by selling 100 pens , a trader gains the cost of 30 pens . find his gain percentage ?

Explanation: "let the cp of each pen be rs . 1 . cp of 100 pens = rs . 100 profit = cost of 30 pens = rs . 30 profit % = 30 / 100 * 100 = 30 % answer : a"

<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(3/10) * 100</gadget>
<output>30</output>
<result>30</result>


out of 3 consecutive odd numbers 11 times the first number is equal to addition of thrice the third number and adding 16 to 4 times the second . what is the first number ?

Explanation: description : = > 11 x = 4 ( x + 2 ) + 16 + 3 ( x + 4 ) = > 11 x = 7 x + 36 = > 4 x = 36 x = 9 answer e

<gadget id="calculator">11 - 4</gadget>
<output>7</output>
<gadget id="calculator">16 - 7</gadget>
<output>9</output>
<result>9</result>


working together at their respective constant rates , machine a and machine b can produce 1600 units in 8 hours . working alone , machine b would complete that same output in 50 % more time . if machine a were to work on its own for an 8 - hour shift , what percent of the 1600 unit total would it produce ?

Explanation: 1 / a + 1 / b = 1 / t 1 / a + 1 / 12 = 1 / 8 ( 50 % more of 8 is 12 ) 1 / a = 1 / 24 machine a can produce 1600 units in 24 hrs , so it can produce 1600 * 8 / 24 = 533.33 units is 8 hrs . 533.33 is 33.33 % of 1600 . b is the answer

multiply(divide(multiply(subtract(divide(1600, 8), divide(1600, multiply(add(divide(50, const_100), const_1), 8))), 8), 1600), const_100)

<gadget id="calculator">1_600 / 8</gadget>
<output>200</output>
<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) + 1</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(3/2) * 8</gadget>
<output>12</output>
<gadget id="calculator">1_600 / 12</gadget>
<output>400/3 = around 133.333333</output>
<gadget id="calculator">200 - (400/3)</gadget>
<output>200/3 = around 66.666667</output>
<gadget id="calculator">(200/3) * 8</gadget>
<output>1_600/3 = around 533.333333</output>
<gadget id="calculator">(1_600/3) / 1_600</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/3) * 100</gadget>
<output>100/3 = around 33.333333</output>
<result>100/3 = around 33.333333</result>


according to the formula f = 9 / 5 ( c ) + 32 , if the temperature in degrees farenheit ( f ) increases by 26 , by how much does the temperature in degrees celsius ( c ) increase ?

Explanation: "you can plug in values . c = 5 / 9 * ( f - 32 ) f = 32 - - > c = 0 ; f = 32 + 26 = 58 - - > c = 5 / 9 * 26 = 14.44 . increase = 14.44 degrees . answer : b ."

<gadget id="calculator">26 * 5</gadget>
<output>130</output>
<gadget id="calculator">130 / 9</gadget>
<output>130/9 = around 14.444444</output>
<result>130/9 = around 14.444444</result>


if price of t . v set is reduced by 20 % , then its sale increases by 80 % , find net effect on sale value

Explanation: "- a + b + ( ( - a ) ( b ) / 100 ) = - 20 + 80 + ( - 20 * 80 ) / 100 = - 20 + 80 - 16 = 44 answer : a"

multiply(subtract(multiply(divide(subtract(const_100, 20), const_100), divide(add(const_100, 80), const_100)), const_1), const_100)

<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">100 + 80</gadget>
<output>180</output>
<gadget id="calculator">180 / 100</gadget>
<output>9/5 = around 1.8</output>
<gadget id="calculator">(4/5) * (9/5)</gadget>
<output>36/25 = around 1.44</output>
<gadget id="calculator">(36/25) - 1</gadget>
<output>11/25 = around 0.44</output>
<gadget id="calculator">(11/25) * 100</gadget>
<output>44</output>
<result>44</result>


the captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average of the team ?

Explanation: "let the average of the whole team be x years . 11 x - ( 26 + 29 ) = 9 ( x - 1 ) = 11 x - 9 x = 46 = 2 x = 46 = > x = 23 so , average age of the team is 23 years . answer a"

divide(subtract(add(26, add(26, 3)), multiply(3, 3)), const_2)

<gadget id="calculator">26 + 3</gadget>
<output>29</output>
<gadget id="calculator">26 + 29</gadget>
<output>55</output>
<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">55 - 9</gadget>
<output>46</output>
<gadget id="calculator">46 / 2</gadget>
<output>23</output>
<result>23</result>


tom and marry each have a bag of marbles , each of which contains 4 red marbles , 10 blue marbles , and 6 yellow marbles . if tom and marry each select one marble from their respective bags , what is the probability that either tom or marry select a blue marble ?

Explanation: probability that either selects a red marble , p ( either ) = 1 - probability that neither selects a blue marble , p ( neither ) probability that tom selects non blue = 10 c 1 / 20 c 1 = 1 / 2 probability that marry selects non blue = 10 c 1 / 20 c 1 = 1 / 2 = > p ( either ) = 1 - ( 1 / 2 * 1 / 2 ) = 1 - 1 / 4 = 3 / 4 . c )

subtract(const_1, multiply(divide(10, add(add(4, 6), 10)), divide(10, add(add(4, 6), 10))))

<gadget id="calculator">4 + 6</gadget>
<output>10</output>
<gadget id="calculator">10 + 10</gadget>
<output>20</output>
<gadget id="calculator">10 / 20</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * (1/2)</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 - (1/4)</gadget>
<output>3/4 = around 0.75</output>
<result>3/4 = around 0.75</result>


if 7 cats can kill 7 rats in 7 minutes , how long will it take 100 cats to kill 100 rats ?

Explanation: "it will take 7 minutes for 100 cats to kill 100 rats . 1 cat can kill 1 rat in 7 minutes , so 100 cats can kill 100 rats in 7 minutes answer c"

<gadget id="calculator">7 * 1</gadget>
<output>7</output>
<result>7</result>


at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.55 , a 20 - pack for $ 3.05 , and a 250 - pack for $ 20.95 . what is the greatest number of hot dogs you can buy at this store with $ 300 ?

Explanation: to maximize number of hot dogs with 300 $ total number of hot dogs bought in 250 - pack = 20.95 * 14 = 293.30 $ amount remaining = 300 - 293.30 = 6.7 $ total number of hot dogs bought in 20 - pack = 3.05 * 2 = 6.10 $ amount remaining = 6.70 - 6.10 = 0.6 $ this amount is too less to buy any 8 - pack . greatest number of hot dogs one can buy with 300 $ = 250 * 14 + 20 * 2 = 3,540 answer d

<gadget id="calculator">300 / 20.95</gadget>
<output>14.319809</output>
<gadget id="calculator">14.319809 * 250</gadget>
<output>3_579.95225</output>
<result>3_579.95225</result>


a person spends 1 / 3 rd of the money with him on clothes , 1 / 5 th of the remaining on food and 1 / 4 th of the remaining on travel . now , he is left with rs 200 . how much did he have with him in the beginning ?

Explanation: suppose the amount in the beginning was rs ’ x ’ money spent on clothes = rs 1 x / 3 balance = rs 2 x / 3 money spent on food = 1 / 5 of 2 x / 3 = rs 2 x / 15 balance = 2 x / 3 - 2 x / 15 = rs 8 x / 15 money spent on travel = 1 / 4 of 8 x / 15 = rs 2 x / 15 = 8 x / 15 - 2 x / 15 = 6 x / 15 = rs 2 x / 5 therefore 2 x / 5 = 200 = 500 answer : b

divide(200, subtract(subtract(subtract(1, divide(1, 3)), divide(subtract(1, divide(1, 3)), 5)), divide(subtract(subtract(1, divide(1, 3)), divide(subtract(1, divide(1, 3)), 5)), 4)))

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 - (1/3)</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) / 5</gadget>
<output>2/15 = around 0.133333</output>
<gadget id="calculator">(2/3) - (2/15)</gadget>
<output>8/15 = around 0.533333</output>
<gadget id="calculator">(8/15) / 4</gadget>
<output>2/15 = around 0.133333</output>
<gadget id="calculator">(8/15) - (2/15)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">200 / (2/5)</gadget>
<output>500</output>
<result>500</result>


the shopkeeper increased the price of a product by 25 % so that customer finds it difficult to purchase the required amount . but somehow the customer managed to purchase only 76 % of the required amount . what is the net difference in the expenditure on that product ?

Explanation: quantity x rate = price 1 x 1 = 1 0.76 x 1.25 = 0.95 decrease in price = ( 0.05 / 1 ) × 100 = 5 % c )

divide(multiply(subtract(multiply(const_100, const_100), multiply(add(const_100, 25), 76)), const_100), multiply(const_100, const_100))

<gadget id="calculator">100 * 100</gadget>
<output>10_000</output>
<gadget id="calculator">100 + 25</gadget>
<output>125</output>
<gadget id="calculator">125 * 76</gadget>
<output>9_500</output>
<gadget id="calculator">10_000 - 9_500</gadget>
<output>500</output>
<gadget id="calculator">500 * 100</gadget>
<output>50_000</output>
<gadget id="calculator">50_000 / 10_000</gadget>
<output>5</output>
<result>5</result>


if a number n is chosen at random from the set of two - digit integers whose digits are both prime numbers , what is the probability r that n is divisible by 3 ?

Explanation: "prime digits are : 2 , 3 , 5 , 7 total number of 2 digit # s with both digits prime are : 4 * 4 = 16 out of these numbers divisible by 3 = 33 , 27 , 57 , 72 and 75 . i had to find the numbers manually using the 4 numbers above . = > prob = 5 / 16 . ans d . took me 3 : 20 mins ."

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

<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">4 * 4</gadget>
<output>16</output>
<gadget id="calculator">5 / 16</gadget>
<output>5/16 = around 0.3125</output>
<result>5/16 = around 0.3125</result>


0 - - - : - | - - - : - - | - : - - : - | - - : - - - | - : - - - - 1 on the number line above , the segment from 0 to 1 has been divided into fifths , as indicated by the large tick marks , and also into sevenths , as indicated by the small tick marks . what is the least possible distance x between any two of the tick marks ?

Explanation: divisions are 0 1 / 7 2 / 7 3 / 7 4 / 7 5 / 7 6 / 7 1 1 / 5 2 / 5 3 / 5 4 / 5 5 / 5 expressing the same in terms of the lcm of 57 , i . e 35 0 7 / 35 14 / 35 21 / 35 28 / 35 35 / 35 5 / 35 10 / 35 15 / 35 20 / 35 25 / 35 30 / 35 by comparing the divisions with each other we can see 1 / 35 is the shortest possible distance between any two selected divisions . x = 1 / 35 answer is b .

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

<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">5 * 7</gadget>
<output>35</output>
<gadget id="calculator">1 / 35</gadget>
<output>1/35 = around 0.028571</output>
<result>1/35 = around 0.028571</result>


find the area of a parallelogram with base 21 cm and height 11 cm ?

Explanation: "area of a parallelogram = base * height = 21 * 11 = 231 cm 2 answer : a"

<gadget id="calculator">21 * 11</gadget>
<output>231</output>
<result>231</result>


a cycle is bought for rs . 1120 and sold for rs . 1200 , find the gain percent ?

Explanation: "explanation : 1120 - - - - 80 100 - - - - ? = > 7 % answer : a"

multiply(divide(subtract(1200, 1120), 1120), const_100)

<gadget id="calculator">1_200 - 1_120</gadget>
<output>80</output>
<gadget id="calculator">80 / 1_120</gadget>
<output>1/14 = around 0.071429</output>
<gadget id="calculator">(1/14) * 100</gadget>
<output>50/7 = around 7.142857</output>
<result>50/7 = around 7.142857</result>


a trader bought a car at 20 % discount on its original price . he sold it at a 70 % increase on the price he bought it . what percent of profit did he make on the original price ?

