an error 3 % in excess is made while measuring the side of a square . the percentage of error in the calculated area of the square is

Explanation: "100 cm is read as 102 cm . a 1 = ( 100 x 100 ) cm 2 and a 2 ( 103 x 103 ) cm 2 . ( a 2 - a 1 ) = [ ( 103 ) 2 - ( 100 ) 2 ] = ( 103 + 100 ) x ( 103 - 100 ) = 609 cm 2 . percentage error = 6.09 e"

divide(multiply(subtract(square_area(add(const_100, 3)), square_area(const_100)), const_100), square_area(const_100))

<gadget id="calculator">100 + 3</gadget>
<output>103</output>
<gadget id="calculator">103 ** 2</gadget>
<output>10_609</output>
<gadget id="calculator">100 ** 2</gadget>
<output>10_000</output>
<gadget id="calculator">10_609 - 10_000</gadget>
<output>609</output>
<gadget id="calculator">609 * 100</gadget>
<output>60_900</output>
<gadget id="calculator">60_900 / 10_000</gadget>
<output>609/100 = around 6.09</output>
<result>609/100 = around 6.09</result>


share rs . 6600 among john , jose & binoy in the ration 2 : 4 : 6 . find the amount received by john ?

Explanation: "amount received by sanjay . 4 / 12 x 6600 = 2200 = ( related ratio / sum of ratio ) x total amount so , the amount received by sanjay is 2200 . a"

subtract(divide(6600, 2), divide(6600, 6))

<gadget id="calculator">6_600 / 2</gadget>
<output>3_300</output>
<gadget id="calculator">6_600 / 6</gadget>
<output>1_100</output>
<gadget id="calculator">3_300 - 1_100</gadget>
<output>2_200</output>
<result>2_200</result>


the cash realised on selling a 14 % stock is rs . 105.25 , brokerage being 1 / 4 % is ?

Explanation: "cash realised = rs . ( 105.25 - 0.25 ) = rs . 106 . answer : d"

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">105.25 - (1/4)</gadget>
<output>105</output>
<result>105</result>


there are 6 boxes numbered 1 , 2 , … , . 6 . each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered . the total number of ways in which this can be done is

Explanation: list down possibilities : from only 1 box all the way to all 6 if only one of the boxes has a green ball , it can be any of the 6 boxes . so , we have 6 possibilities . if two of the boxes have green balls and then there are 5 consecutive sets of 2 boxes . 12 , 23 , 34 , 45 , 56 . if 3 of the boxes have green balls , there are 4 possibilities : 123 , 234 , 345 , 456 . if 4 boxes have green balls , there are 3 possibilities : 1234 , 2345 , 3456 . if 5 boxes have green balls , there are 2 possibilities : 12345 , 23456 . if all 6 boxes have green balls , there is just 1 possibility . total number of possibilities = 6 + 5 + 4 + 3 + 2 + 1 = 21 . ans : b

<gadget id="calculator">6 + 1</gadget>
<output>7</output>
<gadget id="calculator">6 * 7</gadget>
<output>42</output>
<gadget id="calculator">42 / 2</gadget>
<output>21</output>
<result>21</result>


a , b , c and d enter into partnership . a subscribes 1 / 3 of the capital b 1 / 4 , c 1 / 5 and d the rest . how much share did a get in a profit of rs . 2490 ?

Explanation: "let the total amount in the partnership be ' x ' . then a ' s share = x / 3 b ' s share = x / 4 c ' s share = x / 5 d ' s share = x - ( x / 3 + x / 4 + x / 5 ) = 13 x / 60 a : b : c : d = x / 3 : x / 4 : x / 5 : 13 x / 60 = 20 : 15 : 12 : 13 a ' s share in the profit of rs . 2490 = 20 ( 2490 / 60 ) = rs . 830 . answer : b"

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">2_490 * (1/3)</gadget>
<output>830</output>
<result>830</result>


a 270 metres long bullet train running at the speed of 120 kmph crosses another bullet train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other bullet train ?

Explanation: b 230 relative speed = ( 120 + 80 ) km / hr = 200 x 5 / 18 = 500 / 9 m / sec then , ( x + 270 ) / 9 = 500 / 9 - - > x + 270 = 500 - - > x = 230 .

multiply(subtract(multiply(add(120, 80), const_0_2778), divide(270, 9)), 9)

<gadget id="calculator">120 + 80</gadget>
<output>200</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">200 * (5/18)</gadget>
<output>500/9 = around 55.555556</output>
<gadget id="calculator">270 / 9</gadget>
<output>30</output>
<gadget id="calculator">(500/9) - 30</gadget>
<output>230/9 = around 25.555556</output>
<gadget id="calculator">(230/9) * 9</gadget>
<output>230</output>
<result>230</result>


winson traveled the entire 60 miles trip . if he did the first 10 miles of at a constant rate 20 miles per hour and the remaining trip of at a constant rate 48 miles per hour , what is the his average speed , in miles per hour ?

Explanation: average speed = sum of distance / sum of time . if he travelled the first 10 miles at 20 miles / hr , it would take 0.5 hr . for the remaining trip , if he went at 48 miles / 1 hr , it would take 1 hour . then , the average speed is 60 miles / ( 0.5 + 1 ) hrs = 40 miles / 1 hr . therefore , the answer is e .

divide(60, add(divide(subtract(60, 10), 48), divide(10, 20)))

<gadget id="calculator">60 - 10</gadget>
<output>50</output>
<gadget id="calculator">50 / 48</gadget>
<output>25/24 = around 1.041667</output>
<gadget id="calculator">10 / 20</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(25/24) + (1/2)</gadget>
<output>37/24 = around 1.541667</output>
<gadget id="calculator">60 / (37/24)</gadget>
<output>1_440/37 = around 38.918919</output>
<result>1_440/37 = around 38.918919</result>


a pet store holds cats and dogs . if the difference between the number of cats and the number of dogs is 7 . what could be the ratio of cats to dogs in the pet store ?

