total profit = 1 : 7 . let the total profit be rs . x then , 1 / 7 = 4000 / x or x = 28000 . answer : b ) 28000"

multiply(add(multiply(const_2, const_3), const_1), 4000)

<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">6 + 1</gadget>
<output>7</output>
<gadget id="calculator">7 * 4_000</gadget>
<output>28_000</output>
<result>28_000</result>


excluding stoppages , the average speed of a bus is 100 km / hr and including stoppages , the average speed of the bus is 40 km / hr . for how many minutes does the bus stop per hour ?

Explanation: in 1 hr , the bus covers 100 km without stoppages and 40 km with stoppages . stoppage time = time take to travel ( 100 - 40 ) km i . e 60 km at 100 km / hr . stoppage time = 60 / 100 hrs = 36 min answer : e

subtract(multiply(const_1, const_60), multiply(divide(40, 100), const_60))

<gadget id="calculator">1 * 60</gadget>
<output>60</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) * 60</gadget>
<output>24</output>
<gadget id="calculator">60 - 24</gadget>
<output>36</output>
<result>36</result>


tom traveled the entire 60 miles trip . if he did the first 15 miles of at a constant rate 24 miles per hour and the remaining trip of at a constant rate 45 miles per hour , what is the his average speed , in miles per hour ?

Explanation: avg speed = total distance / total time = ( d 1 + d 2 ) / ( t 1 + t 2 ) = ( 15 + 45 ) / ( ( 15 / 24 ) + ( 45 / 45 ) ) = 60 * 2 / 3 = 36.92 mph d

divide(60, add(divide(45, subtract(60, 15)), divide(15, 24)))

<gadget id="calculator">60 - 15</gadget>
<output>45</output>
<gadget id="calculator">45 / 45</gadget>
<output>1</output>
<gadget id="calculator">15 / 24</gadget>
<output>5/8 = around 0.625</output>
<gadget id="calculator">1 + (5/8)</gadget>
<output>13/8 = around 1.625</output>
<gadget id="calculator">60 / (13/8)</gadget>
<output>480/13 = around 36.923077</output>
<result>480/13 = around 36.923077</result>


if w is the set of all the integers between 49 and 114 , inclusive , that are either multiples of 3 or multiples of 2 or multiples of both , then w contains how many numbers ?

Explanation: "official solution : number of multiples of 3 step 1 . subtract the extreme multiples of 3 within the range ( the greatest is 114 , the smallest is 51 ) : 114 - 51 = 63 step 2 . divide by 3 : 63 / 3 = 21 step 3 . add 1 : 21 + 1 = 22 . so there are 22 multiples of 3 within the range : examples are 51 , 54 , 57 , 60 , etc . number of multiples of 2 step 1 . subtract the extreme multiples of 2 within the range ( the greatest is 114 , the smallest is 50 ) : 114 - 50 = 64 step 2 . divide by 2 : 64 / 2 = 32 step 3 . add 1 : 32 + 1 = 33 . so there are 33 multiples of 2 within the range : examples are 50 , 52 , 54 , 56 , 58 , 60 etc . add the 22 multiples of 3 and the 33 multiples of 2 : 22 + 33 = 55 . however , by adding the multiples of 2 and the multiples of 3 , we are effectively counting several numbers twice : for example , 54 and 60 are parts of both the lists above . so we ca n ' t just take 22 + 33 = 55 . find the number of multiples of 6 ( which are the double counted , as 6 is divisible by both 2 and 3 ) , and subtract it from 55 : step 1 . subtract the extreme multiples of 6 within the range ( the greatest is 72 , the smallest is 54 ) : 114 - 54 = 60 step 2 . divide by 6 : 60 / 6 = 10 step 3 . add 1 : 10 + 1 = 11 . so there are 11 multiples of 6 within the range : we counted 11 numbers twice . subtract the 11 multiples of 6 from the sum of the multiples of 2 and 3 : = 22 + 33 - 11 = 55 - 11 = 44 therefore , the final number of multiples of 2 , 3 or 6 is 44 . hence , this is the correct answer . ( b )"

subtract(add(floor(divide(subtract(114, 49), 3)), divide(subtract(114, 49), 2)), floor(divide(subtract(114, 49), multiply(2, 3))))

<gadget id="calculator">114 - 49</gadget>
<output>65</output>
<gadget id="calculator">65 / 3</gadget>
<output>65/3 = around 21.666667</output>
<gadget id="calculator">floor(65/3)</gadget>
<output>21</output>
<gadget id="calculator">65 / 2</gadget>
<output>65/2 = around 32.5</output>
<gadget id="calculator">21 + (65/2)</gadget>
<output>107/2 = around 53.5</output>
<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">65 / 6</gadget>
<output>65/6 = around 10.833333</output>
<gadget id="calculator">floor(65/6)</gadget>
<output>10</output>
<gadget id="calculator">(107/2) - 10</gadget>
<output>87/2 = around 43.5</output>
<result>87/2 = around 43.5</result>


a shopkeeper sold 8 articles at the cost price of 10 articles . then find the profit % or lost %

Explanation: "here 8 articles selling price = 10 articles cost price so the difference = 10 - 8 = 2 % of profit = 2 * 100 / 8 = 25 % correct option is b"

multiply(divide(subtract(10, 8), 8), const_100)

<gadget id="calculator">10 - 8</gadget>
<output>2</output>
<gadget id="calculator">2 / 8</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<result>25</result>


the general hospital is comprised of , 3 / 5 pediatricians , 1 / 4 surgeons , and the rest are gp doctors . if 1 / 4 of the surgeons are heart surgeons , and the hospital doubles the number of gp doctors , what proportion of the hospital are now heart surgeons ?

Explanation: ped = 3 / 5 = 12 / 20 sur = 1 / 4 = 4 / 20 gp = 1 - ( 12 / 20 + 4 / 20 ) = 1 - 16 / 20 = 4 / 20 hsur = ( 1 / 4 ) ( 4 / 20 ) = 1 / 20 if gp doubled = > ( 2 ) ( 4 ) = 8 ; then , total = 12 + 4 + 8 = 24 , and 1 is hsur = > proportion = 1 / 24 . answer : d

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

<gadget id="calculator">1 + 1</gadget>
<output>2</output>
<gadget id="calculator">3 - 2</gadget>
<output>1</output>
<gadget id="calculator">4 * 5</gadget>
<output>20</output>
<gadget id="calculator">20 + 4</gadget>
<output>24</output>
<gadget id="calculator">1 / 24</gadget>
<output>1/24 = around 0.041667</output>
<result>1/24 = around 0.041667</result>


45 pupil , out of them 12 in debate only and 22 in singing only . then how many in both ?

Explanation: the intersection for two = 45 - 12 - 22 = 11 play both games . answer : c

<gadget id="calculator">12 + 22</gadget>
<output>34</output>
<gadget id="calculator">45 - 34</gadget>
<output>11</output>
<result>11</result>


of the 75 cars on a car lot , 45 have air - conditioning , 35 have power steering , and 12 have both air - conditioning and power steering . how many of the cars on the lot have neither air - conditioning nor power steering ?

Explanation: "total - neither = all air conditioning + all power steering - both or 75 - neither = 45 + 35 - 12 = 68 . = > neither = 7 , hence a . answer : a"

<gadget id="calculator">45 + 35</gadget>
<output>80</output>
<gadget id="calculator">80 - 12</gadget>
<output>68</output>
<gadget id="calculator">75 - 68</gadget>
<output>7</output>
<result>7</result>


a corporation 5 times its annual bonus to 10 of its employees . what percent of the employees ’ new bonus is the increase ?

Explanation: let the annual bonus be x . a corporation triples its annual bonus . so new bonus = 5 x . increase = 5 x - x = 4 x the increase is what percent of the employees ’ new bonus = ( 4 x / 5 x ) * 100 = 80 % hence c .

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

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


the sum of ages of 5 children born at the intervals of 3 years each is 50 years . what is the age of the youngest child ?