Explanation: "original price = 100 cp = 80 s = 80 * ( 170 / 100 ) = 136 100 - 136 = 36 % answer : e"

multiply(subtract(divide(divide(multiply(subtract(const_100, 20), add(const_100, 70)), const_100), const_100), const_1), const_100)

<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">100 + 70</gadget>
<output>170</output>
<gadget id="calculator">80 * 170</gadget>
<output>13_600</output>
<gadget id="calculator">13_600 / 100</gadget>
<output>136</output>
<gadget id="calculator">136 / 100</gadget>
<output>34/25 = around 1.36</output>
<gadget id="calculator">(34/25) - 1</gadget>
<output>9/25 = around 0.36</output>
<gadget id="calculator">(9/25) * 100</gadget>
<output>36</output>
<result>36</result>


a boat having a length 9 m and breadth 3 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of the man is :

Explanation: "volume of water displaced = ( 9 x 3 x 0.01 ) m 3 = 0.27 m 3 . mass of man = volume of water displaced x density of water = ( 0.27 x 1000 ) kg = 270 kg . answer : e"

multiply(multiply(multiply(9, 3), divide(1, const_100)), const_1000)

<gadget id="calculator">9 * 3</gadget>
<output>27</output>
<gadget id="calculator">1 / 100</gadget>
<output>1/100 = around 0.01</output>
<gadget id="calculator">27 * (1/100)</gadget>
<output>27/100 = around 0.27</output>
<gadget id="calculator">(27/100) * 1_000</gadget>
<output>270</output>
<result>270</result>


what annual payment will discharge a debt of rs . 1030 due in 2 years at the rate of 5 % compound interest ?

Explanation: "explanation : let each installment be rs . x . then , x / ( 1 + 5 / 100 ) + x / ( 1 + 5 / 100 ) 2 = 1030 820 x + 1030 * 441 x = 553.94 so , value of each installment = rs . 553.94 answer : option a"

divide(multiply(power(add(divide(5, const_100), const_1), 2), 1030), 2)

<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/20) + 1</gadget>
<output>21/20 = around 1.05</output>
<gadget id="calculator">(21/20) ** 2</gadget>
<output>441/400 = around 1.1025</output>
<gadget id="calculator">(441/400) * 1_030</gadget>
<output>45_423/40 = around 1_135.575</output>
<gadget id="calculator">(45_423/40) / 2</gadget>
<output>45_423/80 = around 567.7875</output>
<result>45_423/80 = around 567.7875</result>


in a factory , there are 90 % technicians and 10 % non - technicians . if the 90 % of the technicians and 10 % of non - technicians are permanent employees , then the percentage of workers who are temporary is ?

Explanation: "total = 100 t = 90 nt = 10 90 * ( 10 / 100 ) = 910 * ( 90 / 100 ) = 9 9 + 9 = 18 = > 100 - 18 = 82 % answer : d"

subtract(const_100, add(multiply(90, divide(10, const_100)), multiply(divide(90, const_100), 10)))

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">90 * (1/10)</gadget>
<output>9</output>
<gadget id="calculator">90 / 100</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">(9/10) * 10</gadget>
<output>9</output>
<gadget id="calculator">9 + 9</gadget>
<output>18</output>
<gadget id="calculator">100 - 18</gadget>
<output>82</output>
<result>82</result>


how many seconds will a 450 metre long train take to cross a man running with a speed of 6 km / hr in the direction of the moving train if the speed of the train is 60 km / hr ?

Explanation: explanation : speed of train relatively to man = ( 60 - 6 ) km / hr = 54 km / hr = ( 54 x 5 / 18 ) m / sec = 15 m / sec time taken to pass the man = ( 450 / 15 ) sec = 30 sec . answer : b

divide(450, multiply(const_0_2778, subtract(60, 6)))

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">60 - 6</gadget>
<output>54</output>
<gadget id="calculator">(5/18) * 54</gadget>
<output>15</output>
<gadget id="calculator">450 / 15</gadget>
<output>30</output>
<result>30</result>


90 kg of an alloy a is mixed with 140 kg of alloy b . if alloy a has lead and tin in the ratio 3 : 4 and alloy b has tin and copper in the ratio 2 : 5 , then the amount of tin in the new alloy is ?

Explanation: "quantity of tin in 90 kg of a = 90 * 4 / 7 = 51.4 kg quantity of tin in 140 kg of b = 140 * 2 / 7 = 40 kg quantity of tin in the new alloy = 51.4 + 40 = 91.4 kg answer is d"

add(multiply(divide(90, add(3, 4)), 4), multiply(divide(140, add(2, 5)), 2))

<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">90 / 7</gadget>
<output>90/7 = around 12.857143</output>
<gadget id="calculator">(90/7) * 4</gadget>
<output>360/7 = around 51.428571</output>
<gadget id="calculator">2 + 5</gadget>
<output>7</output>
<gadget id="calculator">140 / 7</gadget>
<output>20</output>
<gadget id="calculator">20 * 2</gadget>
<output>40</output>
<gadget id="calculator">(360/7) + 40</gadget>
<output>640/7 = around 91.428571</output>
<result>640/7 = around 91.428571</result>


a rectangular garden is to be twice as long as it is wide . if 180 yards of fencing , including the gate , will completely enclose the garden , what will be the length of the garden , in yards ?

Explanation: "alternate approach backsolving ( using answer options to reach the correct answer ) can work wonders here if one is fast in calculations . given perimeter is 180 so , 2 ( l + b ) = 180 or , l + b = 90 now use the answer options ( given length ; breath will be half the length ) ( a ) 60 l = 60 ; b = 30 l + b = 90 ( b ) 70 l = 70 ; b = 35 l + b = 105 ( c ) 80 l = 80 ; b = 40 l + b = 120 ( d ) 90 l = 90 ; b = 45 l + b = 135 ( e ) 100 l = 100 ; b = 50 l + b = 150 thus you see no , need of any calculations , u can reach the correct option only by checking options ; correct answer will be ( a )"

multiply(divide(180, multiply(add(const_2, const_1), const_2)), const_2)

<gadget id="calculator">2 + 1</gadget>
<output>3</output>
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">180 / 6</gadget>
<output>30</output>
<gadget id="calculator">30 * 2</gadget>
<output>60</output>
<result>60</result>


if the sides of a cube are in the ratio 9 : 7 . what is the ratio of their diagonals ?

Explanation: "explanation : diagonal of a cube = a √ 3 where a is side a 1 : a 2 = 9 : 7 d 1 : d 2 = 9 : 7 where √ 3 cancelled both side answer : c"

<gadget id="calculator">9 / 7</gadget>
<output>9/7 = around 1.285714</output>
<result>9/7 = around 1.285714</result>


last year elaine spent 20 % of her annual earnings on rent . this year she earned 20 % more than last year and she spent 30 % of her annual earnings on rent . the amount she spent on rent this year is what percent of the amount spent on rent last year ?

Explanation: "for this it is easiest to use simple numbers . let ' s assume that elaine ' s annual earnings last year were $ 100 . she would ' ve spent $ 20 of this on rent . this year she earned 20 % more , or $ 120 she would ' ve spent 30 % of this on rent , or $ 36 do $ 36 / $ 20 this will give you 180 % b is the correct answer ."

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

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) + 1</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">(6/5) * 30</gadget>
<output>36</output>
<gadget id="calculator">36 / 20</gadget>
<output>9/5 = around 1.8</output>
<gadget id="calculator">(9/5) * 100</gadget>
<output>180</output>
<result>180</result>


two bullet train s 140 m and 200 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time ( in seconds ) which they take to cross each other , is :

Explanation: relative speed = ( 60 + 40 ) km / hr = 100 x 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = ( 140 + 200 ) m = 340 m . required time = 340 x 9 / 250 = 54 / 5 = 12.24 sec . answer b

<gadget id="calculator">140 + 200</gadget>
<output>340</output>
<gadget id="calculator">60 + 40</gadget>
<output>100</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">100 * (5/18)</gadget>
<output>250/9 = around 27.777778</output>
<gadget id="calculator">340 / (250/9)</gadget>
<output>306/25 = around 12.24</output>
<result>306/25 = around 12.24</result>


in 1950 , richard was 4 times as old as robert . in 1955 , richard was 3 times as old as robert . in which year was richard 1.5 times as old as robert ?

Explanation: "in 1950 : ri = 4 ro - - - - - - - - - - - - - - eq 1 in 1955 : ri + 5 = 3 ( ro + 5 ) - - - - - - - - - eq 2 thus in 1950 , solving eq 1 and eq 2 ro = 10 , ri = 40 now for each year we can calculate : 2000 : ri = 60 , ro = 90 thus ans : e"

<gadget id="calculator">4 + 3</gadget>
<output>7</output>
<gadget id="calculator">1.5 + 7</gadget>
<output>8.5</output>
<gadget id="calculator">1_950 + 8.5</gadget>
<output>1_958.5</output>
<result>1_958.5</result>


in what ratio must tea at rs . 60 per kg be mixed with tea at rs . 70 per kg so that the mixture must be worth rs . 67.5 per kg ?

Explanation: "required ratio = 250 : 750 = 1 : 3 answer d"

divide(subtract(70, 67.5), subtract(67.5, 60))

<gadget id="calculator">70 - 67.5</gadget>
<output>2.5</output>
<gadget id="calculator">67.5 - 60</gadget>
<output>7.5</output>
<gadget id="calculator">2.5 / 7.5</gadget>
<output>0.333333</output>
<result>0.333333</result>


in what time will a train 50 m long cross an electric pole , it its speed be 360 km / hr ?

Explanation: "speed = 360 * 5 / 18 = 100 m / sec time taken = 50 / 100 = 0.5 sec . answer : b"

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">360 * (5/18)</gadget>
<output>100</output>
<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<result>1/2 = around 0.5</result>


each of the products produced yesterday was checked by worker x or worker y . 0.5 % of the products checked by worker x are defective and 0.8 % of the products checked by worker y are defective . if the total defective rate of all the products checked by worker x and worker y is 0.74 % , what fraction of the products was checked by worker y ?

Explanation: "x : 0.5 % is 0.24 % - points from 0.74 % . y : 0.8 % is 0.06 % - points from 0.74 % . therefore the ratio of products checked by y : x is 4 : 1 . thus , worker y checked 4 / 5 of the products . the answer is e ."

divide(subtract(0.74, 0.5), subtract(0.8, 0.5))

<gadget id="calculator">0.74 - 0.5</gadget>
<output>0.24</output>
<gadget id="calculator">0.8 - 0.5</gadget>
<output>0.3</output>
<gadget id="calculator">0.24 / 0.3</gadget>
<output>0.8</output>
<result>0.8</result>


workers at a campaign office have 2000 fliers to send out . if they send out 1 / 4 of them in the morning and 1 / 5 of the remaining ones out during the afternoon , how many are left for the next day ?

Explanation: "( 1 / 4 ) * 2000 = 500 remaining = 2000 - 500 = 1500 ( 1 / 5 ) of remaining = ( 1 / 5 ) * 1600 = 320 remaining now = 1500 - 320 = 1180 answer : option e"

subtract(subtract(2000, divide(2000, 4)), divide(subtract(2000, divide(2000, 4)), 5))

<gadget id="calculator">2_000 / 4</gadget>
<output>500</output>
<gadget id="calculator">2_000 - 500</gadget>
<output>1_500</output>
<gadget id="calculator">1_500 / 5</gadget>
<output>300</output>
<gadget id="calculator">1_500 - 300</gadget>
<output>1_200</output>
<result>1_200</result>


abcd is a square where ab = â ˆ š 4032 . let x be a point on ab and y be a point on cd such that ax = cy . compute the area of trapezoid axyd .

Explanation: note that trapezoids axy d and bxy c are congruent , so the area of axy d is always 4032 / 2 = 2016 . correct answer d

<gadget id="calculator">4_032 / 2</gadget>
<output>2_016</output>
<result>2_016</result>


a sports equipment store sold ping pong rackets for a total of $ 637 . if the average ( arithmetic mean ) price of a pair of rackets is $ 9.8 , how many pairs were sold ?

Explanation: "average price for a pair of rackets = $ 9.8 total cost = $ 9.8 * x = $ 637 x = 65 pairs were sold . answer : c"

<gadget id="calculator">637 / 9.8</gadget>
<output>65</output>
<result>65</result>


a farmer has enough food to feed her 1000 cows for 50 days . after 10 days some of the cows run away and the food was now enough for the same period of 50 days as before . how many cows ran away ?

Explanation: 1000 - - - - 50 1000 - - - - 40 x - - - - 50 x * 50 = 1000 * 40 x = 800 1000 - - - - - - - 200 answer = b

multiply(1000, subtract(const_1, multiply(subtract(50, 10), divide(const_1, 50))))

<gadget id="calculator">50 - 10</gadget>
<output>40</output>
<gadget id="calculator">1 / 50</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">40 * (1/50)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">1 - (4/5)</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1_000 * (1/5)</gadget>
<output>200</output>
<result>200</result>


a certain number of men can do a work in 60 days . if there were 8 men less it could be finished in 10 days more . how many men are there ?