Explanation: "say theratioof cats to dogs is a / b . then thenumberof cats would be ax and thenumberof dogs bx , for some positive integer x . we are told that ax - bx = 7 - - > x ( a - b ) = 7 . since 7 is a prime number it could be broken into the product of two positive multiples only in one way : x ( a - b ) = 1 * 7 . the above implies that either x = 1 and a - b = 7 or x = 7 and ( a - b ) = 1 . therefore the correct answer should have the difference between numerator and denominator equal to 1 or 7 . for the original question only option which fits is e , 4 : 5 . cats = 7 * 4 = 28 and dogs = 7 * 5 = 35 . answer : c ."

divide(multiply(7, const_4), add(multiply(7, const_4), 7))

<gadget id="calculator">7 * 4</gadget>
<output>28</output>
<gadget id="calculator">28 + 7</gadget>
<output>35</output>
<gadget id="calculator">28 / 35</gadget>
<output>4/5 = around 0.8</output>
<result>4/5 = around 0.8</result>


a train running at the speed of 60 km / hr crosses a pole in 18 seconds . find the length of the train ?

Explanation: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 18 = 300 meter answer : d"

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

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


the h . c . f of two numbers is 23 and the other two factors of their l . c . m are 13 and 14 . the larger of the two numbers is :

Explanation: "clearly , the numbers are ( 23 * 13 ) and ( 23 * 14 ) . larger number = ( 23 * 14 ) = 322 . answer : c"

<gadget id="calculator">23 * 14</gadget>
<output>322</output>
<result>322</result>


Explanation: ( . 02 ) 2 + ( 0.52 ) 2 + ( 0.035 ) 2 / ( 0.002 ) 2 + ( 0.052 ) 2 + ( 0.0035 ) 2 = a 2 + b 2 + c 2 / ( a / 10 ) 2 + ( b / 10 ) 2 + ( c / 10 ) 2 where a = . 02 , b = . 52 , c = . 035 = 100 ( a 2 + b 2 + c 2 ) / a 2 + b 2 + c 2 = 100 answer : a

<gadget id="calculator">2 / 100</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">(1/50) ** 2</gadget>
<output>1/2_500 = around 0.0004</output>
<gadget id="calculator">0.52 ** 2</gadget>
<output>0.2704</output>
<gadget id="calculator">(1/2_500) + 0.2704</gadget>
<output>0.2708</output>
<gadget id="calculator">0.035 ** 2</gadget>
<output>0.001225</output>
<gadget id="calculator">0.2708 + 0.001225</gadget>
<output>0.272025</output>
<gadget id="calculator">0.002 ** 2</gadget>
<output>0.000004</output>
<gadget id="calculator">0.052 ** 2</gadget>
<output>0.002704</output>
<gadget id="calculator">0.000004 + 0.002704</gadget>
<output>0.002708</output>
<gadget id="calculator">0.0035 ** 2</gadget>
<output>0.000012</output>
<gadget id="calculator">0.002708 + 0.000012</gadget>
<output>0.00272</output>
<gadget id="calculator">0.272025 / 0.00272</gadget>
<output>100.009191</output>
<result>100.009191</result>


how much time does a train 160 metres long running at 72 km / hr take to pass a pole ?

Explanation: "explanation : 72 km / hr = 72 * 5 / 18 = 20 m / s speed = distance / time ; v = d / t 20 = 160 / t t = 8 s answer : a"

multiply(divide(divide(160, const_1000), 72), const_3600)

<gadget id="calculator">160 / 1_000</gadget>
<output>4/25 = around 0.16</output>
<gadget id="calculator">(4/25) / 72</gadget>
<output>1/450 = around 0.002222</output>
<gadget id="calculator">(1/450) * 3_600</gadget>
<output>8</output>
<result>8</result>


find the smallest 4 - digit number which is a multiple of 112 .

Explanation: the smallest four digit number is 1000 . if 1000 is divided by 112 , the remainder is 104 . 112 - 104 = 8 , if 8 is added to 1000 , it will become the smallest four digit number and a multiple of 112 . answer : b

<gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">9 * 112</gadget>
<output>1_008</output>
<result>1_008</result>


the average age of 15 students of a class is 15 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years , the age of the 15 th student is

Explanation: "explanation : age of the 15 th student = [ 15 * 15 - ( 14 * 5 + 16 * 9 ) ] = ( 225 - 214 ) = 11 years . answer : a ) 11"

subtract(multiply(15, 15), add(multiply(5, 14), multiply(9, 16)))

<gadget id="calculator">15 * 15</gadget>
<output>225</output>
<gadget id="calculator">5 * 14</gadget>
<output>70</output>
<gadget id="calculator">9 * 16</gadget>
<output>144</output>
<gadget id="calculator">70 + 144</gadget>
<output>214</output>
<gadget id="calculator">225 - 214</gadget>
<output>11</output>
<result>11</result>


the sale price of a trolley bag including the sale tax is rs . 560 . the rate of sale tax is 12 % . if the shopkeeper has made a profit of 25 % , the cost price of the trolley bag is :

Explanation: "explanation : 112 % of s . p . = 560 s . p . = rs . ( 560 x 100 / 112 ) = rs . 500 . c . p . = rs ( 100 / 125 x 500 ) = rs 400 answer : c"

divide(subtract(560, multiply(560, divide(12, const_100))), add(divide(25, const_100), const_1))

<gadget id="calculator">12 / 100</gadget>
<output>3/25 = around 0.12</output>
<gadget id="calculator">560 * (3/25)</gadget>
<output>336/5 = around 67.2</output>
<gadget id="calculator">560 - (336/5)</gadget>
<output>2_464/5 = around 492.8</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) + 1</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">(2_464/5) / (5/4)</gadget>
<output>9_856/25 = around 394.24</output>
<result>9_856/25 = around 394.24</result>


stacy and heather are 40 miles apart and walk towards each other along the same route . stacy walks at constant rate that is 1 mile per hour faster than heather ' s constant rate of 5 miles / hour . if heather starts her journey 24 minutes after stacy , how far from the original destination has heather walked when the two meet ?