Explanation: "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 ) = 50 5 x = 20 x = 4 . age of the youngest child = x = 4 years . answer a"

<gadget id="calculator">50 / 5</gadget>
<output>10</output>
<gadget id="calculator">10 - 3</gadget>
<output>7</output>
<gadget id="calculator">7 - 3</gadget>
<output>4</output>
<result>4</result>


yearly subscription to professional magazines cost a company $ 940.00 . to make a 25 % cut in the magazine budget , how much less must be spent ?

Explanation: total cost 940 940 * 25 / 100 = 235 so the cut in amount is 235 the less amount to be spend is 940 - 235 = 705 answer : a

multiply(divide(subtract(const_100, 25), const_100), 940)

<gadget id="calculator">100 - 25</gadget>
<output>75</output>
<gadget id="calculator">75 / 100</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(3/4) * 940</gadget>
<output>705</output>
<result>705</result>


the mean of 50 observations was 40 . it was found later that an observation 48 was wrongly taken as 23 . the corrected new mean is

Explanation: "sol . therefore correct sum = ( 40 × 50 + 48 – 23 ) = 2023 . therefore correct mean = 2023 / 50 = 40.46 . answer a"

divide(add(multiply(40, 50), subtract(subtract(50, const_2), 23)), 50)

<gadget id="calculator">40 * 50</gadget>
<output>2_000</output>
<gadget id="calculator">50 - 2</gadget>
<output>48</output>
<gadget id="calculator">48 - 23</gadget>
<output>25</output>
<gadget id="calculator">2_000 + 25</gadget>
<output>2_025</output>
<gadget id="calculator">2_025 / 50</gadget>
<output>81/2 = around 40.5</output>
<result>81/2 = around 40.5</result>


a certain tests consists 8 sections with 25 questions , numbered from 1 to 25 , in each section . if a student answered all of the even - numbered questions correctly and 3 / 4 of the odd - numbered questions correctly , what was the total number of questions he answered correctly ? a . 150 b . 172 c . 174 d . 175 e . 176

Explanation: each set has 12 even and 13 odd numbered questions leading to total 96 even and 104 odd questions . 96 + 3 / 4 â ˆ — 104 = 96 + 78 = 17496 + 3 / 4 â ˆ — 104 = 96 + 78 = 174 answer : a

add(divide(multiply(8, 25), const_2), multiply(divide(multiply(8, 25), const_2), divide(3, 4)))

<gadget id="calculator">8 * 25</gadget>
<output>200</output>
<gadget id="calculator">200 / 2</gadget>
<output>100</output>
<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">100 * (3/4)</gadget>
<output>75</output>
<gadget id="calculator">100 + 75</gadget>
<output>175</output>
<result>175</result>


a train running at the speed of 60 km / hr crosses a pole in 30 seconds . what is the length of the train ?

Explanation: "speed = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec length of the train = ( speed x time ) = ( 50 / 3 * 30 ) m = 500 m . answer : a"

multiply(divide(multiply(60, const_1000), const_3600), 30)

<gadget id="calculator">60 * 1_000</gadget>
<output>60_000</output>
<gadget id="calculator">60_000 / 3_600</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">(50/3) * 30</gadget>
<output>500</output>
<result>500</result>


when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 15 - inch boxes . if the university pays $ 0.60 for every box , and if the university needs 3.06 million cubic inches to package the collection , what is the minimum amount the university must spend on boxes ?

Explanation: "total no . of boxes = 3060000 / ( 20 × 20 × 15 ) = 510 total cost = 510 × $ 0.6 = $ 306 answer a"

multiply(divide(multiply(3.06, multiply(const_1000, const_1000)), multiply(multiply(20, 20), 15)), 0.60)

<gadget id="calculator">1_000 * 1_000</gadget>
<output>1_000_000</output>
<gadget id="calculator">3.06 * 1_000_000</gadget>
<output>3_060_000</output>
<gadget id="calculator">20 * 20</gadget>
<output>400</output>
<gadget id="calculator">400 * 15</gadget>
<output>6_000</output>
<gadget id="calculator">3_060_000 / 6_000</gadget>
<output>510</output>
<gadget id="calculator">510 * 0.6</gadget>
<output>306</output>
<result>306</result>


the sum of ages of 5 children born at the intervals of 3 years each is 80 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 ) = 80 5 x = 50 x = 10 . age of the youngest child = x = 10 years . e )"

<gadget id="calculator">80 / 5</gadget>
<output>16</output>
<gadget id="calculator">16 - 3</gadget>
<output>13</output>
<gadget id="calculator">13 - 3</gadget>
<output>10</output>
<result>10</result>


Explanation: "2 = x * 40 / 100 x = 5 % ans ; c"

<gadget id="calculator">2 / 40</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/20) * 100</gadget>
<output>5</output>
<result>5</result>


tea worth rs . 126 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs . 153 per kg , the price of the third variety per kg

Explanation: "explanation : since first second varieties are mixed in equal proportions , so their average price = rs . ( 126 + 135 / 2 ) = rs . 130.50 so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . cost of 1 kg tea of 1 st kind cost of 1 kg tea of 2 nd kind x - 153 / 22.50 = 1 = > x - 153 = 22.50 = > x = 175.50 . hence , price of the third variety = rs . 175.50 per kg . answer : c ) rs . 175.50"

divide(subtract(multiply(153, add(add(1, 1), 2)), add(126, 126)), 2)

<gadget id="calculator">1 + 1</gadget>
<output>2</output>
<gadget id="calculator">2 + 2</gadget>
<output>4</output>
<gadget id="calculator">153 * 4</gadget>
<output>612</output>
<gadget id="calculator">126 + 126</gadget>
<output>252</output>
<gadget id="calculator">612 - 252</gadget>
<output>360</output>
<gadget id="calculator">360 / 2</gadget>
<output>180</output>
<result>180</result>


in an examination , a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 80 questions and secures 120 marks , the number of questions he attempts correctly , is :

Explanation: "let the number of correct answers be x . number of incorrect answers = ( 80 â € “ x ) . 4 x â € “ 1 ( 80 â € “ x ) = 120 or 5 x = 200 or x = 40 . answer : e"

<gadget id="calculator">120 + 80</gadget>
<output>200</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">200 / 5</gadget>
<output>40</output>
<result>40</result>


a no . when divided by the sum of 555 and 445 gives 2 times their difference as quotient & 10 as remainder . find the no . is ?

Explanation: "( 555 + 445 ) * 2 * 110 + 10 = 220000 + 10 = 220010 a"

add(multiply(multiply(add(555, 445), 2), subtract(555, 445)), 10)

<gadget id="calculator">555 + 445</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 * 2</gadget>
<output>2_000</output>
<gadget id="calculator">555 - 445</gadget>
<output>110</output>
<gadget id="calculator">2_000 * 110</gadget>
<output>220_000</output>
<gadget id="calculator">220_000 + 10</gadget>
<output>220_010</output>
<result>220_010</result>


in a sports club with 55 members , 23 play badminton and 29 play tennis and 7 do not play either . how many members play both badminton and tennis ?

Explanation: "23 + 29 = 52 but where as total number is 55 - 7 = 48 therefore answer is 52 - 48 = 4 hence answer is c"

<gadget id="calculator">23 + 29</gadget>
<output>52</output>
<gadget id="calculator">52 + 7</gadget>
<output>59</output>
<gadget id="calculator">59 - 55</gadget>
<output>4</output>
<result>4</result>


a garrison of 500 men has provisions for 20 days . at the end of 14 days , a reinforcement arrives , and it is now found that the provisions will last only for 3 days more . what is the reinforcement ?

Explanation: "500 - - - - 20 500 - - - - 6 x - - - - - 3 x * 3 = 500 * 6 x = 1000 500 - - - - - - - 500 answer : a"

subtract(divide(subtract(multiply(500, 20), multiply(500, 14)), 3), 500)

<gadget id="calculator">500 * 20</gadget>
<output>10_000</output>
<gadget id="calculator">500 * 14</gadget>
<output>7_000</output>
<gadget id="calculator">10_000 - 7_000</gadget>
<output>3_000</output>
<gadget id="calculator">3_000 / 3</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 - 500</gadget>
<output>500</output>
<result>500</result>


how long does a train 165 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length ?