Explanation: "the original number of men = 8 ( 60 + 10 ) / 10 = 56 men answer is a"

<gadget id="calculator">60 + 10</gadget>
<output>70</output>
<gadget id="calculator">70 * 8</gadget>
<output>560</output>
<gadget id="calculator">560 / 10</gadget>
<output>56</output>
<result>56</result>


if - 3 x + 4 y = 28 and 3 x - 2 y = 8 , what is the product of x and y ?

Explanation: given - 3 x + 4 y = 28 - - - eq 1 3 x - 2 y = 8 - - eq 2 sum both eqns we get 2 y = 36 = > y = 18 sub 2 y in eq 2 = > 3 x - 36 = 8 . = > x = 44 / 3 now xy = 44 / 3 * 18 = 264 . option a is correct answer .

multiply(divide(add(8, multiply(divide(add(28, 8), 2), 2)), 3), divide(add(28, 8), 2))

<gadget id="calculator">28 + 8</gadget>
<output>36</output>
<gadget id="calculator">36 / 2</gadget>
<output>18</output>
<gadget id="calculator">18 * 2</gadget>
<output>36</output>
<gadget id="calculator">8 + 36</gadget>
<output>44</output>
<gadget id="calculator">44 / 3</gadget>
<output>44/3 = around 14.666667</output>
<gadget id="calculator">(44/3) * 18</gadget>
<output>264</output>
<result>264</result>


two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 25 hours and 81 hours respectively . the ratio of their speeds is :

Explanation: "let us name the trains as a and b . then , ( a ' s speed ) : ( b ' s speed ) = â ˆ š b : â ˆ š a = â ˆ š 81 : â ˆ š 25 = 9 : 5 . answer c"

<gadget id="calculator">81 ** (1/2)</gadget>
<output>9</output>
<gadget id="calculator">25 ** (1/2)</gadget>
<output>5</output>
<gadget id="calculator">9 / 5</gadget>
<output>9/5 = around 1.8</output>
<result>9/5 = around 1.8</result>


a train 100 m long takes 6 sec to cross a man walking at 5 kmph in a direction opposite to that of the train . find the speed of the train ?

Explanation: "let the speed of the train be x kmph speed of the train relative to man = x + 5 = ( x + 5 ) * 5 / 18 m / sec 100 / [ ( x + 5 ) * 5 / 18 ] = 6 30 ( x + 5 ) = 1800 x = 55 kmph answer is b"

subtract(divide(divide(100, 6), const_0_2778), 5)

<gadget id="calculator">100 / 6</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">(50/3) / (5/18)</gadget>
<output>60</output>
<gadget id="calculator">60 - 5</gadget>
<output>55</output>
<result>55</result>


Explanation: "according to order of operations , 12 ? 3 ? 25 ( division and multiplication ) is done first from left to right 12 / 2 = 4 * 25 = 100 hence 96385 + 12 * 3 * 2 = 96385 + 100 = 96485 correct answer d"

subtract(96385, multiply(multiply(12, 3), 25))

<gadget id="calculator">12 * 3</gadget>
<output>36</output>
<gadget id="calculator">36 * 25</gadget>
<output>900</output>
<gadget id="calculator">96_385 - 900</gadget>
<output>95_485</output>
<result>95_485</result>


if y > 0 , ( 9 y ) / 20 + ( 3 y ) / 10 is what percent of y ?

Explanation: "can be reduced to 9 y / 20 + 6 y / 20 = 15 y / 20 = 75 % answer e"

multiply(const_100, add(divide(9, 20), divide(3, 10)))

<gadget id="calculator">9 / 20</gadget>
<output>9/20 = around 0.45</output>
<gadget id="calculator">3 / 10</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(9/20) + (3/10)</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">100 * (3/4)</gadget>
<output>75</output>
<result>75</result>


all the students of class are told to sit in circle shape . here the boy at the 5 th position is exactly opposite to 20 th boy . total number of boys in the class ?

Explanation: "as half the circle shape consist of 20 - 5 = 15 boys , so total number of boys in full circle = 2 * 15 = 30 answer : a"

<gadget id="calculator">20 - 5</gadget>
<output>15</output>
<gadget id="calculator">15 * 2</gadget>
<output>30</output>
<result>30</result>


an equal number of desks and bookcases are to be placed along a library wall that is 15 meters long . each desk is 2 meters long , and each bookshelf is 1.5 meters long . if the maximum possible number of desks and bookcases are to be placed along the wall , then the space along the wall that is left over will be how many meters f long ?

Explanation: "let x be the number of desks and bookcases that are placed along the library wall . 2 x + 1.5 x < 15 3.5 x < 15 since x is a non negative integer , the largest number x can be is 4 . when x is 4 , the desks and bookcases take up 3.5 * 4 = 14 m , leaving 1 m of empty space . thus , i believe the answer is b ) 1"

subtract(15, add(multiply(const_4, 2), multiply(const_4, 1.5)))

<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">4 * 1.5</gadget>
<output>6</output>
<gadget id="calculator">8 + 6</gadget>
<output>14</output>
<gadget id="calculator">15 - 14</gadget>
<output>1</output>
<result>1</result>


for every even positive integer m , f ( m ) represents the product of all even integers from 2 to m , inclusive . for example , f ( 12 ) = 2 x 4 x 6 x 8 x 10 x 12 . what is the greatest prime factor of f ( 24 ) ?

Explanation: f ( 24 ) = 2 * 4 * 6 * 8 * 10 * 12 * 14 * 16 * 18 * 20 * 22 * 24 = 2 ^ 12 * ( 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11 ) - - > the greatest prime factor is 11 . answer : e .

<gadget id="calculator">24 / 2</gadget>
<output>12</output>
<gadget id="calculator">12 - 1</gadget>
<output>11</output>
<result>11</result>


a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 80 percent of books that were loaned out are returned and there are 66 books in the special collection at that time , how many books of the special collection were loaned out during that month ?

Explanation: "there are 9 books less ( 75 - 66 ) which represents 20 % of the loaned books ( 100 - 80 ) so total loaned out books = 45 answer d"

divide(subtract(75, 66), subtract(const_1, divide(80, const_100)))

<gadget id="calculator">75 - 66</gadget>
<output>9</output>
<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">1 - (4/5)</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">9 / (1/5)</gadget>
<output>45</output>
<result>45</result>


find the simple interest on rs . 70,000 at 16 2 / 3 % per year for 9 months .

Explanation: "p = rs . 70000 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . simple interest = ( p * r * t ) / 100 = rs . ( 70,000 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 8750 answer is c ."

multiply(multiply(multiply(add(multiply(multiply(multiply(2, 3), const_100), const_100), multiply(multiply(multiply(3, 3), const_100), multiply(add(3, 2), 2))), divide(add(multiply(16, 3), 2), 3)), divide(multiply(3, 3), multiply(2, multiply(2, 3)))), divide(const_1, const_100))

<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">6 * 100</gadget>
<output>600</output>
<gadget id="calculator">600 * 100</gadget>
<output>60_000</output>
<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">9 * 100</gadget>
<output>900</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">900 * 10</gadget>
<output>9_000</output>
<gadget id="calculator">60_000 + 9_000</gadget>
<output>69_000</output>
<gadget id="calculator">16 * 3</gadget>
<output>48</output>
<gadget id="calculator">48 + 2</gadget>
<output>50</output>
<gadget id="calculator">50 / 3</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">69_000 * (50/3)</gadget>
<output>1_150_000</output>
<gadget id="calculator">2 * 6</gadget>
<output>12</output>
<gadget id="calculator">9 / 12</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">1_150_000 * (3/4)</gadget>
<output>862_500</output>
<gadget id="calculator">1 / 100</gadget>
<output>1/100 = around 0.01</output>
<gadget id="calculator">862_500 * (1/100)</gadget>
<output>8_625</output>
<result>8_625</result>


a is twice as good a workman as b and they took 6 days together to do the work b alone can do it in .

Explanation: "wc = 2 : 1 2 x + x = 1 / 6 x = 1 / 18 = > 18 days answer : a"

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

<gadget id="calculator">2 + 1</gadget>
<output>3</output>
<gadget id="calculator">6 * 3</gadget>
<output>18</output>
<gadget id="calculator">18 / 2</gadget>
<output>9</output>
<gadget id="calculator">9 * 2</gadget>
<output>18</output>
<result>18</result>


donovan and michael are racing around a circular 400 - meter track . if donovan runs each lap in 45 seconds and michael runs each lap in 36 seconds , how many laps will michael have to complete in order to pass donovan , assuming they start at the same time ?

Explanation: "one way of approaching this question is by relative speed method 1 . speed / rate of donovan = distance / time = > 400 / 45 = > 80 / 9 2 . speed / rate of michael = distance / time = > 400 / 36 = > 100 / 9 relative speed between them = 100 / 9 - 80 / 9 = > 20 / 9 ( we subtract the rates if moving in the same direction and add the rates if moving in the opposite direction ) in order to pass donovan - distance to be covered = 400 , relative rate = 20 / 9 total time taken by micheal to surpass donovan = distance / rate = > 400 * 9 / 20 = > 3600 / 10 = > 180 no . of laps taken by michael = total time / michael ' s rate = > 180 / 36 = > 5 hence correct answer is 5 laps . d"

divide(divide(400, subtract(divide(400, 36), divide(400, 45))), 36)

<gadget id="calculator">400 / 36</gadget>
<output>100/9 = around 11.111111</output>
<gadget id="calculator">400 / 45</gadget>
<output>80/9 = around 8.888889</output>
<gadget id="calculator">(100/9) - (80/9)</gadget>
<output>20/9 = around 2.222222</output>
<gadget id="calculator">400 / (20/9)</gadget>
<output>180</output>
<gadget id="calculator">180 / 36</gadget>
<output>5</output>
<result>5</result>


if 3 people can do 3 times of a particular work in 3 days , then how many days would it take 9 people to do 9 times of that particular work ?

Explanation: "3 people can do the work one time in one day . 1 person can do 1 / 3 of the work in one day . 9 people can do 9 / 3 of the work in one day . 9 people can do 9 times the work in 3 days . the answer is c ."

<gadget id="calculator">9 / 9</gadget>
<output>1</output>
<gadget id="calculator">3 * 1</gadget>
<output>3</output>
<result>3</result>


the average age of students of a class is 15.8 years . the average age of boys in the class is 16.5 years and that of the girls is 15.4 years . the ration of the number of boys to the number of girls in the class is :

Explanation: "let the ratio be k : 1 . then , k * 16.5 + 1 * 15.4 = ( k + 1 ) * 15.8 = ( 16.5 - 15.8 ) k = ( 15.8 - 15.4 ) = k = 0.4 / 0.7 = 4 / 7 required ratio = 4 / 7 : 1 = 4 : 7 . answer : e"

<gadget id="calculator">15.8 - 15.4</gadget>
<output>0.4</output>
<gadget id="calculator">16.5 - 15.8</gadget>
<output>0.7</output>
<gadget id="calculator">0.4 / 0.7</gadget>
<output>0.571429</output>
<result>0.571429</result>


4 wolves , wolverine , man - hunter , blue - wolf , and jasmine , caught rabbits for their evening meal . if man - hunter caught 3 more rabbits than blue - wolf did , jasmine caught 3 less than wolverine did , and wolverine caught 1 more than man - hunter did , how many more fewer rabbits did blue - wolf catch than jasmine ?

Explanation: in this word problem , the first key is to turn the story into equations : man - hunter caught 3 more than blue - wolf did : m = 3 + b jasmine caught 3 less than wolverine did : j = w - 3 wolverine caught 3 more than man - hunter did : w = 1 + m then , in classic gmat style , the problem does n ' t ask you to solve for a single variable , but instead to solve for the difference between b and j ( how many more rabbits did blue - wolf catch than jasmine did ? ) . this means that your goal is to get the equations in terms of b and j so that you can solve for the expression b - j . taking the first equation and solving for b , you have b = m - 3 . taking the second equation and solving for j you have j = w - 3 , and then with the third equation you can replace w with 1 + m so that both b and j are in terms of m : j = ( 1 + m ) - 3 . so if b = m - 3 and j = m - 2 , then : b - j = ( m - 3 ) - ( m - 2 ) b - j = m - 3 - m + 2 ( remove the parentheses by distributing the multiplication ) b - j = - 1 , so the answer is e .

<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">3 + 3</gadget>
<output>6</output>
<gadget id="calculator">5 - 6</gadget>
<output>-1</output>
<result>-1</result>


a bullet train 160 m long is running with a speed of 70 kmph . in what time will it pass a man who is running at 8 kmph in the direction opposite to that in which the bullet train is going ?