Explanation: "original distance between s and h = 40 miles . speed of s = 5 + 1 = 6 mph , speed of h = 5 mph . time traveled by h = t hours - - - > time traveled by s = t + 24 / 60 = t + 2 / 5 hours . now , the total distances traveled by s and h = 40 miles - - - > 6 * ( t + 2 / 5 ) + 5 * t = 40 - - - > t = 188 / 55 hours . thus h has traveled for 188 / 55 hours giving you a total distance for h = 5 * 188 / 55 = 17 miles . c is thus the correct answer . p . s . : based on the wording of the question , you should calculatehow far from theoriginal destination has heather walkedwhen the two meet . ' original destination ' for h does not make any sense . original destination for h was situated at a distance of 20 miles ."

multiply(divide(subtract(40, multiply(24, divide(add(1, 5), const_60))), add(5, add(1, 5))), 5)

<gadget id="calculator">1 + 5</gadget>
<output>6</output>
<gadget id="calculator">6 / 60</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">24 * (1/10)</gadget>
<output>12/5 = around 2.4</output>
<gadget id="calculator">40 - (12/5)</gadget>
<output>188/5 = around 37.6</output>
<gadget id="calculator">5 + 6</gadget>
<output>11</output>
<gadget id="calculator">(188/5) / 11</gadget>
<output>188/55 = around 3.418182</output>
<gadget id="calculator">(188/55) * 5</gadget>
<output>188/11 = around 17.090909</output>
<result>188/11 = around 17.090909</result>


a motorcyclist goes from bombay to pune , a distance of 128 kms at an average of 32 kmph speed . another man starts from bombay by car 2 ½ hours after the first , and reaches pune ½ hour earlier . what is the ratio of the speed of the motorcycle and the car ?

Explanation: "t = 128 / 32 = 4 h t = 4 - 3 = 1 time ratio = 4 : 1 = 4 : 1 speed ratio = 1 : 4 answer : c"

divide(divide(128, divide(128, 32)), divide(128, subtract(divide(128, 32), const_3)))

<gadget id="calculator">128 / 32</gadget>
<output>4</output>
<gadget id="calculator">128 / 4</gadget>
<output>32</output>
<gadget id="calculator">4 - 3</gadget>
<output>1</output>
<gadget id="calculator">128 / 1</gadget>
<output>128</output>
<gadget id="calculator">32 / 128</gadget>
<output>1/4 = around 0.25</output>
<result>1/4 = around 0.25</result>


a man whose speed is 5.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph , find his average speed for the total journey ?

Explanation: "explanation : speed of man = 5.5 kmph speed of stream = 1.5 kmph speed in downstream = 7 kmph speed in upstream = 4 kmph average speed = ( 2 x 7 x 4 ) / 11 = 5 kmph . answer : b"

divide(add(5.5, subtract(5.5, 1.5)), const_2)

<gadget id="calculator">5.5 - 1.5</gadget>
<output>4</output>
<gadget id="calculator">5.5 + 4</gadget>
<output>9.5</output>
<gadget id="calculator">9.5 / 2</gadget>
<output>4.75</output>
<result>4.75</result>


when positive integer x is divided by 11 , the quotient is y and the remainder is 4 . when 2 x is divided by 5 , the quotient is 3 y and the remainder is 4 . what is the value of 4 y – x ?

Explanation: "( 1 ) x = 11 y + 4 ( 2 ) 2 x = 15 y + 4 let ' s subtract equation ( 1 ) from equation ( 2 ) . 4 y = x 4 y - x = 0 the answer is c ."

subtract(multiply(4, divide(subtract(multiply(2, 4), 4), subtract(multiply(5, 3), multiply(2, 11)))), add(multiply(11, divide(subtract(multiply(2, 4), 4), subtract(multiply(5, 3), multiply(2, 11)))), 4))

<gadget id="calculator">2 * 4</gadget>
<output>8</output>
<gadget id="calculator">8 - 4</gadget>
<output>4</output>
<gadget id="calculator">5 * 3</gadget>
<output>15</output>
<gadget id="calculator">2 * 11</gadget>
<output>22</output>
<gadget id="calculator">15 - 22</gadget>
<output>-7</output>
<gadget id="calculator">4 / (-7)</gadget>
<output>-4/7 = around -0.571429</output>
<gadget id="calculator">4 * (-4/7)</gadget>
<output>-16/7 = around -2.285714</output>
<gadget id="calculator">11 * (-4/7)</gadget>
<output>-44/7 = around -6.285714</output>
<gadget id="calculator">(-44/7) + 4</gadget>
<output>-16/7 = around -2.285714</output>
<gadget id="calculator">(-16/7) - (-16/7)</gadget>
<output>0</output>
<result>0</result>


martin bought 10 concert tickets , some at the full price of $ 2.00 per ticket , and some at a discounted price of $ 1.60 per ticket . if he spent a total of $ 18.40 , how many discounted tickets did he buy ?

Explanation: let x be the number of tickets he bought at $ 2 per ticket . then 2 x + ( 10 - x ) 1.6 = 18.4 0.4 x = 2.4 = > x = 6 discounted tickets = 10 - x = 4 ans : b

subtract(multiply(10, 2), multiply(1.6, 10))

<gadget id="calculator">10 * 2</gadget>
<output>20</output>
<gadget id="calculator">1.6 * 10</gadget>
<output>16</output>
<gadget id="calculator">20 - 16</gadget>
<output>4</output>
<result>4</result>


the area of a square field is 625 km 2 . how long will it take for a horse to run around at the speed of 25 km / h ?

Explanation: explanation area of field = 625 km 2 . then , each side of field = √ 625 = 25 km distance covered by the horse = perimeter of square field = 25 × 4 = 100 km ∴ time taken by horse = distances / peed = 100 / 25 = 4 h answer d

<gadget id="calculator">625 ** (1/2)</gadget>
<output>25</output>
<gadget id="calculator">4 * 25</gadget>
<output>100</output>
<gadget id="calculator">100 / 25</gadget>
<output>4</output>
<result>4</result>


how is 3 % expressed as a decimal fraction ?

Explanation: "3 / 100 = 0.03 answer : b"

<gadget id="calculator">3 / 100</gadget>
<output>3/100 = around 0.03</output>
<result>3/100 = around 0.03</result>


the cross section of a canal is trapezium in shape . the canal is 12 m wide at the top and 8 m wide at the bottom . if the area of the cross section is 840 sq . m , the depth of the canal is :

Explanation: ½ ( 12 + 8 ) d = 840 or d = 84 m answer : b

divide(840, divide(add(12, 8), const_2))

<gadget id="calculator">12 + 8</gadget>
<output>20</output>
<gadget id="calculator">20 / 2</gadget>
<output>10</output>
<gadget id="calculator">840 / 10</gadget>
<output>84</output>
<result>84</result>


if x / 4 years ago roger was 21 years old and x / 4 years from now he will be 4 x years old , how old will he be 5 x years from now ?