Explanation: "t = ( 660 + 165 ) / 54 * 18 / 5 t = 55 answer a"

<gadget id="calculator">165 + 660</gadget>
<output>825</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">54 * (5/18)</gadget>
<output>15</output>
<gadget id="calculator">825 / 15</gadget>
<output>55</output>
<result>55</result>


in covering a distance of 54 km , abhay takes 2 hours more than sameer . if abhay doubles his speed , then he would take 1 hour less than sameer . abhay ' s speed is :

Explanation: "let abhay ' s speed be x km / hr . then , 54 / x - 54 / 2 x = 3 6 x = 54 x = 9 km / hr . answer : option e"

divide(subtract(54, divide(54, 2)), add(1, 2))

<gadget id="calculator">54 / 2</gadget>
<output>27</output>
<gadget id="calculator">54 - 27</gadget>
<output>27</output>
<gadget id="calculator">1 + 2</gadget>
<output>3</output>
<gadget id="calculator">27 / 3</gadget>
<output>9</output>
<result>9</result>


john has $ 1600 at the beginning of his trip , after spending money , he still has exactly $ 600 less than he spent on the trip . how much money does john still have ?

Explanation: suppose total money spent = x not spend ( money he still has ) = x - 600 x + x - 600 = 1600 x = 1100 money not spend = 1100 - 600 = 500 answer : e

<gadget id="calculator">1_600 - 600</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 / 2</gadget>
<output>500</output>
<result>500</result>


students at a school were on average 180 cm tall . the average female height was 170 cm , and the average male height was 181 cms . what was the ratio of men to women ?

Explanation: we ' re given a few facts to work with : 1 ) the average height of the females is 170 cm 2 ) the average height of the males is 181 cm 3 ) the average of the group is 180 cm we ' re asked for the ratio of men to women . w = number of women m = number of men ( 170 w + 181 m ) / ( w + m ) = 180 170 w + 181 m = 180 w + 180 m 1 m = 10 w m / w = 10 / 1 the ratio of men to women is 10 to 1 . e

divide(subtract(180, 170), subtract(181, 180))

<gadget id="calculator">180 - 170</gadget>
<output>10</output>
<gadget id="calculator">181 - 180</gadget>
<output>1</output>
<gadget id="calculator">10 / 1</gadget>
<output>10</output>
<result>10</result>


if the length of the longest chord of a certain circle is 18 , what is the radius of that certain circle ?

Explanation: "longest chord of a circle is the diameter of the circle diameter = 2 * radius if diameter of the circle is given as 18 = 2 * 9 so radius of the circle = 9 correct answer - b"

<gadget id="calculator">18 / 2</gadget>
<output>9</output>
<result>9</result>


a cistern 10 meters long and 4 meters wide contains water up to a depth of 1 meter 25 cm . what is the total area of the wet surface ?

Explanation: area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 4 x 1.25 + 10 x 1.25 ) + 10 x 4 ] = 75 the answer is d .

add(add(multiply(10, 4), multiply(const_2, multiply(4, add(1, divide(25, const_100))))), multiply(const_2, multiply(10, add(1, divide(25, const_100)))))

<gadget id="calculator">10 * 4</gadget>
<output>40</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 + (1/4)</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">4 * (5/4)</gadget>
<output>5</output>
<gadget id="calculator">2 * 5</gadget>
<output>10</output>
<gadget id="calculator">40 + 10</gadget>
<output>50</output>
<gadget id="calculator">10 * (5/4)</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">2 * (25/2)</gadget>
<output>25</output>
<gadget id="calculator">50 + 25</gadget>
<output>75</output>
<result>75</result>


if 50 % of ( x - y ) = 30 % of ( x + y ) then what percent of x is y ?

Explanation: "50 % of ( x - y ) = 30 % of ( x + y ) ( 50 / 100 ) ( x - y ) = ( 30 / 100 ) ( x + y ) 5 ( x - y ) = 3 ( x + y ) 2 x = 8 y x = 4 y therefore required percentage = ( ( y / x ) x 100 ) % = ( ( y / 4 y ) x 100 ) = 25 % answer is e ."

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

<gadget id="calculator">50 - 30</gadget>
<output>20</output>
<gadget id="calculator">50 + 30</gadget>
<output>80</output>
<gadget id="calculator">20 / 80</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<result>25</result>


how many seconds does sandy take to cover a distance of 600 meters , if sandy runs at a speed of 18 km / hr ?

Explanation: 18 km / hr = 18000 m / 3600 s = 5 m / s time = 600 / 5 = 120 seconds the answer is b .

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">18 * (5/18)</gadget>
<output>5</output>
<gadget id="calculator">600 / 5</gadget>
<output>120</output>
<result>120</result>


calculate how many days it will take for 10 boys to paint a 80 m long wall if 6 boys can paint a 70 m long wall in 8 days ,

Explanation: "the length of wall painted by one boy in one day = 70 / 6 * 1 / 8 = 1.46 m no . of days required to paint 50 m cloth by 8 boys = 80 / 10 * 1 / 1.46 = 5.48 days . d"

divide(multiply(multiply(6, 8), 80), multiply(70, 10))

<gadget id="calculator">6 * 8</gadget>
<output>48</output>
<gadget id="calculator">48 * 80</gadget>
<output>3_840</output>
<gadget id="calculator">70 * 10</gadget>
<output>700</output>
<gadget id="calculator">3_840 / 700</gadget>
<output>192/35 = around 5.485714</output>
<result>192/35 = around 5.485714</result>


a no . when divided by the sum of 555 and 445 gives 2 times their difference as quotient & 60 as remainder . find the no . is ?

Explanation: "( 555 + 445 ) * 2 * 110 + 60 = 220000 + 60 = 220060 e"

add(multiply(multiply(add(555, 445), 2), subtract(555, 445)), 60)

<gadget id="calculator">555 + 445</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 * 2</gadget>
<output>2_000</output>
<gadget id="calculator">555 - 445</gadget>
<output>110</output>
<gadget id="calculator">2_000 * 110</gadget>
<output>220_000</output>
<gadget id="calculator">220_000 + 60</gadget>
<output>220_060</output>
<result>220_060</result>


a monkey start climbing up a tree 18 ft tall . each hour it hops 3 ft and slips back 2 ft . how much time would it take the monkey to reach the top .

Explanation: "if monkey hops 3 ft and slips back 2 ft in a hour , it means the monkey hops ( 3 ft - 2 ft ) = 1 ft / hr . similarly in 15 hrs it wil be 15 ft . bt since the height of the tree is 18 ft , so if the monkey hops up the tree in the next hr i . e 16 th hr then it reaches at the top of the tree . hence it takes 16 hrs for monkey to reach at the top answer : e"

<gadget id="calculator">3 - 2</gadget>
<output>1</output>
<gadget id="calculator">18 / 1</gadget>
<output>18</output>
<gadget id="calculator">18 - 2</gadget>
<output>16</output>
<result>16</result>


jane and ashley take 8 days and 40 days respectively to complete a project when they work on it alone . they thought if they worked on the project together , they would take fewer days to complete it . during the period that they were working together , jane took an eight day leave from work . this led to jane ' s working for four extra days on her own to complete the project . how long did it take to finish the project ?