Explanation: "c 7.38 sec speed of the bullet train relative to man = ( 70 + 8 ) kmph = 78 * 5 / 18 m / sec = 65 / 3 m / sec . time taken by the bullet train to cross the man = time taken by it to cover 160 m at ( 65 / 3 ) m / sec = ( 160 * 3 / 65 ) sec = 7.38 sec"

divide(160, divide(multiply(add(70, 8), const_1000), const_3600))

<gadget id="calculator">70 + 8</gadget>
<output>78</output>
<gadget id="calculator">78 * 1_000</gadget>
<output>78_000</output>
<gadget id="calculator">78_000 / 3_600</gadget>
<output>65/3 = around 21.666667</output>
<gadget id="calculator">160 / (65/3)</gadget>
<output>96/13 = around 7.384615</output>
<result>96/13 = around 7.384615</result>


a man can do a job in 5 days . his father takes 20 days and his son finishes it in 25 days . how long will they take to complete the job if they all work together ?

Explanation: "1 day work of the three persons = ( 1 / 5 + 1 / 20 + 1 / 25 ) = 29 / 100 so , all three together will complete the work in 100 / 29 = 3.5 days . answer : c"

divide(const_1, add(divide(const_1, 25), add(divide(const_1, 5), divide(const_1, 20))))

<gadget id="calculator">1 / 25</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/5) + (1/20)</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/25) + (1/4)</gadget>
<output>29/100 = around 0.29</output>
<gadget id="calculator">1 / (29/100)</gadget>
<output>100/29 = around 3.448276</output>
<result>100/29 = around 3.448276</result>


in a kilometer race , a beats b by 52 meters or 18 seconds . what time does a take to complete the race ?

Explanation: "time taken by b run 1000 meters = ( 1000 * 18 ) / 52 = 346 sec . time taken by a = 346 - 18 = 328 sec . answer : c"

subtract(divide(multiply(const_1, const_1000), divide(52, 18)), 18)

<gadget id="calculator">1 * 1_000</gadget>
<output>1_000</output>
<gadget id="calculator">52 / 18</gadget>
<output>26/9 = around 2.888889</output>
<gadget id="calculator">1_000 / (26/9)</gadget>
<output>4_500/13 = around 346.153846</output>
<gadget id="calculator">(4_500/13) - 18</gadget>
<output>4_266/13 = around 328.153846</output>
<result>4_266/13 = around 328.153846</result>


a towel , when bleached , lost 30 % of its length and 25 % of its breadth . what is the percentage decrease in area ?

Explanation: "percentage change in area = ( − 30 − 25 + ( 30 × 25 ) / 100 ) % = − 47.5 % i . e . , area is decreased by 47.5 % answer : e"

divide(subtract(multiply(const_100, const_100), multiply(subtract(const_100, 30), subtract(const_100, 25))), const_100)

<gadget id="calculator">100 * 100</gadget>
<output>10_000</output>
<gadget id="calculator">100 - 30</gadget>
<output>70</output>
<gadget id="calculator">100 - 25</gadget>
<output>75</output>
<gadget id="calculator">70 * 75</gadget>
<output>5_250</output>
<gadget id="calculator">10_000 - 5_250</gadget>
<output>4_750</output>
<gadget id="calculator">4_750 / 100</gadget>
<output>95/2 = around 47.5</output>
<result>95/2 = around 47.5</result>


a train 270 metres long is moving at a speed of 25 kmph . it will cross a man coming from the opposite direction at a speed of 2 km per hour in :

Explanation: "relative speed = ( 25 + 2 ) km / hr = 27 km / hr = ( 27 × 5 / 18 ) m / sec = 15 / 2 m / sec . time taken by the train to pass the man = ( 270 × 2 / 15 ) sec = 36 sec answer : c"

multiply(const_3600, divide(divide(270, const_1000), add(25, 2)))

<gadget id="calculator">270 / 1_000</gadget>
<output>27/100 = around 0.27</output>
<gadget id="calculator">25 + 2</gadget>
<output>27</output>
<gadget id="calculator">(27/100) / 27</gadget>
<output>1/100 = around 0.01</output>
<gadget id="calculator">3_600 * (1/100)</gadget>
<output>36</output>
<result>36</result>


speed of a boat in standing water is 14 kmph and the speed of the stream is 1.2 kmph . a man rows to a place at a distance of 4864 km and comes back to the starting point . the total time taken by him is :

Explanation: "explanation : speed downstream = ( 14 + 1.2 ) = 15.2 kmph speed upstream = ( 14 - 1.2 ) = 12.8 kmph total time taken = 4864 / 15.2 + 4864 / 12.8 = 320 + 380 = 700 hours . answer : a"

<gadget id="calculator">14 + 1.2</gadget>
<output>15.2</output>
<gadget id="calculator">4_864 / 15.2</gadget>
<output>320</output>
<gadget id="calculator">14 - 1.2</gadget>
<output>12.8</output>
<gadget id="calculator">4_864 / 12.8</gadget>
<output>380</output>
<gadget id="calculator">320 + 380</gadget>
<output>700</output>
<result>700</result>


you enter a weight loss challenge game and manage to lose 13 % of your body weight . for the final weigh in you are forced to wear clothes that add 2 % to your weight . what percentage of weight loss is measured at the final weigh in ?

Explanation: ( 100 % - 13 % ) * ( 100 % + 2 % ) = 0.87 * 1.02 = 11.26 % the weigh in records your weight loss at 11.26 % ! the answer is c

multiply(subtract(const_1, multiply(subtract(const_1, divide(13, const_100)), add(const_1, divide(2, const_100)))), const_100)

<gadget id="calculator">13 / 100</gadget>
<output>13/100 = around 0.13</output>
<gadget id="calculator">1 - (13/100)</gadget>
<output>87/100 = around 0.87</output>
<gadget id="calculator">2 / 100</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">1 + (1/50)</gadget>
<output>51/50 = around 1.02</output>
<gadget id="calculator">(87/100) * (51/50)</gadget>
<output>4_437/5_000 = around 0.8874</output>
<gadget id="calculator">1 - (4_437/5_000)</gadget>
<output>563/5_000 = around 0.1126</output>
<gadget id="calculator">(563/5_000) * 100</gadget>
<output>563/50 = around 11.26</output>
<result>563/50 = around 11.26</result>


i bought two books ; for rs . 500 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ?

Explanation: "x * ( 85 / 100 ) = ( 500 - x ) 119 / 100 x = 291.67 answer : e"

divide(multiply(500, add(const_100, 19)), add(subtract(const_100, 15), add(const_100, 19)))

<gadget id="calculator">100 + 19</gadget>
<output>119</output>
<gadget id="calculator">500 * 119</gadget>
<output>59_500</output>
<gadget id="calculator">100 - 15</gadget>
<output>85</output>
<gadget id="calculator">85 + 119</gadget>
<output>204</output>
<gadget id="calculator">59_500 / 204</gadget>
<output>875/3 = around 291.666667</output>
<result>875/3 = around 291.666667</result>


in a group of ducks and cows , the total number of legs are 40 more than twice the number of heads . find the total number of cows .

Explanation: "let the number of ducks be d and number of cows be c then , total number of legs = 2 d + 4 c = 2 ( d + 2 c ) total number of heads = c + d given that total number of legs are 40 more than twice the number of heads = > 2 ( d + 2 c ) = 40 + 2 ( c + d ) = > d + 2 c = 20 + c + d = > 2 c = 20 + c = > c = 20 i . e . , total number of cows = 20 answer is e ."

<gadget id="calculator">40 / 2</gadget>
<output>20</output>
<result>20</result>


a student chose a number , multiplied it by 2 , then subtracted 138 from the result and got 102 . what was the number he chose ?

Explanation: "solution : let x be the number he chose , then 2 * x * 138 = 102 2 x = 240 x = 120 correct answer c"

<gadget id="calculator">102 + 138</gadget>
<output>240</output>
<gadget id="calculator">240 / 2</gadget>
<output>120</output>
<result>120</result>


the product of two successive numbers is 4160 . which is the smaller of the two numbers ?

Explanation: "b 4160 from the given alternatives , 64 × 65 = 4160 ∴ smaller number = 64"

<gadget id="calculator">4_160 ** (1/2)</gadget>
<output>8*sqrt(65) = around 64.498062</output>
<result>8*sqrt(65) = around 64.498062</result>


soymilk are sold in packages of two or 3 only . if hannah bought 17 soymilk exactly , what could be the number of large packs hannah bought ?

Explanation: let number of packs of three = t let number of packs of two = w 3 t + 2 w = 17 now , we need to test for values of w . since sum 17 is odd and 2 w will always be even , therefore w ca n ' t be even . now , we can test for values w = 1 , 3 and 5 2 * 4 + 3 * 3 = 8 + 9 = 17 answer c

divide(subtract(17, multiply(const_2, const_4)), 3)

<gadget id="calculator">2 * 4</gadget>
<output>8</output>
<gadget id="calculator">17 - 8</gadget>
<output>9</output>
<gadget id="calculator">9 / 3</gadget>
<output>3</output>
<result>3</result>


what ratio must a shopkeeper mix peas and soybean of rs . 16 and rs . 25 / kg , as to obtain a mixture of rs . 21.50 ?

Explanation: "correct option : ( c ) use rule of alligation , to determine the ratio the required ratio of soybean and peas = 3.50 : 5.50 = 7 : 11"

<gadget id="calculator">25 - 21.5</gadget>
<output>3.5</output>
<gadget id="calculator">21.5 - 16</gadget>
<output>5.5</output>
<gadget id="calculator">3.5 / 5.5</gadget>
<output>0.636364</output>
<result>0.636364</result>


a 300 meter long train crosses a platform in 33 seconds while it crosses a signal pole in 18 seconds . what is the length of the platform ?

Explanation: "speed = [ 300 / 18 ] m / sec = 50 / 3 m / sec . let the length of the platform be x meters . then , x + 300 / 33 = 50 / 3 3 ( x + 300 ) = 1650 è x = 250 m . answer : a"

subtract(multiply(divide(300, 18), 33), 300)

<gadget id="calculator">300 / 18</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">(50/3) * 33</gadget>
<output>550</output>
<gadget id="calculator">550 - 300</gadget>
<output>250</output>
<result>250</result>


bucket p has thrice the capacity as bucket q . it takes 60 turns for bucket p to fill the empty drum . how many turns it will take for both the buckets p and q , having each turn together to fill the empty drum ?

Explanation: "let capacity of p be x liters then capacity of q = x / 3 liters capacity of the drum = 60 x required number of turns = 60 x / ( x + x / 3 ) = 60 x * 3 / 4 x = 45 answer is b"

divide(const_1, add(divide(const_1, 60), divide(const_1, multiply(60, const_3))))

<gadget id="calculator">1 / 60</gadget>
<output>1/60 = around 0.016667</output>
<gadget id="calculator">60 * 3</gadget>
<output>180</output>
<gadget id="calculator">1 / 180</gadget>
<output>1/180 = around 0.005556</output>
<gadget id="calculator">(1/60) + (1/180)</gadget>
<output>1/45 = around 0.022222</output>
<gadget id="calculator">1 / (1/45)</gadget>
<output>45</output>
<result>45</result>


Explanation: "the expression 4 / ( 1 + 3 / x ) = 1 should have been equal to something . if 4 / ( 1 + 3 / x ) = 1 = > 4 x / ( x + 3 ) = 1 = > 4 x = x + 3 = > 3 x = 3 = > x = 1 correct option : b"

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


a 16 % stock yielding 10 % is quoted at :

Explanation: "solution to earn rs . 10 , money invested = rs . 100 . to earn rs . 16 , money invested = rs . ( 100 / 10 x 16 ) = rs . 160 . â ˆ ´ market value of rs . 100 stock = rs . 160 answer e"

<gadget id="calculator">100 / 10</gadget>
<output>10</output>
<gadget id="calculator">10 * 16</gadget>
<output>160</output>
<result>160</result>


there are , in a certain league , 20 teams , and each team face another team for a total of 10 times . how many games are played in the season ?

Explanation: "1 st team : 190 2 nd team : 180 3 rd team : 170 similarly the last team will play 0 therefore ( 190 + 180 + 170 . . . . 10 ) 10 ( 19 + 18 + 17 + 16 . . . . 1 ) 10 ( n ( n + 1 ) / 2 ) = 10 ( 19 * 20 / 2 ) = 1900 answer : a"

multiply(multiply(subtract(20, const_1), 10), divide(20, const_2))

<gadget id="calculator">20 - 1</gadget>
<output>19</output>
<gadget id="calculator">19 * 10</gadget>
<output>190</output>
<gadget id="calculator">20 / 2</gadget>
<output>10</output>
<gadget id="calculator">190 * 10</gadget>
<output>1_900</output>
<result>1_900</result>


if integer k is equal to the sum of all even multiples of 15 between 390 and 615 , what is the greatest prime factor of k ?