Explanation: assume the current age = a a - x / 4 = 28 ( i ) a + x / 4 = 4 x or a = 15 x / 4 ( ii ) putting the value of a from ( ii ) in ( i ) 15 x / 4 - x / 4 = 28 or 14 x / 4 = 28 therefore x = 8 and a = 30 5 x years from now , age will be 30 + 5 * 8 = 70 option e

subtract(multiply(multiply(4, 5), 4), divide(subtract(21, const_1), const_2))

<gadget id="calculator">4 * 5</gadget>
<output>20</output>
<gadget id="calculator">20 * 4</gadget>
<output>80</output>
<gadget id="calculator">21 - 1</gadget>
<output>20</output>
<gadget id="calculator">20 / 2</gadget>
<output>10</output>
<gadget id="calculator">80 - 10</gadget>
<output>70</output>
<result>70</result>


a producer of tea blends two varieties of tea from two tea gardens one costing rs 18 per kg and another rs 20 per kg in the ratio 5 : 3 . if he sells the blended variety at rs 21 per kg , then his gain percent is

Explanation: "explanation : suppose he bought 5 kg and 3 kg of tea . cost price = rs . ( 5 x 18 + 3 x 20 ) = rs . 150 . selling price = rs . ( 8 x 21 ) = rs . 168 . profit = 168 - 150 = 18 so , profit % = ( 18 / 150 ) * 100 = 12 % option a"

divide(multiply(subtract(multiply(21, add(5, 3)), add(multiply(5, 18), multiply(3, 20))), const_100), add(multiply(5, 18), multiply(3, 20)))

<gadget id="calculator">5 + 3</gadget>
<output>8</output>
<gadget id="calculator">21 * 8</gadget>
<output>168</output>
<gadget id="calculator">5 * 18</gadget>
<output>90</output>
<gadget id="calculator">3 * 20</gadget>
<output>60</output>
<gadget id="calculator">90 + 60</gadget>
<output>150</output>
<gadget id="calculator">168 - 150</gadget>
<output>18</output>
<gadget id="calculator">18 * 100</gadget>
<output>1_800</output>
<gadget id="calculator">1_800 / 150</gadget>
<output>12</output>
<result>12</result>


Explanation: "45 - [ 28 - { 37 - ( 15 - * ) } ] = 54 = > 45 - [ 28 - { 37 - 15 + * } ] = 54 45 - [ 28 - 37 + 15 - * ] = 54 = > 45 [ 43 - 37 - * ] = 54 45 - [ 6 - * ] = 54 = > 45 - 6 + * = 54 39 + * = 54 = > * = 54 - 39 = 19 answer : c"

subtract(54, subtract(45, add(subtract(28, 37), 15)))

<gadget id="calculator">28 - 37</gadget>
<output>-9</output>
<gadget id="calculator">(-9) + 15</gadget>
<output>6</output>
<gadget id="calculator">45 - 6</gadget>
<output>39</output>
<gadget id="calculator">54 - 39</gadget>
<output>15</output>
<result>15</result>


if 2 tic equals 3 tacs and 2 tacs equal 7 tocs , what is the ratio of one tic to one toc ?

Explanation: 2 tic = 3 * tac and 2 * tac = 7 * toc ; 4 * tic = 6 * tac and 6 * tac = 21 * toc - - > 4 * tic = 21 * toc - - > tic / toc = 21 / 4 . answer : c .

<gadget id="calculator">7 / 2</gadget>
<output>7/2 = around 3.5</output>
<gadget id="calculator">3 / 2</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(7/2) + (3/2)</gadget>
<output>5</output>
<result>5</result>


how many prime numbers are between 29 / 3 and 87 / 6 ?

Explanation: "29 / 3 = 58 / 6 = 10 - 87 / 6 = 15 - prime numbers between 10 and 15 are 11 and 13 - sign signifies that the number is marginally less . answer b"

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


find the greatest number which leaves the same remainder when it divides 25 , 57 and 105 .

Explanation: 105 - 57 = 48 57 - 25 = 32 105 - 25 = 80 the h . c . f of 32 , 48 and 80 is 16 . answer : d

<gadget id="calculator">57 - 25</gadget>
<output>32</output>
<gadget id="calculator">32 / 2</gadget>
<output>16</output>
<result>16</result>


find large no . from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder

Explanation: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 15 5 x = 1350 x = 270 large number = 270 + 1365 = 1635 e"

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

<gadget id="calculator">1_365 - 15</gadget>
<output>1_350</output>
<gadget id="calculator">6 - 1</gadget>
<output>5</output>
<gadget id="calculator">1_350 / 5</gadget>
<output>270</output>
<gadget id="calculator">270 * 6</gadget>
<output>1_620</output>
<gadget id="calculator">1_620 + 15</gadget>
<output>1_635</output>
<result>1_635</result>


a furniture store owner decided to drop the price of her recliners by 20 % to spur business . by the end of the week she had sold 50 % more recliners . what is the percentage increase of the gross ?

Explanation: "say a recliner is actually worth $ 100 if she sells 100 recliners then she earns $ 10000 after the discount of 20 % , she will earn $ 80 per recliner and she sells 50 % more ie . , 150 recliners hence her sales yields 150 * 80 = $ 12000 increase in sales = 12000 - 10000 = $ 2000 so % increase = 2000 * 100 / 10000 = 20 % c is the answer"

subtract(multiply(multiply(subtract(const_1, divide(20, const_100)), add(const_1, divide(50, const_100))), const_100), const_100)

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 + (1/2)</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(4/5) * (3/2)</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">(6/5) * 100</gadget>
<output>120</output>
<gadget id="calculator">120 - 100</gadget>
<output>20</output>
<result>20</result>


Explanation: explanation : ( a + b ) 2 + ( a â ˆ ’ b ) 2 = 2 ( a 2 + b 2 ) ( reference : basic algebraic formulas ) 1082 + 922 = ( 100 + 8 ) 2 + ( 100 â ˆ ’ 8 ) 2 = 2 ( 1002 + 82 ) = 2 ( 10000 + 64 ) = 20128 . answer : option c

add(subtract(power(108, const_2), 108), subtract(power(92, const_2), 92))

<gadget id="calculator">108 ** 2</gadget>
<output>11_664</output>
<gadget id="calculator">11_664 - 108</gadget>
<output>11_556</output>
<gadget id="calculator">92 ** 2</gadget>
<output>8_464</output>
<gadget id="calculator">8_464 - 92</gadget>
<output>8_372</output>
<gadget id="calculator">11_556 + 8_372</gadget>
<output>19_928</output>
<result>19_928</result>


1 - 1 - 1 - 1 - 1 - 1 do any operations between the numbers to make the sum as 37 ?