Explanation: "let us assume that the work is laying 40 bricks . jane = 5 bricks per day ashley = 1 brick per day together = 6 bricks per day let ' s say first 8 days ashley works alone , no of bricks = 8 last 4 days jane works alone , no . of bricks = 20 remaining bricks = 40 - 28 = 12 so together , they would take 12 / 6 = 2 total no . of days = 8 + 4 + 2 = 14 answer is a"

add(add(divide(subtract(subtract(const_1, multiply(const_4, divide(const_1, 8))), multiply(add(const_4, const_4), divide(const_1, 40))), add(divide(const_1, 8), divide(const_1, 40))), add(const_4, const_4)), const_4)

<gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">4 * (1/8)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 - (1/2)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">4 + 4</gadget>
<output>8</output>
<gadget id="calculator">1 / 40</gadget>
<output>1/40 = around 0.025</output>
<gadget id="calculator">8 * (1/40)</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/2) - (1/5)</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(1/8) + (1/40)</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">(3/10) / (3/20)</gadget>
<output>2</output>
<gadget id="calculator">2 + 8</gadget>
<output>10</output>
<gadget id="calculator">10 + 4</gadget>
<output>14</output>
<result>14</result>


if an integer n is to be selected at random from 1 to 100 , inclusive , what is probability n ( n + 1 ) will be divisible by 32 ?

Explanation: "because n ( n + 1 ) is always an even product of even * odd or odd * even factors , there is a probability of 1 that that it will be divisible by 2 , and , thus , a probability of 1 / 2 that it will be divisible by 4 and , thus , a probability of 1 / 4 that it will be divisible by 8 and , thus , a probability of 1 / 8 that it will be divisible by 16 and , thus , a probability of 1 / 16 that it will be divisible by 32 1 * 1 / 16 = 1 / 16 answer : c"

<gadget id="calculator">2 / 32</gadget>
<output>1/16 = around 0.0625</output>
<result>1/16 = around 0.0625</result>


today jim is twice as old as fred , and sam is 4 years younger than fred . 4 years ago jim was 8 times as old as sam . how old is jim now ?

Explanation: we ' re asked how old jim is now . we ' re given three facts to work with : 1 ) today , jim is twice as old as fred 2 ) today , sam is 4 years younger than fred 3 ) four years ago , jim was 8 times as old as sam . let ' s test answer d : 20 if . . . . jim is currently 20 years old . . . . fred is 10 years old sam is 6 years old 4 years ago , jim was 16 and sam was 2 , so jim was 8 times sam ' s age . this is an exact match for what we were told , so this must be the answer . d

multiply(divide(subtract(multiply(8, 8), 4), subtract(8, const_2)), const_2)

<gadget id="calculator">8 * 8</gadget>
<output>64</output>
<gadget id="calculator">64 - 4</gadget>
<output>60</output>
<gadget id="calculator">8 - 2</gadget>
<output>6</output>
<gadget id="calculator">60 / 6</gadget>
<output>10</output>
<gadget id="calculator">10 * 2</gadget>
<output>20</output>
<result>20</result>


a bullet train 150 m long is running with a speed of 30 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the bullet train is going ?

Explanation: e 15 sec speed of the bullet train relative to man = ( 30 + 6 ) kmph = 36 * 5 / 18 m / sec = 30 / 3 m / sec . time taken by the bullet train to cross the man = time taken by it to cover 150 m at ( 30 / 3 ) m / sec = ( 150 * 3 / 30 ) sec = 15 sec

divide(150, divide(multiply(add(30, 6), const_1000), const_3600))

<gadget id="calculator">30 + 6</gadget>
<output>36</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">150 / 10</gadget>
<output>15</output>
<result>15</result>


the sum of all the integers k such that – 21 < k < 24 is

Explanation: "- 20 - - - - - - - - - - - - - - - - - - 0 - - - - - - - - - - - - - - - - - 23 values upto + 23 cancels outwe are left with only - 20 - 19 sum of which is - 39 . hence option d . d"

add(add(negate(21), const_1), add(add(negate(21), const_1), const_1))

<gadget id="calculator">-21</gadget>
<output>-21</output>
<gadget id="calculator">(-21) + 1</gadget>
<output>-20</output>
<gadget id="calculator">(-20) + 1</gadget>
<output>-19</output>
<gadget id="calculator">(-20) + (-19)</gadget>
<output>-39</output>
<result>-39</result>


a dealer purchases 15 articles for rs . 25 and sells 12 articles for rs . 30 . find the profit percentage ?

Explanation: "l . c . m of 15 and 12 = 60 cp of 60 articles = rs . 100 ( 25 * 4 ) sp of 60 articles = rs . 150 ( 30 * 5 ) profit percentage = ( 150 - 100 ) / 100 * 100 = 50 % answer : b"

subtract(multiply(30, add(const_4, const_1)), multiply(25, const_4))

<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">30 * 5</gadget>
<output>150</output>
<gadget id="calculator">25 * 4</gadget>
<output>100</output>
<gadget id="calculator">150 - 100</gadget>
<output>50</output>
<result>50</result>


a worker ' s daily wage is increased by 50 % and the new wage is $ 30 per day . what was the worker ' s daily wage before the increase ?

Explanation: let x be the daily wage before the increase . 1.5 x = $ 30 x = $ 20 the answer is c .

divide(30, add(const_1, divide(50, const_100)))

<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 + (1/2)</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">30 / (3/2)</gadget>
<output>20</output>
<result>20</result>


if the weight of 12 meters long rod is 13.4 kg . what is the weight of 6 meters long rod ?

Explanation: "answer ∵ weight of 12 m long rod = 13.4 kg ∴ weight of 1 m long rod = 13.4 / 12 kg ∴ weight of 6 m long rod = 13.4 x 6 / 12 = 6.7 kg option : a"

<gadget id="calculator">6 * 13.4</gadget>
<output>80.4</output>
<gadget id="calculator">80.4 / 12</gadget>
<output>6.7</output>
<result>6.7</result>


a store sells 2 kinds of jelly beans mixes ( a and b ) both made up of red and yellow beans . if b contains 20 % more red beans than a but 10 % fewer yellow beans . and jar a contains twice as many red beans as yellow by what percent is the number of beans in jar b larger than the number in jar a

Explanation: a has 10 yellows 20 reds total = 30 so b has 1.2 x 20 = 24 reds 0.9 x 10 = 9 yellows total = 33 difference = 3 / 30 = 10 % answer : e

multiply(subtract(divide(add(add(const_100, 20), subtract(const_100, 10)), const_100), const_2), const_100)

<gadget id="calculator">100 + 20</gadget>
<output>120</output>
<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">120 + 90</gadget>
<output>210</output>
<gadget id="calculator">210 / 100</gadget>
<output>21/10 = around 2.1</output>
<gadget id="calculator">(21/10) - 2</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) * 100</gadget>
<output>10</output>
<result>10</result>


find the greatest common factor ( gfc ) of 24 , 40 and 60 .

Explanation: we first write the prime factorization of each given number 24 = 2 × 2 × 2 × 3 = 23 * cubic * × 3 40 = 2 × 2 × 2 × 5 = 23 * cubic * × 5 60 = 2 × 2 × 3 × 5 = 22 * square * × 3 × 5 gfc = 22 * square * = 4 corect answer is d ) 4

<gadget id="calculator">gcd(24, 40)</gadget>
<output>8</output>
<gadget id="calculator">gcd(8, 60)</gadget>
<output>4</output>
<result>4</result>


when 242 is divided by a certain divisor the remainder obtained is 12 . when 698 is divided by the same divisor the remainder obtained is 16 . however , when the sum of the two numbers 242 and 698 is divided by the divisor , the remainder obtained is 10 . what is the value of the divisor ?

Explanation: "let that divisor be x since remainder is 12 or 16 it means divisor is greater than 16 . now 242 - 12 = 230 = kx ( k is an integer and 234 is divisble by x ) similarly 698 - 16 = 682 = lx ( l is an integer and 689 is divisible by x ) adding both 698 and 242 = ( 230 + 682 ) + 12 + 16 = x ( k + l ) + 28 when we divide this number by x then remainder will be equal to remainder of ( 28 divided by x ) = 10 hence x = 28 - 10 = 18 hence b"

<gadget id="calculator">12 + 16</gadget>
<output>28</output>
<gadget id="calculator">28 - 10</gadget>
<output>18</output>
<result>18</result>


the cost price of an article is 64 % of the marked price . calculate the gain percent after allowing a discount of 20 % ?