Explanation: "if we break down what the stem is asking what is the sum of all mult of 30 between 390 and 600 . using arithmetic progression to find n : 600 = 390 + ( n - 1 ) 30 210 + 30 = 30 n 240 = 3 n = > n = 8 the sum would be : 8 * mean mean = [ 600 + 390 ] / 2 = 495 8 * 495 c"

divide(add(divide(subtract(multiply(floor(divide(615, 15)), 15), multiply(floor(divide(390, 15)), 15)), 15), const_1), const_2)

<gadget id="calculator">615 / 15</gadget>
<output>41</output>
<gadget id="calculator">floor(41)</gadget>
<output>41</output>
<gadget id="calculator">41 * 15</gadget>
<output>615</output>
<gadget id="calculator">390 / 15</gadget>
<output>26</output>
<gadget id="calculator">floor(26)</gadget>
<output>26</output>
<gadget id="calculator">26 * 15</gadget>
<output>390</output>
<gadget id="calculator">615 - 390</gadget>
<output>225</output>
<gadget id="calculator">225 / 15</gadget>
<output>15</output>
<gadget id="calculator">15 + 1</gadget>
<output>16</output>
<gadget id="calculator">16 / 2</gadget>
<output>8</output>
<result>8</result>


a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 30 paisa . if the share of y is rs . 54 , what is the total amount ?

Explanation: "x : y : z = 100 : 45 : 30 20 : 9 : 6 9 - - - 54 35 - - - ? = > 210 answer : e"

add(add(multiply(divide(const_100, 45), 54), multiply(divide(30, 45), 54)), 54)

<gadget id="calculator">100 / 45</gadget>
<output>20/9 = around 2.222222</output>
<gadget id="calculator">(20/9) * 54</gadget>
<output>120</output>
<gadget id="calculator">30 / 45</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) * 54</gadget>
<output>36</output>
<gadget id="calculator">120 + 36</gadget>
<output>156</output>
<gadget id="calculator">156 + 54</gadget>
<output>210</output>
<result>210</result>


the expenditure of a businessman increase consistently by 10 % per year . if his present expenditure is rs . 20000 then what will his expenditure be after 2 years ?

Explanation: explanation : expenditure = 20000 x 1.1 x 1.1 = 24200 answer : option d

multiply(20000, power(divide(add(const_100, 10), const_100), 2))

<gadget id="calculator">100 + 10</gadget>
<output>110</output>
<gadget id="calculator">110 / 100</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">(11/10) ** 2</gadget>
<output>121/100 = around 1.21</output>
<gadget id="calculator">20_000 * (121/100)</gadget>
<output>24_200</output>
<result>24_200</result>


farm tax is levied on the 25 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . william . mr . william paid only $ 480 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :

Explanation: "this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 3840 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 25 ) = 50 % the correct answer is ( c ) ."

divide(multiply(multiply(divide(480, 3840), const_100), const_100), 25)

<gadget id="calculator">480 / 3_840</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">(1/8) * 100</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">(25/2) * 100</gadget>
<output>1_250</output>
<gadget id="calculator">1_250 / 25</gadget>
<output>50</output>
<result>50</result>


a textile manufacturing firm employees 100 looms . it makes fabrics for a branded company . the aggregate sales value of the output of the 100 looms is rs 5 , 00,000 and the monthly manufacturing expenses is rs 1 , 50,000 . assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms . monthly establishment charges are rs 75000 . if one loom breaks down and remains idle for one month , the decrease in profit is :

Explanation: "explanation : profit = 5 , 00,000 â ˆ ’ ( 1 , 50,000 + 75,000 ) = rs . 2 , 75,000 . since , such loom contributes equally to sales and manufacturing expenses . but the monthly charges are fixed at rs 75,000 . if one loan breaks down sales and expenses will decrease . new profit : - = > 500000 ã — ( 99 / 100 ) â ˆ ’ 150000 ã — ( 99 / 100 ) â ˆ ’ 75000 . = > rs 2 , 68,000 . decrease in profit = > 2 , 75,000 â ˆ ’ 2 , 71,500 = > rs . 3,500 . answer : d"

subtract(subtract(multiply(multiply(5, const_1000), const_100), add(multiply(75000, const_2), 75000)), subtract(subtract(multiply(divide(subtract(100, 1), 100), multiply(multiply(5, const_1000), const_100)), multiply(multiply(75000, const_2), divide(subtract(100, 1), 100))), 75000))

<gadget id="calculator">5 * 1_000</gadget>
<output>5_000</output>
<gadget id="calculator">5_000 * 100</gadget>
<output>500_000</output>
<gadget id="calculator">75_000 * 2</gadget>
<output>150_000</output>
<gadget id="calculator">150_000 + 75_000</gadget>
<output>225_000</output>
<gadget id="calculator">500_000 - 225_000</gadget>
<output>275_000</output>
<gadget id="calculator">100 - 1</gadget>
<output>99</output>
<gadget id="calculator">99 / 100</gadget>
<output>99/100 = around 0.99</output>
<gadget id="calculator">(99/100) * 500_000</gadget>
<output>495_000</output>
<gadget id="calculator">150_000 * (99/100)</gadget>
<output>148_500</output>
<gadget id="calculator">495_000 - 148_500</gadget>
<output>346_500</output>
<gadget id="calculator">346_500 - 75_000</gadget>
<output>271_500</output>
<gadget id="calculator">275_000 - 271_500</gadget>
<output>3_500</output>
<result>3_500</result>


it is the new year and mandy has made a resolution to lose weight this year . she plans to exercise and do yoga . for exercise she plans to workout at the gym and ride her bicycle in the ratio of 2 : 3 everyday . she will also do yoga in the ratio , yoga : exercise = 2 : 3 . if she rides her bike for 18 minutes , how much time will she spend doing yoga ? ( rounded to minutes )

Explanation: "the ratio is 2 : 3 = gym : ride , so ( 18 ) ( 3 / 2 ) = 27 minutes at the gym , and 27 + 18 = 45 minutes exercise , so ( 2 / 3 ) ( 45 ) = 30 minutes yoga . answer : a"

divide(multiply(18, divide(3, add(2, 3))), multiply(divide(3, add(2, 3)), divide(3, add(2, 3))))

<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">18 * (3/5)</gadget>
<output>54/5 = around 10.8</output>
<gadget id="calculator">(3/5) * (3/5)</gadget>
<output>9/25 = around 0.36</output>
<gadget id="calculator">(54/5) / (9/25)</gadget>
<output>30</output>
<result>30</result>


when positive integer x is divided by 11 , the quotient is y and the remainder is 4 . when 2 x is divided by 8 , the quotient is 3 y and the remainder is 1 . what is the value of 13 y – x ?

Explanation: ( 1 ) x = 11 y + 4 ( 2 ) 2 x = 24 y + 1 let ' s subtract equation ( 1 ) from equation ( 2 ) . 13 y - 3 = x 13 y - x = 3 the answer is b .

subtract(multiply(13, divide(subtract(multiply(2, 4), 1), subtract(multiply(8, 3), multiply(2, 11)))), add(multiply(11, divide(subtract(multiply(2, 4), 1), subtract(multiply(8, 3), multiply(2, 11)))), 4))

<gadget id="calculator">2 * 4</gadget>
<output>8</output>
<gadget id="calculator">8 - 1</gadget>
<output>7</output>
<gadget id="calculator">8 * 3</gadget>
<output>24</output>
<gadget id="calculator">2 * 11</gadget>
<output>22</output>
<gadget id="calculator">24 - 22</gadget>
<output>2</output>
<gadget id="calculator">7 / 2</gadget>
<output>7/2 = around 3.5</output>
<gadget id="calculator">13 * (7/2)</gadget>
<output>91/2 = around 45.5</output>
<gadget id="calculator">11 * (7/2)</gadget>
<output>77/2 = around 38.5</output>
<gadget id="calculator">(77/2) + 4</gadget>
<output>85/2 = around 42.5</output>
<gadget id="calculator">(91/2) - (85/2)</gadget>
<output>3</output>
<result>3</result>


what is the least number of squares tiles required to pave the floor of a room 15.17 m long and 9.02 m broad ?

Explanation: explanation : length of largest tile = h . c . f . of 1517 cm and 902 cm = 41 cm . area of each tile = required number of tiles = = 814 answer : a ) 814

divide(rectangle_area(multiply(15.17, const_100), multiply(9.02, const_100)), square_area(add(multiply(const_4, const_10), const_1)))

<gadget id="calculator">15.17 * 100</gadget>
<output>1_517</output>
<gadget id="calculator">9.02 * 100</gadget>
<output>902</output>
<gadget id="calculator">1_517 * 902</gadget>
<output>1_368_334</output>
<gadget id="calculator">4 * 10</gadget>
<output>40</output>
<gadget id="calculator">40 + 1</gadget>
<output>41</output>
<gadget id="calculator">41 ** 2</gadget>
<output>1_681</output>
<gadget id="calculator">1_368_334 / 1_681</gadget>
<output>814</output>
<result>814</result>


if a drawing has an outer circle of diameter 30 and an inner circle of diameter 24 , then what fraction of outer circle ' s surface is not covered by the inner circle ?

Explanation: the questions asks us to find the surface which is not covered by the inner circle i . e . , area of the surface not covered . where as circumference is the length along the edge of the circle , 2 * pi * r implies the length of the curve pi * r ^ 2 implies area enclosed by that curve . . hence area of the circle is considered for this problem area of the inner circle = pi * r ^ 2 , where r = 12 = > pi * 144 area of the outer circle = pi * 225 surface not covered by the inner circle = pi * 225 - pi * 144 = pi * 81 fraction of outer circle ' s surface is not covered by the inner circle = pi * 81 / total area of the outer circle = > pi * 81 / pi * 225 = 9 / 25 answer is d

divide(subtract(multiply(const_pi, power(divide(30, const_2), const_2)), multiply(const_pi, power(divide(24, const_2), const_2))), multiply(const_pi, power(divide(30, const_2), const_2)))

<gadget id="calculator">30 / 2</gadget>
<output>15</output>
<gadget id="calculator">15 ** 2</gadget>
<output>225</output>
<gadget id="calculator">pi * 225</gadget>
<output>225*pi = around 706.858347</output>
<gadget id="calculator">24 / 2</gadget>
<output>12</output>
<gadget id="calculator">12 ** 2</gadget>
<output>144</output>
<gadget id="calculator">pi * 144</gadget>
<output>144*pi = around 452.389342</output>
<gadget id="calculator">(225*pi) - (144*pi)</gadget>
<output>81*pi = around 254.469005</output>
<gadget id="calculator">(81*pi) / (225*pi)</gadget>
<output>9/25 = around 0.36</output>
<result>9/25 = around 0.36</result>


x can finish a work in 24 days . y can finish the same work in 16 days . yworked for 10 days and left the job . how many days does x alone need to finish the remaining work ?

Explanation: "work done by x in 1 day = 1 / 24 work done by y in 1 day = 1 / 16 work done by y in 10 days = 10 / 16 = 5 / 8 remaining work = 1 – 5 / 8 = 3 / 8 number of days in which x can finish the remaining work = ( 3 / 8 ) / ( 1 / 24 ) = 9 e"

divide(subtract(const_1, multiply(10, divide(const_1, 16))), divide(const_1, 24))

<gadget id="calculator">1 / 16</gadget>
<output>1/16 = around 0.0625</output>
<gadget id="calculator">10 * (1/16)</gadget>
<output>5/8 = around 0.625</output>
<gadget id="calculator">1 - (5/8)</gadget>
<output>3/8 = around 0.375</output>
<gadget id="calculator">1 / 24</gadget>
<output>1/24 = around 0.041667</output>
<gadget id="calculator">(3/8) / (1/24)</gadget>
<output>9</output>
<result>9</result>


some of 45 % - intensity red paint is replaced with 25 % solution of red paint such that the new paint intensity is 40 % . what fraction of the original paint was replaced ?