Explanation: 1 + 1 + 1 = 3 3 factorial = 6 6 to the power 1 + 1 = 6 ^ 2 = 36 36 + 1 = 37 answer : d

<gadget id="calculator">1 + 1</gadget>
<output>2</output>
<gadget id="calculator">2 ** 2</gadget>
<output>4</output>
<gadget id="calculator">2 ** 4</gadget>
<output>16</output>
<gadget id="calculator">2 * 16</gadget>
<output>32</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">32 + 5</gadget>
<output>37</output>
<result>37</result>


two trains of equal length are running on parallel lines in the same directions at 46 km / hr . and 36 km / hr . the faster trains pass the slower train in 18 seconds . the length of each train is :

Explanation: "explanation : the relative speed of train is 46 - 36 = 10 km / hr = ( 10 x 5 ) / 18 = 25 / 9 m / s 10 × 518 = 259 m / s in 18 secs the total distance traveled is 18 x 25 / 9 = 50 m . therefore the length of each train is = 50 / 2 = 25 m . answer a"

divide(multiply(divide(multiply(subtract(46, 36), const_1000), const_3600), 18), const_2)

<gadget id="calculator">46 - 36</gadget>
<output>10</output>
<gadget id="calculator">10 * 1_000</gadget>
<output>10_000</output>
<gadget id="calculator">10_000 / 3_600</gadget>
<output>25/9 = around 2.777778</output>
<gadget id="calculator">(25/9) * 18</gadget>
<output>50</output>
<gadget id="calculator">50 / 2</gadget>
<output>25</output>
<result>25</result>


275 metres long yard , 26 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between 2 consecutive trees

Explanation: "26 trees have 25 gaps between them , required distance ( 275 / 25 ) = 11 a"

divide(275, add(subtract(26, 2), const_1))

<gadget id="calculator">26 - 2</gadget>
<output>24</output>
<gadget id="calculator">24 + 1</gadget>
<output>25</output>
<gadget id="calculator">275 / 25</gadget>
<output>11</output>
<result>11</result>


a group of boy scouts and girls scouts is going on a rafting trip . 60 % of the scouts arrived with signed permission slips . if 45 % of the scouts were boy scouts and 50 % of the boy scouts arrived with signed permission slips , then what percentage of the girl scouts arrived with signed permission slips ? round to the nearest percent .

Explanation: "45 % were boy scouts so 55 % ( 100 - 45 = 55 ) were girl scouts . # of boy scouts with permission slips signed + # of girl scouts with permission slips signed = total # with permission slip signed ( 50 % of 45 % of the total going ) + ( ? % of 55 % of the total going ) = 60 % of the total going we can let the ` ` total going ' ' = 1,000 arbitrarily since we only care about the percent ( of girl scouts w / permission signed ) . 50 * . 45 * 1,000 + x * . 55 * 1,000 = . 60 * 1,000 225 + x * 550 = 600 550 x = 375 x = 375 / 550 x = . 6818181818 which converts to a percent of 68.18181818 % which rounds to 68 % b"

multiply(divide(subtract(60, divide(multiply(45, 50), const_100)), subtract(const_100, 45)), const_100)

<gadget id="calculator">45 * 50</gadget>
<output>2_250</output>
<gadget id="calculator">2_250 / 100</gadget>
<output>45/2 = around 22.5</output>
<gadget id="calculator">60 - (45/2)</gadget>
<output>75/2 = around 37.5</output>
<gadget id="calculator">100 - 45</gadget>
<output>55</output>
<gadget id="calculator">(75/2) / 55</gadget>
<output>15/22 = around 0.681818</output>
<gadget id="calculator">(15/22) * 100</gadget>
<output>750/11 = around 68.181818</output>
<result>750/11 = around 68.181818</result>


the length of the bridge , which a train 155 metres long and travelling at 45 km / hr can cross in 30 seconds , is ?

Explanation: "speed = [ 45 x 5 / 18 ] m / sec = [ 25 / 2 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 155 + x ) / 30 = 25 / 2 = > 2 ( 155 + x ) = 750 = > x = 220 m . answer : c"

subtract(multiply(divide(multiply(45, speed(const_1000, const_1)), speed(const_3600, const_1)), 30), 155)

<gadget id="calculator">1_000 / 1</gadget>
<output>1_000</output>
<gadget id="calculator">45 * 1_000</gadget>
<output>45_000</output>
<gadget id="calculator">3_600 / 1</gadget>
<output>3_600</output>
<gadget id="calculator">45_000 / 3_600</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">(25/2) * 30</gadget>
<output>375</output>
<gadget id="calculator">375 - 155</gadget>
<output>220</output>
<result>220</result>


the shopkeeper sale , all of the prices of the items sold were different . if the price of a radio sold at the shopkeeper sale was both the 9 th highest price and the 14 th lowest price among the prices of the items sold , how many items were sold at the shopkeeper sale ?

Explanation: 8 + 13 + 1 = 22 answer : b

<gadget id="calculator">9 + 14</gadget>
<output>23</output>
<result>23</result>


Explanation: "answer 2 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ] = 2 x [ ( 36 x 48 x 250 ) / ( 12 x 9 x 5 ) ] = 2 x 4 x 4 x 50 = 1600 correct option : d"

multiply(divide(multiply(multiply(3.6, 0.48), 2.50), multiply(multiply(0.12, 0.09), 0.5)), 2)

<gadget id="calculator">3.6 * 0.48</gadget>
<output>1.728</output>
<gadget id="calculator">1.728 * 2.5</gadget>
<output>4.32</output>
<gadget id="calculator">0.12 * 0.09</gadget>
<output>0.0108</output>
<gadget id="calculator">0.0108 * 0.5</gadget>
<output>0.0054</output>
<gadget id="calculator">4.32 / 0.0054</gadget>
<output>800</output>
<gadget id="calculator">800 * 2</gadget>
<output>1_600</output>
<result>1_600</result>


20 is subtracted from 80 % of a number , the result is 60 . find the number ?