Explanation: "explanation : let marked price = rs . 100 . then , c . p . = rs . 64 , s . p . = rs . 80 gain % = 16 / 64 * 100 = 25 % . answer : option e"

multiply(subtract(divide(subtract(const_100, 20), 64), const_1), const_100)

<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">80 / 64</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">(5/4) - 1</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<result>25</result>


by selling 22 pens for a rupee a woman loses 10 % . how many for a rupee should he sell in order to gain 50 % ?

Explanation: "d 90 % - - - 22 150 % - - - ? 90 / 150 * 22 = 13"

inverse(add(divide(divide(const_100, subtract(const_100, 10)), 22), divide(multiply(divide(divide(const_100, subtract(const_100, 10)), 22), 50), const_100)))

<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">100 / 90</gadget>
<output>10/9 = around 1.111111</output>
<gadget id="calculator">(10/9) / 22</gadget>
<output>5/99 = around 0.050505</output>
<gadget id="calculator">(5/99) * 50</gadget>
<output>250/99 = around 2.525253</output>
<gadget id="calculator">(250/99) / 100</gadget>
<output>5/198 = around 0.025253</output>
<gadget id="calculator">(5/99) + (5/198)</gadget>
<output>5/66 = around 0.075758</output>
<gadget id="calculator">1 / (5/66)</gadget>
<output>66/5 = around 13.2</output>
<result>66/5 = around 13.2</result>


a and b start a business jointly . a invests rs 16000 for 8 month and b remains in the business for 4 months . out of total profit , b claims 2 / 7 of the profit . how much money was contributed by b ?

Explanation: b claims 2 / 7 of the profit a claims remaining 5 / 7 of the profit = > a : b = 5 / 7 : 2 / 7 = 5 : 2 let the money contributed by b = b then a : b = 16000 × 8 : b × 4 therefore , 16000 × 8 : b × 4 = 5 : 2 16000 × 8 × 2 = b × 4 × 5 16000 × 2 × 2 = b × 5 3200 × 2 × 2 = b b = 12800 answer is a .

divide(multiply(multiply(16000, 8), divide(8, 4)), multiply(4, add(4, const_1)))

<gadget id="calculator">16_000 * 8</gadget>
<output>128_000</output>
<gadget id="calculator">8 / 4</gadget>
<output>2</output>
<gadget id="calculator">128_000 * 2</gadget>
<output>256_000</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">4 * 5</gadget>
<output>20</output>
<gadget id="calculator">256_000 / 20</gadget>
<output>12_800</output>
<result>12_800</result>


john and steve are speed walkers in a race . john is 10 meters behind steve when he begins his final push . john blazes to the finish at a pace of 4.2 m / s , while steve maintains a blistering 3.7 m / s speed . if john finishes the race 2 meters ahead of steve , how long was john ’ s final push ?

Explanation: "let t be the time that john spent for his final push . thus , per the question , 4.2 t = 3.7 t + 10 + 2 - - - > 0.5 t = 12 - - - > t = 24 seconds . c is the correct answer ."

<gadget id="calculator">10 + 2</gadget>
<output>12</output>
<gadget id="calculator">3.7 * 12</gadget>
<output>44.4</output>
<gadget id="calculator">4.2 - 3.7</gadget>
<output>0.5</output>
<gadget id="calculator">44.4 / 0.5</gadget>
<output>88.8</output>
<gadget id="calculator">88.8 + 12</gadget>
<output>100.8</output>
<gadget id="calculator">100.8 / 4.2</gadget>
<output>24</output>
<result>24</result>


in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the ` ` sport ' ' formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the ` ` sport ' ' formulation contains 3 ounces of corn syrup , how many ounces of water does it contain ?

Explanation: f : c : w 1 : 12 : 30 sport version : f : c 3 : 12 f : w 1 : 60 or 3 : 180 so c : f : w = 12 : 3 : 180 c / w = 12 / 180 = 3 ounces / x ounces x = 3 * 180 / 12 = 45 ounces of water answer : a

multiply(multiply(30, const_2), divide(3, const_4))

<gadget id="calculator">30 * 2</gadget>
<output>60</output>
<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">60 * (3/4)</gadget>
<output>45</output>
<result>45</result>


two employees x and y are paid a total of rs . 440 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?

Explanation: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 440 but x = 120 % of y = 120 y / 100 = 12 y / 10 â ˆ ´ 12 y / 10 + y = 440 â ‡ ’ y [ 12 / 10 + 1 ] = 440 â ‡ ’ 22 y / 10 = 440 â ‡ ’ 22 y = 4400 â ‡ ’ y = 4400 / 22 = 400 / 2 = rs . 200 b )"

divide(multiply(440, multiply(add(const_1, const_4), const_2)), multiply(add(multiply(add(const_1, const_4), const_2), const_1), const_2))

<gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">440 * 10</gadget>
<output>4_400</output>
<gadget id="calculator">10 + 1</gadget>
<output>11</output>
<gadget id="calculator">11 * 2</gadget>
<output>22</output>
<gadget id="calculator">4_400 / 22</gadget>
<output>200</output>
<result>200</result>


how many gallons of milk that is 10 percent butter - fat must be added to 8 gallons of milk that is 25 percent butterfat to obtain milk that is 20 percent butterfat ?

Explanation: "equate the fat : 0.1 x + 0.25 * 8 = 0.2 ( x + 8 ) - - > x = 4 . answer : a ."

divide(multiply(subtract(25, 20), 8), 10)

<gadget id="calculator">25 - 20</gadget>
<output>5</output>
<gadget id="calculator">5 * 8</gadget>
<output>40</output>
<gadget id="calculator">40 / 10</gadget>
<output>4</output>
<result>4</result>


a envelop weight 8.5 gm , if 820 of these envelop are sent with an advertisement mail . how much wieght ?

Explanation: "820 * 8.5 6970.0 gm 6.97 kg answer : d"

<gadget id="calculator">8.5 * 820</gadget>
<output>6_970</output>
<gadget id="calculator">6_970 / 1_000</gadget>
<output>697/100 = around 6.97</output>
<result>697/100 = around 6.97</result>


the area of a rectangular field is equal to 500 square meters . its perimeter is equal to 90 meters . find the width of this rectangle .

Explanation: "l * w = 500 : area , l is the length and w is the width . 2 l + 2 w = 90 : perimeter l = 45 - w : solve for l ( 45 - w ) * w = 500 : substitute in the area equation w = 20 and l = 25 correct answer d"

divide(subtract(divide(90, const_2), sqrt(subtract(multiply(divide(90, const_2), divide(90, const_2)), multiply(const_4, 500)))), const_2)

<gadget id="calculator">90 / 2</gadget>
<output>45</output>
<gadget id="calculator">45 * 45</gadget>
<output>2_025</output>
<gadget id="calculator">4 * 500</gadget>
<output>2_000</output>
<gadget id="calculator">2_025 - 2_000</gadget>
<output>25</output>
<gadget id="calculator">25 ** (1/2)</gadget>
<output>5</output>
<gadget id="calculator">45 - 5</gadget>
<output>40</output>
<gadget id="calculator">40 / 2</gadget>
<output>20</output>
<result>20</result>


the angle between the minute hand and the hour hand of a clock when the time is 11.30 , is

Explanation: angle between hands of a clock when the minute hand is behind the hour hand , the angle between the two hands at m minutes past h ' o clock = 30 ( h − m / 5 ) + m / 2 degree when the minute hand is ahead of the hour hand , the angle between the two hands at m minutes past h ' o clock = 30 ( m / 5 − h ) − m / 2 degree here h = 11 , m = 30 and minute hand is behind the hour hand . hence the angle = 30 ( h − m / 5 ) + m / 2 = 30 ( 11 − 30 / 5 ) + 30 / 2 = 30 ( 11 − 6 ) + 15 = 30 × 5 + 15 = 165 ° answer is d .

divide(multiply(subtract(multiply(divide(multiply(const_3, const_4), subtract(multiply(const_3, const_4), const_1)), multiply(add(const_4, const_1), subtract(multiply(const_3, const_4), const_1))), divide(const_60, const_2)), subtract(multiply(const_3, const_4), const_1)), const_2)

<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">12 - 1</gadget>
<output>11</output>
<gadget id="calculator">12 / 11</gadget>
<output>12/11 = around 1.090909</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">5 * 11</gadget>
<output>55</output>
<gadget id="calculator">(12/11) * 55</gadget>
<output>60</output>
<gadget id="calculator">60 / 2</gadget>
<output>30</output>
<gadget id="calculator">60 - 30</gadget>
<output>30</output>
<gadget id="calculator">30 * 11</gadget>
<output>330</output>
<gadget id="calculator">330 / 2</gadget>
<output>165</output>
<result>165</result>


there are 16 bees in the hive , then 6 more fly . how many bees are there in all ?