Explanation: "let total paint = 1 let amount replaced = x 45 ( 1 - x ) + 25 x = 40 x = 1 / 4 answer : b"

divide(subtract(divide(40, const_100), divide(45, const_100)), subtract(divide(25, const_100), divide(45, const_100)))

<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">45 / 100</gadget>
<output>9/20 = around 0.45</output>
<gadget id="calculator">(2/5) - (9/20)</gadget>
<output>-1/20 = around -0.05</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) - (9/20)</gadget>
<output>-1/5 = around -0.2</output>
<gadget id="calculator">(-1/20) / (-1/5)</gadget>
<output>1/4 = around 0.25</output>
<result>1/4 = around 0.25</result>


what will be the cost of building a fence around a square plot with area equal to 289 sq ft , if the price per foot of building the fence is rs . 59 ?

Explanation: "explanation : let the side of the square plot be a ft . a 2 = 289 = > a = 17 length of the fence = perimeter of the plot = 4 a = 68 ft . cost of building the fence = 68 * 59 = rs . 4012 . answer : option e"

<gadget id="calculator">289 ** (1/2)</gadget>
<output>17</output>
<gadget id="calculator">4 * 17</gadget>
<output>68</output>
<gadget id="calculator">68 * 59</gadget>
<output>4_012</output>
<result>4_012</result>


at jerri ’ s pet shop , 60 cups of bird seed are used every 5 days to feed 20 parakeets . how many cups of bird seed would be required to feed 10 parakeets for 5 days ?

Explanation: let ' s go step - by - step . 60 cups are used over a 5 day period , which means 12 cups a day . this feeds 20 parakeets , which means each parakeet needs . 60 of a cup every day . for 10 parakeets , we need 10 * . 60 cups = 6 cups a day . over 5 days , we need 30 cups . choice d .

<gadget id="calculator">60 / 2</gadget>
<output>30</output>
<result>30</result>


a jar of 180 marbles is divided equally among a group of marble - players today . if 2 people joined the group in the future , each person would receive 1 marble less . how many people are there in the group today ?

Explanation: "180 = 18 * 10 = 20 * 9 there are 18 people in the group today . the answer is b ."

divide(subtract(sqrt(add(multiply(multiply(180, 2), const_4), power(2, 2))), 2), 2)

<gadget id="calculator">180 * 2</gadget>
<output>360</output>
<gadget id="calculator">360 * 4</gadget>
<output>1_440</output>
<gadget id="calculator">2 ** 2</gadget>
<output>4</output>
<gadget id="calculator">1_440 + 4</gadget>
<output>1_444</output>
<gadget id="calculator">1_444 ** (1/2)</gadget>
<output>38</output>
<gadget id="calculator">38 - 2</gadget>
<output>36</output>
<gadget id="calculator">36 / 2</gadget>
<output>18</output>
<result>18</result>


a cricketer whose bowling average is 12.4 runs per wicket takes 5 wickets for 26 runs and there by decreases his average by 0.4 . the number age of the family now is :

Explanation: "let the number of wickets taken till the last match be x . then , ( 12.4 x + 26 ) / ( x + 5 ) = 12 = 12.4 x + 26 = 12 x + 60 = 0.4 x = 34 = x = 340 / 4 = 85 . answer : d"

divide(subtract(multiply(5, subtract(12.4, 0.4)), 26), 0.4)

<gadget id="calculator">12.4 - 0.4</gadget>
<output>12</output>
<gadget id="calculator">5 * 12</gadget>
<output>60</output>
<gadget id="calculator">60 - 26</gadget>
<output>34</output>
<gadget id="calculator">34 / 0.4</gadget>
<output>85</output>
<result>85</result>


the average of first 5 multiples of 5 is

Explanation: solution average = 5 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 75 / 5 . = 15 answer e

divide(add(add(add(add(5, multiply(5, const_2)), multiply(5, const_3)), multiply(5, const_4)), multiply(5, 5)), 5)

<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">5 + 10</gadget>
<output>15</output>
<gadget id="calculator">5 * 3</gadget>
<output>15</output>
<gadget id="calculator">15 + 15</gadget>
<output>30</output>
<gadget id="calculator">5 * 4</gadget>
<output>20</output>
<gadget id="calculator">30 + 20</gadget>
<output>50</output>
<gadget id="calculator">5 * 5</gadget>
<output>25</output>
<gadget id="calculator">50 + 25</gadget>
<output>75</output>
<gadget id="calculator">75 / 5</gadget>
<output>15</output>
<result>15</result>


a technician makes a round - trip to and from a certain service center by the same route . if the technician completes the drive to the center and then completes 50 percent of the drive from the center , what percent of the round - trip has the technician completed ?

Explanation: "round trip means 2 trips i . e . to and fro . he has completed one i . e 50 % completed . then he traveled another 50 % of 50 % i . e 25 % . so he completed 50 + 25 = 75 % of total trip . d"

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

<gadget id="calculator">100 / 2</gadget>
<output>50</output>
<gadget id="calculator">50 * 50</gadget>
<output>2_500</output>
<gadget id="calculator">2_500 / 100</gadget>
<output>25</output>
<gadget id="calculator">50 + 25</gadget>
<output>75</output>
<result>75</result>


the difference of two numbers is 1415 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder . what is the smaller number ?

Explanation: let the smaller number be x . then larger number = ( x + 1415 ) . x + 1415 = 6 x + 15 5 x = 1400 x = 280 smaller number = 280 . b )

divide(add(1415, 15), subtract(6, const_1))

<gadget id="calculator">1_415 + 15</gadget>
<output>1_430</output>
<gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">1_430 / 5</gadget>
<output>286</output>
<result>286</result>


the price of a jacket is reduced by 25 % . during a special sale the price of the jacket is reduced another 25 % . by approximately what percent must the price of the jacket now be increased in order to restore it to its original amount ?

Explanation: "1 ) let the price of jacket initially be $ 100 . 2 ) then it is decreased by 25 % , therefore bringing down the price to $ 75 . 3 ) again it is further discounted by 10 % , therefore bringing down the price to $ 56.25 4 ) now 56.25 has to be added byx % in order to equal the original price . 56.25 + ( x % ) 56.25 = 100 . solving this eq for x , we get x = 77.78 ans is b ."

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

<gadget id="calculator">100 - 25</gadget>
<output>75</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">75 * (1/4)</gadget>
<output>75/4 = around 18.75</output>
<gadget id="calculator">75 - (75/4)</gadget>
<output>225/4 = around 56.25</output>
<gadget id="calculator">100 - (225/4)</gadget>
<output>175/4 = around 43.75</output>
<gadget id="calculator">(175/4) / (225/4)</gadget>
<output>7/9 = around 0.777778</output>
<gadget id="calculator">100 * (7/9)</gadget>
<output>700/9 = around 77.777778</output>
<result>700/9 = around 77.777778</result>


of the 180 people at a party , 70 were women , and 30 women tried the appetizer . if 50 people did not try the appetizer , what is the total number of men who tried the appetizer ?

Explanation: "total people at party = 180 women = 70 so men 180 - 70 = 110 no . of pple who tried appetizer = 180 - 50 ( given info ) = 130 no of women who tried appetizer = 30 so remaining ppl ( men ) who tried the appetizer = 130 - 30 = 100 correct option e"

<gadget id="calculator">180 - 50</gadget>
<output>130</output>
<gadget id="calculator">130 - 30</gadget>
<output>100</output>
<result>100</result>


danny and steve are running towards each other , each one from his own house . danny can reach steve ' s house in 25 minutes of running , which is half the time it takes steve to reach danny ' s house . if the two started to run at the same time , how much time longer will it take steve to reach the halfway point between their houses than danny to reach the halfway point between their houses ?

Explanation: "if the distance between the two houses is d . then speed of danny = ( d / 25 ) speed of steve = ( d / 50 ) [ steve takes 50 minutes to reach danny ' s house . double the time taken by danny ) obviously speed of danny is twice that of steve . now in order to cover distance ( d / 2 ) [ they meet in middle ] , steve will take : ( d / 2 ) / ( d / 50 ) = 25 minutes . distance is same and danny ' s speed is twice of steve . thus he will take 12.5 minutes to cover this same distance . steve take 25 - 12.5 = 12.5 minutes longer . a is the answer ."

<gadget id="calculator">25 / 2</gadget>
<output>25/2 = around 12.5</output>
<result>25/2 = around 12.5</result>


we run a business that rents out canoes and kayaks . a canoe rental costs $ 15 per day , and a kayak rental costs $ 18 dollars per day . one day , our business rents out 3 canoes for every 2 kayaks and receives a total of $ 405 in revenue . how many more canoes than kayaks were rented out ?

Explanation: "let x be the number of canoes . then 2 x / 3 is the number of kayaks . 15 x + ( 2 x / 3 ) * 18 = 405 15 x + 12 x = 405 27 x = 405 x = 15 ( canoes ) 2 x / 3 = 10 ( kayaks ) there were 15 - 10 = 5 more canoes rented out . the answer is a ."

multiply(subtract(3, 2), divide(405, add(multiply(3, 15), multiply(2, 18))))

<gadget id="calculator">3 - 2</gadget>
<output>1</output>
<gadget id="calculator">3 * 15</gadget>
<output>45</output>
<gadget id="calculator">2 * 18</gadget>
<output>36</output>
<gadget id="calculator">45 + 36</gadget>
<output>81</output>
<gadget id="calculator">405 / 81</gadget>
<output>5</output>
<gadget id="calculator">1 * 5</gadget>
<output>5</output>
<result>5</result>


in a company the manager wants to give some gifts to all of the workers . in each block there are about 100 workers are there . the total amount for giving the gifts for all the workers is $ 4000 . the worth of the gift is $ 4 . how many blocks are there in the company ?

Explanation: each employee will get a gift worth of = $ 4 total employees = 4000 / 4 = 1000 total blocks = 1000 / 100 = 10 correct option is b

<gadget id="calculator">4_000 / 4</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 / 100</gadget>
<output>10</output>
<result>10</result>


in what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way ?

Explanation: "t = 60 / 36 * 18 / 5 = 6 sec answer : d"

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">36 * (5/18)</gadget>
<output>10</output>
<gadget id="calculator">60 / 10</gadget>
<output>6</output>
<result>6</result>


a man buys 54 pens at marked price of 46 pens from a whole seller . if he sells these pens giving a discount of 1 % , what is the profit percent ?

Explanation: "explanation : let marked price be re . 1 each c . p . of 54 pens = rs . 46 s . p . of 54 pens = 99 % of rs . 54 = rs . 53.46 profit % = ( profit / c . p . ) x 100 profit % = ( 7.46 / 46 ) x 100 = 16.21 % answer : c"

multiply(const_100, divide(subtract(multiply(54, subtract(const_100, 1)), multiply(46, const_100)), multiply(46, const_100)))

<gadget id="calculator">100 - 1</gadget>
<output>99</output>
<gadget id="calculator">54 * 99</gadget>
<output>5_346</output>
<gadget id="calculator">46 * 100</gadget>
<output>4_600</output>
<gadget id="calculator">5_346 - 4_600</gadget>
<output>746</output>
<gadget id="calculator">746 / 4_600</gadget>
<output>373/2_300 = around 0.162174</output>
<gadget id="calculator">100 * (373/2_300)</gadget>
<output>373/23 = around 16.217391</output>
<result>373/23 = around 16.217391</result>


find the area of a cuboid of length 15 cm , breadth 10 cm . and height 16 cm .

Explanation: "area of a cuboid = lxbxh = 15 cm x 10 cm x 16 cm = 2400 cm cube answer : a"

<gadget id="calculator">15 * 10</gadget>
<output>150</output>
<gadget id="calculator">150 * 16</gadget>
<output>2_400</output>
<result>2_400</result>


a can do a piece of work in 15 days . a does the work for 5 days only and leaves the job . b does the remaining work in 6 days . in how many days b alone can do the work ?

Explanation: "explanation : a ’ s 5 day work = 5 * 1 / 15 = 1 / 3 remaining work = 1 - 1 / 3 = 2 / 3 b completes 2 / 3 work in 6 days b alone can do in x days 2 / 3 * x = 6 x = 9 days answer : option d"

inverse(multiply(inverse(6), subtract(const_1, multiply(5, inverse(15)))))

<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">5 * (1/15)</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 - (1/3)</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(1/6) * (2/3)</gadget>
<output>1/9 = around 0.111111</output>
<gadget id="calculator">1 / (1/9)</gadget>
<output>9</output>
<result>9</result>


the sum of first n consecutive odd integers is n ^ 2 . what is the sum of all odd integers between 15 and 41 inclusive .