Explanation: "( 80 / 100 ) * x – 20 = 60 8 x = 800 x = 100 answer : c"

divide(add(20, 60), divide(80, const_100))

<gadget id="calculator">20 + 60</gadget>
<output>80</output>
<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">80 / (4/5)</gadget>
<output>100</output>
<result>100</result>


a rectangular grassy plot 110 m . by 65 m has a gravel path 2.5 m wide all round it on the inside . find the cost of gravelling the path at 40 paise per sq . metre

Explanation: area of the plot = 110 m * 65 m = 7150 sq . m area of plot excluding gravel = 105 m * 60 m = 6300 sq . m area of gravel = 7150 sq . m - 6300 sq . m = 850 sq . m cost of building it = 850 sq . m * 40 = 34000 p in rs = 34000 / 100 = rs 340 answer : a

divide(multiply(subtract(multiply(110, 65), multiply(subtract(110, multiply(2.5, const_2)), subtract(65, multiply(2.5, const_2)))), 40), const_100)

<gadget id="calculator">110 * 65</gadget>
<output>7_150</output>
<gadget id="calculator">2.5 * 2</gadget>
<output>5</output>
<gadget id="calculator">110 - 5</gadget>
<output>105</output>
<gadget id="calculator">65 - 5</gadget>
<output>60</output>
<gadget id="calculator">105 * 60</gadget>
<output>6_300</output>
<gadget id="calculator">7_150 - 6_300</gadget>
<output>850</output>
<gadget id="calculator">850 * 40</gadget>
<output>34_000</output>
<gadget id="calculator">34_000 / 100</gadget>
<output>340</output>
<result>340</result>


there are 280 doctors and nurses at a hospital . if the ratio of doctors to nurses is 5 to 9 , how many nurses are at the hospital ?

Explanation: the number of nurses at the hospital is ( 9 / 14 ) * 280 = 180 . the answer is d .

<gadget id="calculator">5 + 9</gadget>
<output>14</output>
<gadget id="calculator">280 / 14</gadget>
<output>20</output>
<gadget id="calculator">20 * 9</gadget>
<output>180</output>
<result>180</result>


a man sells a car to his friend at 10 % loss . if the friend sells it for rs . 54000 and gains 20 % , the original c . p . of the car was :

Explanation: "explanation : s . p = rs . 54,000 . gain earned = 20 % c . p = rs . [ 100 / 120 × 54000 ] = rs . 45000 this is the price the first person sold to the second at at loss of 10 % . now s . p = rs . 45000 and loss = 10 % c . p . rs . [ 10090 × 45000 ] = rs . 50000 . correct option : c"

divide(multiply(divide(multiply(54000, const_100), add(const_100, 20)), const_100), subtract(const_100, 10))

<gadget id="calculator">54_000 * 100</gadget>
<output>5_400_000</output>
<gadget id="calculator">100 + 20</gadget>
<output>120</output>
<gadget id="calculator">5_400_000 / 120</gadget>
<output>45_000</output>
<gadget id="calculator">45_000 * 100</gadget>
<output>4_500_000</output>
<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">4_500_000 / 90</gadget>
<output>50_000</output>
<result>50_000</result>


jim ’ s taxi service charges an initial fee of $ 2.25 at the beginning of a trip and an additional charge of $ 0.35 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?

Explanation: "let the fixed charge of jim ’ s taxi service = 2.25 $ and charge per 2 / 5 mile ( . 4 mile ) = . 35 $ total charge for a trip of 3.6 miles = 2.25 + ( 3.6 / . 4 ) * . 35 = 2.25 + 9 * . 35 = 5.4 $ answer e"

<gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">3.6 / (2/5)</gadget>
<output>9</output>
<gadget id="calculator">0.35 * 9</gadget>
<output>3.15</output>
<gadget id="calculator">2.25 + 3.15</gadget>
<output>5.4</output>
<result>5.4</result>


fred and sam are standing 55 miles apart and they start walking in a straight line toward each other at the same time . if fred walks at a constant speed of 6 miles per hour and sam walks at a constant speed of 5 miles per hour , how many miles has sam walked when they meet ?

Explanation: "relative distance = 55 miles relative speed = 6 + 5 = 11 miles per hour time taken = 55 / 11 = 5 hours distance travelled by sam = 5 * 5 = 25 miles = c"

<gadget id="calculator">6 + 5</gadget>
<output>11</output>
<gadget id="calculator">55 / 11</gadget>
<output>5</output>
<gadget id="calculator">5 * 5</gadget>
<output>25</output>
<result>25</result>


a prize of $ 1200 is to be distributed among 40 winners , each of whom must be awarded at least $ 40 . if 2 / 5 of the prize will be distributed to 3 / 5 of the winners , what is the greatest possible individual award ?

Explanation: "total value of the prize = $ 1200 number of people = 40 2 / 5 of 1200 ( = $ 480 ) should be distributed among 3 / 5 of 40 ( = 24 people ) with each getting $ 40 each . remaining money = 1200 - 480 = $ 720 . now in order to ' maximize ' 1 prize , we need to minimise the others and we have been given that each should get $ 40 . thus , minimising the remaining 15 people ( = 40 - 24 - 1 . ' - 1 ' to exclude 1 that needs to be maximised ) = 15 * 40 = 600 . thus the maximum award can be = 720 - 600 = $ 120 , hence b is the correct answer ."

subtract(subtract(1200, divide(multiply(1200, 2), 5)), multiply(subtract(subtract(40, divide(multiply(40, 3), 5)), const_1), 40))

<gadget id="calculator">1_200 * 2</gadget>
<output>2_400</output>
<gadget id="calculator">2_400 / 5</gadget>
<output>480</output>
<gadget id="calculator">1_200 - 480</gadget>
<output>720</output>
<gadget id="calculator">40 * 3</gadget>
<output>120</output>
<gadget id="calculator">120 / 5</gadget>
<output>24</output>
<gadget id="calculator">40 - 24</gadget>
<output>16</output>
<gadget id="calculator">16 - 1</gadget>
<output>15</output>
<gadget id="calculator">15 * 40</gadget>
<output>600</output>
<gadget id="calculator">720 - 600</gadget>
<output>120</output>
<result>120</result>


the profits of qrs company rose 20 % from march to april , then dropped 20 % from april to may , then rose 50 % from may to june . what was the percent increase for the whole quarter , from march to june ?