Explanation: 16 + 6 = 22 . answer is c .

<gadget id="calculator">16 + 6</gadget>
<output>22</output>
<result>22</result>


a train moves with a speed of 108 kmph . its speed in metres per second is :

Explanation: "explanation : 108 kmph = ( 108 x 5 / 18 ) m / sec = 30 m / s . answer : c"

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">108 * (5/18)</gadget>
<output>30</output>
<result>30</result>


20 is subtracted from 60 % of a number , the result is 88 . find the number ?

Explanation: "( 60 / 100 ) * x â € “ 20 = 88 6 x = 1080 x = 180 answer : c"

divide(add(20, 88), divide(60, const_100))

<gadget id="calculator">20 + 88</gadget>
<output>108</output>
<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">108 / (3/5)</gadget>
<output>180</output>
<result>180</result>


by how much is 50 % of 250 greater than 25 % of 400 .

Explanation: "( 50 / 100 ) * 250 â € “ ( 25 / 100 ) * 400 125 - 100 = 25 answer : b"

subtract(multiply(250, divide(50, const_100)), multiply(divide(25, const_100), 400))

<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">250 * (1/2)</gadget>
<output>125</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 400</gadget>
<output>100</output>
<gadget id="calculator">125 - 100</gadget>
<output>25</output>
<result>25</result>


find the ratio in which rice at rs . 7.20 a kg be mixed with rice at rs . 5.70 a kg to produce a mixture worth rs . 6.30 a kg ?

Explanation: solution required ratio = 60 : 90 = 2 : 3 answer b

divide(subtract(6.3, 5.7), subtract(7.2, 6.3))

<gadget id="calculator">6.3 - 5.7</gadget>
<output>0.6</output>
<gadget id="calculator">7.2 - 6.3</gadget>
<output>0.9</output>
<gadget id="calculator">0.6 / 0.9</gadget>
<output>0.666667</output>
<result>0.666667</result>


a solution contains 8 parts of water for every 7 parts of lemonade syrup . how many parts of the solution should be removed and replaced with water so that the solution will now contain 35 % lemonade syrup ?

Explanation: "let the total solution is 150 l with 80 l water 70 l syrup . to make 35 % syrup solution , the result solution must have 97.5 l syrup and 52.5 l syrup . therefore we are taking 17.5 l of syrup from initial solution and replacing with water . using urinary method : 70 l syrup in 150 l solution 17.5 l syrup in 37.5 l solution we started by multiplying 10 now to get to the result we need to divide by 17.5 = > amount of solution to be replaced with water ( 37.5 / 17.5 ) = 2.14 . correct option : c"

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

<gadget id="calculator">8 + 7</gadget>
<output>15</output>
<gadget id="calculator">7 / 15</gadget>
<output>7/15 = around 0.466667</output>
<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(7/15) - (2/5)</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">(1/15) / (7/15)</gadget>
<output>1/7 = around 0.142857</output>
<gadget id="calculator">(1/7) * 15</gadget>
<output>15/7 = around 2.142857</output>
<result>15/7 = around 2.142857</result>


running at the same constant rate , 100 identical machines can produce a total of 500 coffee bar per minute . at this rate , how many bottles could 20 such machines produce in 2 minutes ?

Explanation: let ' s take the approach that uses the answer choices to eliminate wasted time . 500 / 100 = 5 coffee bar per minute per machine . 20 machines = 100 per minute . 2 minutes worth = 200 coffe bar . looking at the answers it is clear . . . we can only choose ( d ) the correct answer is d .

multiply(multiply(divide(500, 100), 2), 20)

<gadget id="calculator">500 / 100</gadget>
<output>5</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">10 * 20</gadget>
<output>200</output>
<result>200</result>


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

Explanation: "- x 2 - ( k + 8 ) x - 8 = - ( x - 2 ) ( x - 4 ) : given - x 2 - ( k + 8 ) x - 8 = - x 2 + 6 x - 8 - ( k + 8 ) = 6 : two polynomials are equal if their corresponding coefficients are equal . k = - 14 : solve the above for k correct answer c"

<gadget id="calculator">4 + 2</gadget>
<output>6</output>
<gadget id="calculator">8 + 6</gadget>
<output>14</output>
<result>14</result>


a , b and c invested rs . 6000 , rs . 4000 and rs . 10000 respectively , in a partnership business . find the share of a in profit of rs . 11000 after a year ?

Explanation: "explanation : 6000 : 4000 : 10000 3 : 2 : 5 3 / 10 * 11000 = 3300 answer : a"

<gadget id="calculator">6_000 + 4_000</gadget>
<output>10_000</output>
<gadget id="calculator">10_000 + 10_000</gadget>
<output>20_000</output>
<gadget id="calculator">6_000 / 20_000</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(3/10) * 11_000</gadget>
<output>3_300</output>
<result>3_300</result>


a group of people participate in some curriculum , 30 of them practice yoga , 20 study cooking , 15 study weaving , 5 of them study cooking only , 8 of them study both the cooking and yoga , 5 of them participate all curriculums . how many people study both cooking and weaving ?

Explanation: "both cooking and weaving = 20 - ( 5 + 8 + 5 ) = 2 so , the correct answer is b ."

subtract(subtract(subtract(20, 8), 5), 5)

<gadget id="calculator">20 - 8</gadget>
<output>12</output>
<gadget id="calculator">12 - 5</gadget>
<output>7</output>
<gadget id="calculator">7 - 5</gadget>
<output>2</output>
<result>2</result>


at what rate percent on simple interest will rs . 750 amount to rs . 825 in 5 years ?

Explanation: "75 = ( 750 * 5 * r ) / 100 r = 2 % . answer : a"

multiply(divide(divide(subtract(825, 750), 750), 5), const_100)

<gadget id="calculator">825 - 750</gadget>
<output>75</output>
<gadget id="calculator">75 / 750</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) / 5</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">(1/50) * 100</gadget>
<output>2</output>
<result>2</result>


two ants , arthur and amy , have discovered a picnic and are bringing crumbs back to the anthill . amy makes twice as many trips and carries one and a half times as many crumbs per trip as arthur . if arthur carries a total of b crumbs to the anthill , how many crumbs will amy bring to the anthill , in terms of b ?

Explanation: lets do it by picking up numbers . let arthur carry 2 crumbs per trip , this means amy carries 3 crumbs per trip . also let arthur make 2 trips and so amy makes 4 trips . thus total crumbs carried by arthur ( b ) = 2 x 2 = 4 , total crumbs carried by amy = 3 x 4 = 12 . 12 is 3 times 4 , so e

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

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 + (1/2)</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">2 * (3/2)</gadget>
<output>3</output>
<result>3</result>


a certain number of badges were distributed among a class of students . the student who got 1 / 6 th of the total number of badges actually got 5 times the average number of badges the others got ! how many students were there in the class ?