Explanation: "we ' re dealing with a sequence of consecutive odd integers : 15 to 41 , inclusive . we ' re asked for the sum of this group . 1 ) start with the sum of the smallest and the biggest : 15 + 41 = 56 2 ) now look at the ' next smallest ' and the ' next biggest ' : 17 + 39 = 56 now we have proof that there is no middle term . we have 7 bunches of 56 . 7 ( 56 ) = 392 b"

subtract(power(divide(add(41, const_1), 2), 2), power(divide(add(subtract(15, 2), const_1), 2), 2))

<gadget id="calculator">41 + 1</gadget>
<output>42</output>
<gadget id="calculator">42 / 2</gadget>
<output>21</output>
<gadget id="calculator">21 ** 2</gadget>
<output>441</output>
<gadget id="calculator">15 - 2</gadget>
<output>13</output>
<gadget id="calculator">13 + 1</gadget>
<output>14</output>
<gadget id="calculator">14 / 2</gadget>
<output>7</output>
<gadget id="calculator">7 ** 2</gadget>
<output>49</output>
<gadget id="calculator">441 - 49</gadget>
<output>392</output>
<result>392</result>


the cost price of a radio is rs . 1800 and it was sold for rs . 1430 , find the loss % ?

Explanation: "1800 - - - - 370 100 - - - - ? = > 20.5 % answer : b"

multiply(divide(subtract(1800, 1430), 1800), const_100)

<gadget id="calculator">1_800 - 1_430</gadget>
<output>370</output>
<gadget id="calculator">370 / 1_800</gadget>
<output>37/180 = around 0.205556</output>
<gadget id="calculator">(37/180) * 100</gadget>
<output>185/9 = around 20.555556</output>
<result>185/9 = around 20.555556</result>


what is the dividend . divisor 17 , the quotient is 8 and the remainder is 5

Explanation: "d = d * q + r d = 17 * 8 + 5 d = 136 + 5 d = 141 answer : b"

<gadget id="calculator">17 * 8</gadget>
<output>136</output>
<gadget id="calculator">136 + 5</gadget>
<output>141</output>
<result>141</result>


a searchlight on top of the watch - tower makes 3 revolutions per minute . what is the probability that a man appearing near the tower will stay in the dark for at least 15 seconds ?

Explanation: "3 revolutions per minute = 1 revolution every 20 seconds so no matter what anybody appearing at the tower can not stay in the dark for more than 20 seconds . this will be our total number of possibilities i . e the denominator . p ( man in dark for at least 15 seconds ) = 1 - p ( man in dark for max of 15 seconds ) = 1 - 15 / 20 = 1 - 3 / 4 = 1 / 4 or the other way would be : p ( man in dark for at least 5 seconds ) is like saying he can be in dark for 5 , 6,7 . . . all the way to 20 seconds because that is the max . in this approach it would be 5 / 20 seconds = 1 / 4 . answer is a"

subtract(const_1, divide(15, divide(multiply(const_60, const_1), 3)))

<gadget id="calculator">60 * 1</gadget>
<output>60</output>
<gadget id="calculator">60 / 3</gadget>
<output>20</output>
<gadget id="calculator">15 / 20</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">1 - (3/4)</gadget>
<output>1/4 = around 0.25</output>
<result>1/4 = around 0.25</result>


john and amanda stand at opposite ends of a straight road and start running towards each other at the same moment . their rates are randomly selected in advance so that john runs at a constant rate of 3 , 4 , or 5 miles per hour and amanda runs at a constant rate of 3 , 4 , 5 , 6 , or 7 miles per hour . what is the probability that john has traveled farther than amanda by the time they meet ?

Explanation: john will run farther if he runs at 5 mph and amanda runs at 4 mph or 3 mph . in this case , p ( john runs farther ) = 1 / 3 * 2 / 5 = 2 / 15 john will run farther if he runs at 4 mph and amanda runs at 3 mph . in this case , p ( john runs farther ) = 1 / 3 * 1 / 5 = 1 / 15 p ( john runs farther ) = 2 / 15 + 1 / 15 = 3 / 15 = 1 / 5 the answer is c .

<gadget id="calculator">3 * 5</gadget>
<output>15</output>
<gadget id="calculator">3 / 15</gadget>
<output>1/5 = around 0.2</output>
<result>1/5 = around 0.2</result>


two bullet train s 140 m and 210 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time ( in seconds ) which they take to cross each other , is :

Explanation: "relative speed = ( 60 + 40 ) km / hr = 100 x 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = ( 140 + 210 ) m = 350 m . required time = 350 x 9 / 250 = 54 / 5 = 12.6 sec . answer b"

<gadget id="calculator">140 + 210</gadget>
<output>350</output>
<gadget id="calculator">60 + 40</gadget>
<output>100</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">100 * (5/18)</gadget>
<output>250/9 = around 27.777778</output>
<gadget id="calculator">350 / (250/9)</gadget>
<output>63/5 = around 12.6</output>
<result>63/5 = around 12.6</result>


4 friends are pooling their money for pizza . emma has 8 dollars . daya has 25 % more money than emma , jeff has 2 / 5 of the money daya has , and brenda has 4 more dollars than jeff . how much money does brenda have ?

Explanation: d 8 emma has 8 dollars . daya has 25 % more dollars than emma . daya = 8 + 8 x 25 % = 8 + 8 x . 25 = 8 + 2 = 10 jeff has 2 / 5 of what daya has . = 10 x 2 / 5 = 4 brenda has 4 more dollars than jeff . = 4 + 4 = 8 brenda has 8 dollars . the correct answer is d .

add(divide(multiply(multiply(divide(add(25, const_100), const_100), 8), 2), 5), 4)

<gadget id="calculator">25 + 100</gadget>
<output>125</output>
<gadget id="calculator">125 / 100</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">(5/4) * 8</gadget>
<output>10</output>
<gadget id="calculator">10 * 2</gadget>
<output>20</output>
<gadget id="calculator">20 / 5</gadget>
<output>4</output>
<gadget id="calculator">4 + 4</gadget>
<output>8</output>
<result>8</result>


in one alloy there is 12 % chromium while in another alloy it is 8 % . 35 kg of the first alloy was melted together with 40 kg of the second one to form a third alloy . find the percentage of chromium in the new alloy .

Explanation: "the amount of chromium in the new 35 + 45 = 80 kg alloy is 0.12 * 35 + 0.08 * 45 = 7.8 kg , so the percentage is 7.8 / 80 * 100 = 9.75 % . answer : b ."

multiply(divide(add(divide(multiply(12, 35), const_100), divide(multiply(8, 40), const_100)), add(35, 40)), const_100)

<gadget id="calculator">12 * 35</gadget>
<output>420</output>
<gadget id="calculator">420 / 100</gadget>
<output>21/5 = around 4.2</output>
<gadget id="calculator">8 * 40</gadget>
<output>320</output>
<gadget id="calculator">320 / 100</gadget>
<output>16/5 = around 3.2</output>
<gadget id="calculator">(21/5) + (16/5)</gadget>
<output>37/5 = around 7.4</output>
<gadget id="calculator">35 + 40</gadget>
<output>75</output>
<gadget id="calculator">(37/5) / 75</gadget>
<output>37/375 = around 0.098667</output>
<gadget id="calculator">(37/375) * 100</gadget>
<output>148/15 = around 9.866667</output>
<result>148/15 = around 9.866667</result>


mike took a taxi to the airport and paid $ 2.50 to start plus $ 0.25 per mile . annie took a different route to the airport and paid $ 2.50 plus $ 5.00 in bridge toll fees plus $ 0.25 per mile . if each was charged exactly the same amount , and annie ' s ride was 26 miles , how many miles was mike ' s ride ?

Explanation: "the cost of annie ' s ride was 2.5 + 5 + ( 0.25 * 26 ) = $ 14 let x be the distance of mike ' s ride . the cost of mike ' s ride is 2.5 + ( 0.25 * x ) = 14 0.25 * x = 11.5 x = 46 miles the answer is d ."

<gadget id="calculator">2.5 + 5</gadget>
<output>7.5</output>
<gadget id="calculator">0.25 * 26</gadget>
<output>6.5</output>
<gadget id="calculator">7.5 + 6.5</gadget>
<output>14</output>
<gadget id="calculator">14 - 2.5</gadget>
<output>11.5</output>
<gadget id="calculator">11.5 / 0.25</gadget>
<output>46</output>
<result>46</result>


fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 8.91 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discount rates is 22 percent , what is the discount rate on pony jeans ?

Explanation: "let x be the discount on pony jeans . then 0.22 - x is the discount on fox jeans . 3 ( 0.22 - x ) ( 15 ) + 2 x ( 18 ) = 8.91 9.9 - 45 x + 36 x = 8.91 9 x = 0.99 x = 0.11 the answer is c ."

multiply(subtract(divide(22, const_100), divide(subtract(8.91, multiply(divide(22, const_100), multiply(18, 2))), subtract(multiply(15, 3), multiply(18, 2)))), const_100)

<gadget id="calculator">22 / 100</gadget>
<output>11/50 = around 0.22</output>
<gadget id="calculator">18 * 2</gadget>
<output>36</output>
<gadget id="calculator">(11/50) * 36</gadget>
<output>198/25 = around 7.92</output>
<gadget id="calculator">8.91 - (198/25)</gadget>
<output>0.99</output>
<gadget id="calculator">15 * 3</gadget>
<output>45</output>
<gadget id="calculator">45 - 36</gadget>
<output>9</output>
<gadget id="calculator">0.99 / 9</gadget>
<output>0.11</output>
<gadget id="calculator">(11/50) - 0.11</gadget>
<output>0.11</output>
<gadget id="calculator">0.11 * 100</gadget>
<output>11</output>
<result>11</result>


find the simple interest on $ 10000 at 4 % per annum for 12 months ?

Explanation: "p = $ 10000 r = 4 % t = 12 / 12 years = 1 year s . i . = p * r * t / 100 = 10000 * 4 * 1 / 100 = $ 400 answer is a"

<gadget id="calculator">4 / 100</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">10_000 * (1/25)</gadget>
<output>400</output>
<result>400</result>


a contractor undertakes to built a walls in 50 days . he employs 40 peoples for the same . however after 25 days he finds that only 40 % of the work is complete . how many more man need to be employed to complete the work in time ?

Explanation: "40 men complete 0.4 work in 25 days . applying the work rule , m 1 × d 1 × w 2 = m 2 × d 2 × w 1 we have , 40 × 25 × 0.6 = m 2 × 25 × 0.4 or m 2 = 40 × 25 × 0.6 / 25 × 0.4 = 60 men answera"

divide(multiply(40, divide(subtract(const_100, 40), const_100)), divide(const_4, const_10))

<gadget id="calculator">100 - 40</gadget>
<output>60</output>
<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">40 * (3/5)</gadget>
<output>24</output>
<gadget id="calculator">4 / 10</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">24 / (2/5)</gadget>
<output>60</output>
<result>60</result>


the average weight of 6 person ' s increases by 4.5 kg when a new person comes in place of one of them weighing 75 kg . what might be the weight of the new person ?

Explanation: "total weight increased = ( 6 x 4.5 ) kg = 27 kg . weight of new person = ( 75 + 27 ) kg = 102 kg option d"

<gadget id="calculator">6 * 4.5</gadget>
<output>27</output>
<gadget id="calculator">27 + 75</gadget>
<output>102</output>
<result>102</result>


sandy buys an old scooter for $ 900 and spends $ 300 on its repairs . if sandy sells the scooter for $ 1500 , what is the gain percent ?

Explanation: "selling price / total cost = 1500 / 1200 = 1.25 the gain percent is 25 % . the answer is d ."

<gadget id="calculator">300 + 900</gadget>
<output>1_200</output>
<gadget id="calculator">1_500 - 1_200</gadget>
<output>300</output>
<gadget id="calculator">300 / 1_200</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<result>25</result>


a , b , c , d , e are the 5 electronic shops in the naza market , which have 20 , 30 , 60 , 80 and 50 t . v . sets with them respectively , then the average number of t . v . sets in each shop is

Explanation: answer average number of t . v . sets = ( 20 + 30 + 60 + 80 + 50 ) / 5 = 48 correct option : b

<gadget id="calculator">60 + 80</gadget>
<output>140</output>
<gadget id="calculator">20 + 30</gadget>
<output>50</output>
<gadget id="calculator">50 + 50</gadget>
<output>100</output>
<gadget id="calculator">140 + 100</gadget>
<output>240</output>
<gadget id="calculator">240 / 5</gadget>
<output>48</output>
<result>48</result>


a no . when divided by 281 gives a remainder 160 , what remainder will be obtainedby dividingthe same no . 21 ?

Explanation: "281 + 160 = 441 / 21 = 21 ( remainder ) a"

<gadget id="calculator">281 + 160</gadget>
<output>441</output>
<gadget id="calculator">441 / 21</gadget>
<output>21</output>
<result>21</result>


in the rectangular coordinate system , points ( 16 , 0 ) and ( – 16 , 0 ) both lie on circle c . what is the maximum possible value of the radius of c ?