Explanation: "assume 100 in march , then 120 in april as 20 % increase , then 96 in may as 20 % decrease from april , and then 144 in june which is 150 % of 96 . so overall increase is from 100 to 144 is 44 % answer c"

multiply(const_100, subtract(multiply(add(const_1, divide(50, const_100)), multiply(add(const_1, divide(20, const_100)), subtract(const_1, divide(20, const_100)))), const_1))

<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 + (1/2)</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 + (1/5)</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(6/5) * (4/5)</gadget>
<output>24/25 = around 0.96</output>
<gadget id="calculator">(3/2) * (24/25)</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">100 * (11/25)</gadget>
<output>44</output>
<result>44</result>


if the speed of a man is 63 km per hour , then what is the distance traveled by him in 25 seconds ?

Explanation: "the distance traveled in 25 sec = 63 * ( 5 / 18 ) * 25 = 437.5 m answer : d"

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">63 * (5/18)</gadget>
<output>35/2 = around 17.5</output>
<gadget id="calculator">(35/2) * 25</gadget>
<output>875/2 = around 437.5</output>
<result>875/2 = around 437.5</result>


if a sum of money doubles itself in 10 years at simple interest , the ratepercent per annum is

Explanation: "explanation : let sum = x then simple interest = x rate = ( 100 * x ) / ( x * 10 ) = 10 option a"

divide(divide(const_2, divide(10, const_100)), const_2)

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">2 / (1/10)</gadget>
<output>20</output>
<gadget id="calculator">20 / 2</gadget>
<output>10</output>
<result>10</result>


a group of hikers is planning a trip that will take them up a mountain using one route and back down using another route . they plan to travel down the mountain at a rate of one and a half times the rate they will use on the way up , but the time each route will take is the same . if they will go up the mountain at a rate of 7 miles per day and it will take them two days , how many miles long is the route down the mountain ?

Explanation: "on the way down , the rate is 1.5 * 7 = 10.5 miles per day . the distance of the route down the mountain is 2 * 10.5 = 21 miles . the answer is d ."

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

<gadget id="calculator">7 * 2</gadget>
<output>14</output>
<gadget id="calculator">3 / 2</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">14 * (3/2)</gadget>
<output>21</output>
<result>21</result>


2.08 can be expressed in terms of percentage as

Explanation: "explanation : while calculation in terms of percentage we need to multiply by 100 , so 2.08 * 100 = 208 answer : option c"

<gadget id="calculator">2.08 * 100</gadget>
<output>208</output>
<result>208</result>


the population of a town is 8000 . it decreases annually at the rate of 30 % p . a . what will be its population after 2 years ?

Explanation: "formula : ( after = 100 denominator ago = 100 numerator ) 8000 ã — 70 / 100 ã — 70 / 100 = 3920 answer : a"

subtract(subtract(8000, multiply(8000, divide(30, const_100))), multiply(subtract(8000, multiply(8000, divide(30, const_100))), divide(30, const_100)))

<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">8_000 * (3/10)</gadget>
<output>2_400</output>
<gadget id="calculator">8_000 - 2_400</gadget>
<output>5_600</output>
<gadget id="calculator">5_600 * (3/10)</gadget>
<output>1_680</output>
<gadget id="calculator">5_600 - 1_680</gadget>
<output>3_920</output>
<result>3_920</result>


a hall is 15 meters long and 10 meters wide . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , what is the volume of the hall ( in cubic meters ) ?

Explanation: "2 hl + 2 hw = 2 lw h = lw / ( l + w ) volume = lwh = ( lw ) ^ 2 / ( l + w ) = 900 the answer is d ."

volume_rectangular_prism(15, 10, divide(multiply(rectangle_area(15, 10), const_2), rectangle_perimeter(15, 10)))

<gadget id="calculator">15 * 10</gadget>
<output>150</output>
<gadget id="calculator">150 * 2</gadget>
<output>300</output>
<gadget id="calculator">2 * (15 + 10)</gadget>
<output>50</output>
<gadget id="calculator">300 / 50</gadget>
<output>6</output>
<gadget id="calculator">15 * 10 * 6</gadget>
<output>900</output>
<result>900</result>


a basketball team composed of 12 players scored 100 points in a particular contest . if none of the individual players scored fewer than 7 points , what is the greatest number of points e that an individual player might have scored ?

Explanation: "general rule for such kind of problems : to maximize one quantity , minimize the others ; to minimize one quantity , maximize the others . thus to maximize the number of points of one particular player minimize the number of points of all other 11 players . minimum number of points for a player is 7 , so the minimum number of points of 11 players is 7 * 11 = 77 . therefore , the maximum number of points e for 12 th player is 100 - 77 = 23 . answer : e ."

<gadget id="calculator">12 * 7</gadget>
<output>84</output>
<gadget id="calculator">100 - 84</gadget>
<output>16</output>
<gadget id="calculator">16 + 7</gadget>
<output>23</output>
<result>23</result>


a certain company retirement plan has arule of 70 provision that allows an employee to retire when the employee ' s age plus years of employment with the company total at least 70 . in what year could a female employee hired in 1990 on her 32 nd birthday first be eligible to retire under this provision ?

Explanation: she must gain at least 70 points , now she has 31 and every year gives her two more points : one for age and one for additional year of employment , so 32 + 2 * ( # of years ) = 70 - - > ( # of years ) = 19 - - > 1990 + 19 = 2009 . answer : b .

add(1990, divide(subtract(70, 32), const_2))

<gadget id="calculator">70 - 32</gadget>
<output>38</output>
<gadget id="calculator">38 / 2</gadget>
<output>19</output>
<gadget id="calculator">1_990 + 19</gadget>
<output>2_009</output>
<result>2_009</result>


the average age of 17 persons in a office is 15 years . out of these , the average age of 5 of them is 14 years and that of the other 9 persons is 16 years . the age of the 15 th person is ?