Explanation: detailed solution let the total students be ( n + 1 ) let total badges be x let the average of ‘ n ’ students be y the student who got 1 / 6 th of x = 5 y or y = x / 30 therefore ‘ n ’ students got 1 / 30 th of total share each or n * x / 30 + 1 * x / 6 = x nx + 5 x = 30 x n + 5 = 30 or n = 25 total = n + 1 = 26 correct answer : b

<gadget id="calculator">6 * 5</gadget>
<output>30</output>
<gadget id="calculator">30 - 5</gadget>
<output>25</output>
<gadget id="calculator">25 + 1</gadget>
<output>26</output>
<result>26</result>


tough and tricky questions : work / rate problems . a group of 4 junior lawyers require 7 hours to complete a legal research assignment . how many hours would it take a group of 3 legal assistants to complete the same research assignment assuming that a legal assistant works at two - thirds the rate of a junior lawyer ? source : chili hot gmat

Explanation: # of people times the # of hours : 4 * 7 = 28 - - > 4 lawyers do 28 worksin 7 hours . 3 * 14 / 3 = 14 - - > 3 assistants do 14 worksin 4 hours so , since the amount of work the assistants do is half the work the lawyers do , the time will be double , soans a

multiply(multiply(divide(const_2, const_3), 3), 7)

<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) * 3</gadget>
<output>2</output>
<gadget id="calculator">2 * 7</gadget>
<output>14</output>
<result>14</result>


mahesh can do a piece of work in 30 days . he works at it for 20 days and then rajesh finished it in 30 days . how long will y take to complete the work ?

Explanation: "work done by mahesh in 30 days = 20 * 1 / 30 = 2 / 3 remaining work = 1 - 2 / 3 = 1 / 3 1 / 3 work is done by rajesh in 30 days whole work will be done by rajesh is 30 * 3 = 90 days answer is a"

divide(const_1, divide(subtract(const_1, multiply(20, divide(const_1, 30))), 30))

<gadget id="calculator">1 / 30</gadget>
<output>1/30 = around 0.033333</output>
<gadget id="calculator">20 * (1/30)</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">1 - (2/3)</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/3) / 30</gadget>
<output>1/90 = around 0.011111</output>
<gadget id="calculator">1 / (1/90)</gadget>
<output>90</output>
<result>90</result>


if x and y are numbers such that ( x + 6 ) ( y - 6 ) = 0 , what is the smallest possible value of x ^ 2 + y ^ 2

Explanation: from ( x + 6 ) ( y - 6 ) = 0 it follows that either x = - 6 or y = 6 . thus either x ^ 2 = 36 or y ^ 2 = 36 . now , if x ^ 2 = 36 , then the least value of y ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 36 + 0 = 36 . similarly if y ^ 2 = 36 , then the least value of x ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 0 + 36 = 36 . answer : d .

<gadget id="calculator">6 ** 2</gadget>
<output>36</output>
<result>36</result>


the difference of a larger number and a smaller number is 6 . the sum of the larger number and twice the smaller is 15 . what is the larger number ?

Explanation: let x be the larger number and y be the smaller number . x - y = 6 x + 2 ( y ) = 15 solve by substitution : y = x - 6 x + 2 ( x - 6 ) = 15 x + 2 x - 12 = 15 3 x = 27 x = 9 the larger number is 9 , so answer c is correct .

divide(add(15, multiply(const_2, 6)), add(const_1, const_2))

<gadget id="calculator">2 * 6</gadget>
<output>12</output>
<gadget id="calculator">15 + 12</gadget>
<output>27</output>
<gadget id="calculator">1 + 2</gadget>
<output>3</output>
<gadget id="calculator">27 / 3</gadget>
<output>9</output>
<result>9</result>


a train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 18 seconds . what is the length of the platform in meters ?

Explanation: "explanation : length of the platform = speed of train * extra time taken to cross the platform . length of platform = 72 kmph * 12 seconds convert 72 kmph into m / sec 1 kmph = 518518 m / s ( this can be easily derived . but if you can remember this conversion , it saves a good 30 seconds ) . ∴ 72 kmph = 518 ∗ 72518 ∗ 72 = 20 m / sec therefore , length of the platform = 20 m / s * 12 sec = 240 meters . correct answer : a"

subtract(multiply(divide(multiply(72, const_1000), const_3600), 30), multiply(divide(multiply(72, const_1000), const_3600), 18))

<gadget id="calculator">72 * 1_000</gadget>
<output>72_000</output>
<gadget id="calculator">72_000 / 3_600</gadget>
<output>20</output>
<gadget id="calculator">20 * 30</gadget>
<output>600</output>
<gadget id="calculator">20 * 18</gadget>
<output>360</output>
<gadget id="calculator">600 - 360</gadget>
<output>240</output>
<result>240</result>


a vessel of capacity 2 litre has 16 % of alcohol and another vessel of capacity 6 litre had 40 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?

Explanation: "16 % of 2 litres = 0.32 litres 40 % of 6 litres = 2.4 litres therefore , total quantity of alcohol is 2.72 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 27.2 % answer : d"

multiply(divide(add(multiply(divide(16, const_100), 2), multiply(divide(40, const_100), 6)), 10), const_100)

<gadget id="calculator">16 / 100</gadget>
<output>4/25 = around 0.16</output>
<gadget id="calculator">(4/25) * 2</gadget>
<output>8/25 = around 0.32</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) * 6</gadget>
<output>12/5 = around 2.4</output>
<gadget id="calculator">(8/25) + (12/5)</gadget>
<output>68/25 = around 2.72</output>
<gadget id="calculator">(68/25) / 10</gadget>
<output>34/125 = around 0.272</output>
<gadget id="calculator">(34/125) * 100</gadget>
<output>136/5 = around 27.2</output>
<result>136/5 = around 27.2</result>


the diameters of two spheres are in the ratio 1 : 2 what is the ratio of their surface area ?

Explanation: 1 : 4 answer : b

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


there are 3 prizes to be distributed among 10 students . if no students gets more than one prize , then this can be done in ?

Explanation: explanation : 3 prize among 10 students can be distributed in 10 c 3 ways = 120 ways . answer : d

add(multiply(10, 3), multiply(subtract(10, const_1), 10))

<gadget id="calculator">10 * 3</gadget>
<output>30</output>
<gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">9 * 10</gadget>
<output>90</output>
<gadget id="calculator">30 + 90</gadget>
<output>120</output>
<result>120</result>


a student got 72 % in math and 82 % in history . to get an overall average of 75 % , how much should the student get in the third subject ?

Explanation: "72 + 82 + x = 3 * 75 x = 71 the answer is b ."

subtract(multiply(const_3, 75), add(72, 82))

<gadget id="calculator">3 * 75</gadget>
<output>225</output>
<gadget id="calculator">72 + 82</gadget>
<output>154</output>
<gadget id="calculator">225 - 154</gadget>
<output>71</output>
<result>71</result>


a starts business with rs . 3500 and after 5 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b ' s contribution in the capital ?

Explanation: let b ' s capital be rs . x . { 3500 \ 12 } / { 7 x } = { 2 } / { 3 } = > x = 9000 . answer : d

divide(multiply(multiply(3500, const_12), 3), multiply(subtract(const_12, 5), 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 - 5</gadget>
<output>7</output>
<gadget id="calculator">7 * 2</gadget>
<output>14</output>
<gadget id="calculator">126_000 / 14</gadget>
<output>9_000</output>
<result>9_000</result>


a car dealership has 40 cars on the lot , 15 % of which are silver . if the dealership receives a new shipment of 80 cars , 45 % of which are not silver , what percentage of total number of cars are silver ?

Explanation: "the number of silver cars is 0.15 * 40 + 0.45 * 80 = 42 the percentage of cars which are silver is 42 / 120 = 35 % the answer is b ."

multiply(divide(add(multiply(40, divide(15, const_100)), multiply(80, divide(45, const_100))), add(40, 80)), const_100)

<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">40 * (3/20)</gadget>
<output>6</output>
<gadget id="calculator">45 / 100</gadget>
<output>9/20 = around 0.45</output>
<gadget id="calculator">80 * (9/20)</gadget>
<output>36</output>
<gadget id="calculator">6 + 36</gadget>
<output>42</output>
<gadget id="calculator">40 + 80</gadget>
<output>120</output>
<gadget id="calculator">42 / 120</gadget>
<output>7/20 = around 0.35</output>
<gadget id="calculator">(7/20) * 100</gadget>
<output>35</output>
<result>35</result>


a person travels from p to q a speed of 60 km / hr and returns by increasing his speed by 20 % . what is his average speed for both the trips ?