Explanation: "d it takes 3 distinct points to define a circle . only 2 are given here . the two points essentially identify a single chord of the circle c . since no other information is provided , however , the radius of the circle can essentially be anything . all this information tell us is that the radius isgreater 16 d"

<gadget id="calculator">16 ** 2</gadget>
<output>256</output>
<gadget id="calculator">256 ** (1/2)</gadget>
<output>16</output>
<result>16</result>


the speed of a railway engine is 74 km per hour when no compartment is attached , and the reduction in speed is directly proportional to the square root of the number of compartments attached . if the speed of the train carried by this engine is 24 km per hour when 9 compartments are attached , the maximum number of compartments that can be carried by the engine is :

Explanation: "the reduction in speed is directly proportional to the square root of the number of compartments attached doesreductionmean amount subtracted ? or percentage decrease ? there are at least two interpretations , and the wording does not provide a clear interpretation between them . evidently what the question intends is the subtraction interpretation . what is subtracted from the speed is directly proportional to the square root of the number of compartments attached . in other words , if s = speed , and n = number of compartments , then s = 74 - k * sqrt ( n ) wherekis a constant of the proportionality . in general , if a is directly proportional to b , we can write a = k * b and solve for k . if n = 9 , then s = 24 24 = 74 - k * sqrt ( 9 ) = 74 - 3 k k = 16.67 now , we need to know : what value of n makes s go to zero ? 0 = 74 - 16.67 * sqrt ( n ) 16.67 * sqrt ( n ) = 74 sqrt ( n ) = 4.44 n = 4.44 ^ 2 > 19 with 20 compartments , the train does not budge . therefore , it would budge if there were one fewer cars . thus , 19 is the maximum number of cars the engine can pull and still move . e"

power(divide(74, divide(subtract(74, 24), sqrt(9))), const_2)

<gadget id="calculator">74 - 24</gadget>
<output>50</output>
<gadget id="calculator">9 ** (1/2)</gadget>
<output>3</output>
<gadget id="calculator">50 / 3</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">74 / (50/3)</gadget>
<output>111/25 = around 4.44</output>
<gadget id="calculator">(111/25) ** 2</gadget>
<output>12_321/625 = around 19.7136</output>
<result>12_321/625 = around 19.7136</result>


the sum of even numbers between 1 and 31 is

Explanation: "solution required numbers are 2 , 4 , 6 , . . 30 . this is an a . p containing 15 terms . required sum = n / 2 ( first term + last term ) ‹ = › 15 / 2 ( 2 + 30 ) ‹ = › 240 . answer c"

multiply(add(31, 1), divide(floor(divide(31, const_2)), const_2))

<gadget id="calculator">31 + 1</gadget>
<output>32</output>
<gadget id="calculator">31 / 2</gadget>
<output>31/2 = around 15.5</output>
<gadget id="calculator">floor(31/2)</gadget>
<output>15</output>
<gadget id="calculator">15 / 2</gadget>
<output>15/2 = around 7.5</output>
<gadget id="calculator">32 * (15/2)</gadget>
<output>240</output>
<result>240</result>


if the average ( arithmetic mean ) of a and b is 45 and the average of b and c is 50 , what is the value of c â ˆ ’ a ?

Explanation: "the arithmetic mean of a and b = ( a + b ) / 2 = 45 - - a + b = 90 - - 1 similarly for b + c = 100 - - 2 subtracting 1 from 2 we have c - a = 10 ; answer : b"

it can not be determined from the information given

subtract(multiply(50, const_2), multiply(45, const_2))

<gadget id="calculator">50 * 2</gadget>
<output>100</output>
<gadget id="calculator">45 * 2</gadget>
<output>90</output>
<gadget id="calculator">100 - 90</gadget>
<output>10</output>
<result>10</result>


a certain plant was 11 feet long on the day it was plantedthe length grows by a constant amount everyday ( inc . the first day it was planted ) . if this plant grew by 30 % b / w the 4 th day and 10 th day after it was planted , how many feet per day does the plant grow

Explanation: if the plant is 11 feet tall when it is planted , it will be 11 + k feet tall at the end of the day ( where k is the constant length it grows by every day ) . similarly , at the end of the 4 th day the plant must be 11 + 4 k feet tall and at the end of the 10 th day it must be 11 + 10 k feet tall . therefore 6 k = 0.3 ( 11 + 4 k ) = > k = 0.69 therefore the plant grows by 0.69 feet every day . option ( c )

divide(subtract(multiply(divide(add(const_100, 30), const_100), 11), 11), subtract(10, multiply(divide(add(const_100, 30), const_100), 4)))

<gadget id="calculator">100 + 30</gadget>
<output>130</output>
<gadget id="calculator">130 / 100</gadget>
<output>13/10 = around 1.3</output>
<gadget id="calculator">(13/10) * 11</gadget>
<output>143/10 = around 14.3</output>
<gadget id="calculator">(143/10) - 11</gadget>
<output>33/10 = around 3.3</output>
<gadget id="calculator">(13/10) * 4</gadget>
<output>26/5 = around 5.2</output>
<gadget id="calculator">10 - (26/5)</gadget>
<output>24/5 = around 4.8</output>
<gadget id="calculator">(33/10) / (24/5)</gadget>
<output>11/16 = around 0.6875</output>
<result>11/16 = around 0.6875</result>


john and steve are speed walkers in a race . john is 14 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 + 14 + 2 - - - > 0.5 t = 16 - - - > t = 32 seconds . d is the correct answer ."

<gadget id="calculator">14 + 2</gadget>
<output>16</output>
<gadget id="calculator">3.7 * 16</gadget>
<output>59.2</output>
<gadget id="calculator">4.2 - 3.7</gadget>
<output>0.5</output>
<gadget id="calculator">59.2 / 0.5</gadget>
<output>118.4</output>
<gadget id="calculator">118.4 + 16</gadget>
<output>134.4</output>
<gadget id="calculator">134.4 / 4.2</gadget>
<output>32</output>
<result>32</result>


the average age of an adult class is 40 years . 12 new students with an avg age of 32 years join the class . therefore decreasing theaverage by 4 year . find what was theoriginal strength of class ?

Explanation: "let original strength = y then , 40 y + 12 x 32 = ( y + 12 ) x 36 ⇒ 40 y + 384 = 36 y + 432 ⇒ 4 y = 48 ∴ y = 12 b"

divide(subtract(multiply(12, subtract(40, 4)), multiply(12, 32)), 4)

<gadget id="calculator">40 - 4</gadget>
<output>36</output>
<gadget id="calculator">12 * 36</gadget>
<output>432</output>
<gadget id="calculator">12 * 32</gadget>
<output>384</output>
<gadget id="calculator">432 - 384</gadget>
<output>48</output>
<gadget id="calculator">48 / 4</gadget>
<output>12</output>
<result>12</result>


running at the same constant rate , 5 identical machines can produce a total of 270 bottles per minute . at this rate , how many bottles could 10 such machines produce in 4 minutes ?

Explanation: "5 machines produce 270 bottles per minute ; 1 machine produces 270 / 5 = 54 bottles per minute ; 10 machines produce 54 * 10 = 540 bottles per minute ; in 4 minutes 10 machines produce 540 * 4 = 2,160 bottles . answer : c ."

multiply(multiply(divide(270, 5), 4), 10)

<gadget id="calculator">270 / 5</gadget>
<output>54</output>
<gadget id="calculator">54 * 4</gadget>
<output>216</output>
<gadget id="calculator">216 * 10</gadget>
<output>2_160</output>
<result>2_160</result>


the radius of the wheel of a bus is 100 cms and the speed of the bus is 66 km / h , then the r . p . m . ( revolutions per minutes ) of the wheel is

Explanation: "radius of the wheel of bus = 100 cm . then , circumference of wheel = 2 ï € r = 200 ï € = 628.57 cm distance covered by bus in 1 minute = 66 â  „ 60 ã — 1000 ã — 100 cms distance covered by one revolution of wheel = circumference of wheel = 440 cm â ˆ ´ revolutions per minute = 6600000 / 60 ã — 628.57 = 175 answer a"

divide(divide(multiply(const_100, multiply(const_1000, 66)), multiply(const_60, const_1)), multiply(multiply(const_2, 100), add(const_3, divide(add(const_2, multiply(const_3, const_4)), power(add(const_2, multiply(const_4, const_2)), const_2)))))

<gadget id="calculator">1_000 * 66</gadget>
<output>66_000</output>
<gadget id="calculator">100 * 66_000</gadget>
<output>6_600_000</output>
<gadget id="calculator">60 * 1</gadget>
<output>60</output>
<gadget id="calculator">6_600_000 / 60</gadget>
<output>110_000</output>
<gadget id="calculator">2 * 100</gadget>
<output>200</output>
<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">2 + 12</gadget>
<output>14</output>
<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">2 + 8</gadget>
<output>10</output>
<gadget id="calculator">10 ** 2</gadget>
<output>100</output>
<gadget id="calculator">14 / 100</gadget>
<output>7/50 = around 0.14</output>
<gadget id="calculator">3 + (7/50)</gadget>
<output>157/50 = around 3.14</output>
<gadget id="calculator">200 * (157/50)</gadget>
<output>628</output>
<gadget id="calculator">110_000 / 628</gadget>
<output>27_500/157 = around 175.159236</output>
<result>27_500/157 = around 175.159236</result>


if n is an integer and 101 n ^ 2 is less than or equal to 6400 , what is the greatest possible value of n ?

Explanation: 101 * n ^ 2 < = 6400 n ^ 2 < = 6400 / 101 which will be less than 81 since 6400 / 100 = 64 which is the square of 9 next closest value of n where n ^ 2 < = 64 is 7 ans a

<gadget id="calculator">6_400 / 101</gadget>
<output>6_400/101 = around 63.366337</output>
<gadget id="calculator">(6_400/101) ** (1/2)</gadget>
<output>80*sqrt(101)/101 = around 7.960298</output>
<gadget id="calculator">floor(80*sqrt(101)/101)</gadget>
<output>7</output>
<result>7</result>


a train 360 m long runs with a speed of 45 km / hr . what time will it take to pass a platform of 390 m long ?

Explanation: "explanation : speed = 45 km / hr = 45 × ( 10 / 36 ) m / s = 150 / 12 = 50 / 4 = 25 / 2 m / s total distance = length of the train + length of the platform = 360 + 390 = 750 meter time taken to cross the platform = 750 / ( 25 / 2 ) = 750 × 2 / 25 = 60 seconds answer : option e"

multiply(divide(add(divide(390, const_1000), divide(360, const_1000)), 45), const_3600)

<gadget id="calculator">390 / 1_000</gadget>
<output>39/100 = around 0.39</output>
<gadget id="calculator">360 / 1_000</gadget>
<output>9/25 = around 0.36</output>
<gadget id="calculator">(39/100) + (9/25)</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(3/4) / 45</gadget>
<output>1/60 = around 0.016667</output>
<gadget id="calculator">(1/60) * 3_600</gadget>
<output>60</output>
<result>60</result>


a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 500 more than d , what is a ' s share ?

Explanation: sol . let the shares of a , b , c and d be rs . 5 x , rs . 2 x , rs . 4 x and rs . 3 x respectively . then , 4 x - 3 x = 500 ⇔ x = 500 . ∴ a ' s share = rs . 5 x = rs . ( 5 x 500 ) = rs . 2500 . answer a

multiply(divide(500, subtract(divide(4, add(add(add(5, 2), 4), 3)), divide(3, add(add(add(5, 2), 4), 3)))), divide(5, add(add(add(5, 2), 4), 3)))

<gadget id="calculator">5 + 2</gadget>
<output>7</output>
<gadget id="calculator">7 + 4</gadget>
<output>11</output>
<gadget id="calculator">11 + 3</gadget>
<output>14</output>
<gadget id="calculator">4 / 14</gadget>
<output>2/7 = around 0.285714</output>
<gadget id="calculator">3 / 14</gadget>
<output>3/14 = around 0.214286</output>
<gadget id="calculator">(2/7) - (3/14)</gadget>
<output>1/14 = around 0.071429</output>
<gadget id="calculator">500 / (1/14)</gadget>
<output>7_000</output>
<gadget id="calculator">5 / 14</gadget>
<output>5/14 = around 0.357143</output>
<gadget id="calculator">7_000 * (5/14)</gadget>
<output>2_500</output>
<result>2_500</result>