Explanation: "speed on return trip = 120 % of 60 = 72 km / hr . average speed of trip = 60 + 72 / 2 = 132 / 2 = 66 km / hr answer : d"

divide(add(multiply(60, add(const_1, divide(20, const_100))), 60), const_2)

<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">60 * (6/5)</gadget>
<output>72</output>
<gadget id="calculator">72 + 60</gadget>
<output>132</output>
<gadget id="calculator">132 / 2</gadget>
<output>66</output>
<result>66</result>


a and b can together finish a work in 10 days . they worked together for 5 days and then b left . after another 5 days , a finished the remaining work . in how many days a alone can finish the job ?

Explanation: "a + b 5 days work = 5 * 1 / 10 = 1 / 2 remaining work = 1 - 1 / 2 = 1 / 2 1 / 2 work is done by a in 5 days whole work will be done by a in 5 * 2 = 10 days answer is a"

divide(multiply(5, 10), subtract(10, 5))

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


a rectangular field has a length 10 meters more than it is width . if the area of the field is 200 , what is the length ( in meters ) of the rectangular field ?

Explanation: "area = l * w = ( l ) * ( l - 10 ) = 200 trial and error : 19 * 9 = 171 ( too low ) 20 * 10 = 200 the length is 20 meters . the answer is a ."

add(10, add(const_0_25, add(const_0_33, divide(divide(200, 10), const_2))))

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">200 / 10</gadget>
<output>20</output>
<gadget id="calculator">20 / 2</gadget>
<output>10</output>
<gadget id="calculator">(1/3) + 10</gadget>
<output>31/3 = around 10.333333</output>
<gadget id="calculator">(1/4) + (31/3)</gadget>
<output>127/12 = around 10.583333</output>
<gadget id="calculator">10 + (127/12)</gadget>
<output>247/12 = around 20.583333</output>
<result>247/12 = around 20.583333</result>


a bag contains 7 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is - .

Explanation: "drawing two balls of same color from seven green balls can be done in ⁷ c ₂ ways . similarly from eight white balls two can be drawn in ways . 7 / 15 answer : e"

add(multiply(divide(8, add(7, 8)), divide(subtract(8, const_1), subtract(add(7, 8), const_1))), multiply(divide(7, add(7, 8)), divide(subtract(7, const_1), subtract(add(7, 8), const_1))))

<gadget id="calculator">7 + 8</gadget>
<output>15</output>
<gadget id="calculator">8 / 15</gadget>
<output>8/15 = around 0.533333</output>
<gadget id="calculator">8 - 1</gadget>
<output>7</output>
<gadget id="calculator">15 - 1</gadget>
<output>14</output>
<gadget id="calculator">7 / 14</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(8/15) * (1/2)</gadget>
<output>4/15 = around 0.266667</output>
<gadget id="calculator">7 / 15</gadget>
<output>7/15 = around 0.466667</output>
<gadget id="calculator">7 - 1</gadget>
<output>6</output>
<gadget id="calculator">6 / 14</gadget>
<output>3/7 = around 0.428571</output>
<gadget id="calculator">(7/15) * (3/7)</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(4/15) + (1/5)</gadget>
<output>7/15 = around 0.466667</output>
<result>7/15 = around 0.466667</result>


if 4 men working 10 hours a day earn rs . 1600 per week , then 9 men working 6 hours a day will earn how much per week ?

Explanation: "explanation : ( men 4 : 9 ) : ( hrs / day 10 : 6 ) : : 1600 : x hence 4 * 10 * x = 9 * 6 * 1600 or x = 9 * 6 * 1600 / 4 * 10 = 2160 answer : d"

multiply(divide(multiply(9, 6), multiply(4, 10)), 1600)

<gadget id="calculator">9 * 6</gadget>
<output>54</output>
<gadget id="calculator">4 * 10</gadget>
<output>40</output>
<gadget id="calculator">54 / 40</gadget>
<output>27/20 = around 1.35</output>
<gadget id="calculator">(27/20) * 1_600</gadget>
<output>2_160</output>
<result>2_160</result>


a student was asked to find 4 / 5 of a number . but the student divided the number by 4 / 5 , thus the student got 9 more than the correct answer . find the number .

Explanation: "let the number be x . ( 5 / 4 ) * x = ( 4 / 5 ) * x + 9 25 x = 16 x + 180 9 x = 180 x = 20 the answer is c ."

divide(divide(multiply(multiply(9, divide(4, 5)), divide(4, 5)), subtract(const_1, multiply(divide(4, 5), divide(4, 5)))), divide(4, 5))

<gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">9 * (4/5)</gadget>
<output>36/5 = around 7.2</output>
<gadget id="calculator">(36/5) * (4/5)</gadget>
<output>144/25 = around 5.76</output>
<gadget id="calculator">(4/5) * (4/5)</gadget>
<output>16/25 = around 0.64</output>
<gadget id="calculator">1 - (16/25)</gadget>
<output>9/25 = around 0.36</output>
<gadget id="calculator">(144/25) / (9/25)</gadget>
<output>16</output>
<gadget id="calculator">16 / (4/5)</gadget>
<output>20</output>
<result>20</result>


raman mixed 24 kg of butter at rs . 150 per kg with 36 kg butter at the rate of rs . 125 per kg . at what price per kg should he sell the mixture to make a profit of 40 % in the transaction ?

Explanation: cp per kg of mixture = [ 24 ( 150 ) + 36 ( 125 ) ] / ( 24 + 36 ) = rs . 135 sp = cp [ ( 100 + profit % ) / 100 ] = 135 * [ ( 100 + 40 ) / 100 ] = rs . 189 . answer : c

add(divide(add(multiply(24, 150), multiply(36, 125)), add(36, 24)), multiply(divide(add(multiply(24, 150), multiply(36, 125)), add(36, 24)), divide(40, const_100)))

<gadget id="calculator">24 * 150</gadget>
<output>3_600</output>
<gadget id="calculator">36 * 125</gadget>
<output>4_500</output>
<gadget id="calculator">3_600 + 4_500</gadget>
<output>8_100</output>
<gadget id="calculator">36 + 24</gadget>
<output>60</output>
<gadget id="calculator">8_100 / 60</gadget>
<output>135</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">135 * (2/5)</gadget>
<output>54</output>
<gadget id="calculator">135 + 54</gadget>
<output>189</output>
<result>189</result>


if jake loses 8 pounds , he will weigh twice as much as his sister kendra . together they now weigh 284 pounds . what is jake ’ s present weight , in pounds ?

Explanation: "j + k = 284 and so k = 284 - j j - 8 = 2 k j - 8 = 2 ( 284 - j ) 3 j = 576 j = 192 the answer is e ."

add(multiply(divide(subtract(284, 8), const_3), const_2), 8)

<gadget id="calculator">284 - 8</gadget>
<output>276</output>
<gadget id="calculator">276 / 3</gadget>
<output>92</output>
<gadget id="calculator">92 * 2</gadget>
<output>184</output>
<gadget id="calculator">184 + 8</gadget>
<output>192</output>
<result>192</result>


arun and tarun can do a work in 10 days . after 4 days tarun went to his village . how many days are required to complete the remaining work by arun alone . arun can do the work alone in 40 days .

Explanation: "they together completed 4 / 10 work in 4 days . balance 6 / 10 work will be completed by arun alone in 40 * 6 / 10 = 24 days . answer : e"

subtract(40, multiply(divide(40, 10), 4))

<gadget id="calculator">40 / 10</gadget>
<output>4</output>
<gadget id="calculator">4 * 4</gadget>
<output>16</output>
<gadget id="calculator">40 - 16</gadget>
<output>24</output>
<result>24</result>