Explanation: "age of the 15 th student = 17 * 15 - ( 14 * 5 + 16 * 9 ) = 255 - 214 = 41 years answer is b"

subtract(subtract(multiply(17, 15), multiply(5, 14)), multiply(9, 16))

<gadget id="calculator">17 * 15</gadget>
<output>255</output>
<gadget id="calculator">5 * 14</gadget>
<output>70</output>
<gadget id="calculator">255 - 70</gadget>
<output>185</output>
<gadget id="calculator">9 * 16</gadget>
<output>144</output>
<gadget id="calculator">185 - 144</gadget>
<output>41</output>
<result>41</result>


ajay can ride 50 km in 1 hour . in how many hours he can ride 1500 km ?

Explanation: "1 hour he ride 50 km he ride 1500 km in = 1500 / 50 * 1 = 30 hours answer is a"

<gadget id="calculator">1_500 / 50</gadget>
<output>30</output>
<result>30</result>


a square mirror has exactly half the area of the rectangular wall on which it is hung . if each side of the mirror is 54 inches and the width of the wall is 68 inches , what is the length of the wall , in inches ?

Explanation: since the mirror is 42 inches in all sides , it must be a square . area of a square is a = a ^ 2 ; 54 ^ 2 = 2916 . area of rectangle is double of that 2 * 2916 = 5832 . now a = lw and we need find w so a / l = w ; 5832 / 68 = 85.7 answer ! answer is d

<gadget id="calculator">54 ** 2</gadget>
<output>2_916</output>
<gadget id="calculator">2 * 2_916</gadget>
<output>5_832</output>
<gadget id="calculator">5_832 / 68</gadget>
<output>1_458/17 = around 85.764706</output>
<result>1_458/17 = around 85.764706</result>


the membership of a committee consists of 3 english teachers , 4 mathematics teachers , and 2 social studies teachers . if 2 committee members are to be selected at random to write the committee ’ s report , what is the probability that the two members selected will both be english teachers ?

Explanation: "probability of first member an english teacher = 3 / 9 probability of second member an english teacher = 2 / 8 probability of both being english teacher = 3 / 9 x 2 / 8 = 1 / 12 ( d ) answer : d"

multiply(divide(3, add(add(3, 4), 2)), divide(2, subtract(add(add(3, 4), 2), const_1)))

<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">7 + 2</gadget>
<output>9</output>
<gadget id="calculator">3 / 9</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">9 - 1</gadget>
<output>8</output>
<gadget id="calculator">2 / 8</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/3) * (1/4)</gadget>
<output>1/12 = around 0.083333</output>
<result>1/12 = around 0.083333</result>


a woman swims downstream 45 km and upstream 15 km taking 3 hours each time , what is the speed of the woman in still water ?

Explanation: 45 - - - 3 ds = 15 ? - - - - 1 15 - - - - 3 us = 5 ? - - - - 1 m = ? m = ( 15 + 5 ) / 2 = 10 answer : a

divide(add(divide(45, 3), divide(15, 3)), const_2)

<gadget id="calculator">45 / 3</gadget>
<output>15</output>
<gadget id="calculator">15 / 3</gadget>
<output>5</output>
<gadget id="calculator">15 + 5</gadget>
<output>20</output>
<gadget id="calculator">20 / 2</gadget>
<output>10</output>
<result>10</result>


in order to obtain an income of rs . 1000 from 50 % stock at rs . 500 , one must make an investment of

Explanation: "explanation : market value = rs . 500 . required income = rs . 1000 . here face value is not given . take face value as rs . 100 if it is not given in the question to obtain rs . 50 ( ie , 50 % of the face value 100 ) , investment = rs . 500 to obtain rs . 1000 , investment = 500 / 50 ã — 1000 = 10000 answer : option d"

<gadget id="calculator">500 / 50</gadget>
<output>10</output>
<gadget id="calculator">10 * 1_000</gadget>
<output>10_000</output>
<result>10_000</result>


jack and jill are marathon runners . jack can finish a marathon ( 40 km ) in 4.5 hours and jill can run a marathon in 4.0 hours . what is the ratio of their average running speed ? ( jack : jill )

Explanation: "average speed of jack = distance / time = 40 / ( 9 / 2 ) = 80 / 9 average speed of jill = 40 / ( 4.0 ) = 10 ratio of average speed of jack to jill = ( 80 / 9 ) / 10 = 8 / 9 answer c"

<gadget id="calculator">40 / 4.5</gadget>
<output>8.888889</output>
<gadget id="calculator">40 / 4</gadget>
<output>10</output>
<gadget id="calculator">8.888889 / 10</gadget>
<output>0.888889</output>
<result>0.888889</result>


5 % people of a village in sri lanka died by bombardment , 20 % of the remainder left the village on account of fear . if now the population is reduced to 3553 , how much was it in the beginning ?

Explanation: "x * ( 95 / 100 ) * ( 80 / 100 ) = 3553 x = 4675 answer : d"

floor(divide(3553, multiply(divide(subtract(const_100, 5), const_100), divide(subtract(const_100, 20), const_100))))

<gadget id="calculator">100 - 5</gadget>
<output>95</output>
<gadget id="calculator">95 / 100</gadget>
<output>19/20 = around 0.95</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(19/20) * (4/5)</gadget>
<output>19/25 = around 0.76</output>
<gadget id="calculator">3_553 / (19/25)</gadget>
<output>4_675</output>
<gadget id="calculator">floor(4_675)</gadget>
<output>4_675</output>
<result>4_675</result>


what is the sum of the odd integers from 35 to 55 , inclusive ?

Explanation: "the mean is 45 . sum = mean ( # of elements ) there are 11 odd numbers between 35 - 55 inclusive . 11 * 45 = 495 a"

<gadget id="calculator">35 * 55</gadget>
<output>1_925</output>
<gadget id="calculator">1_925 / 4</gadget>
<output>1_925/4 = around 481.25</output>
<result>1_925/4 = around 481.25</result>


every monday , marina eats one croissant and every tuesday she eats two croissants . on each subsequent day of the week , she eats a number of croissants equal to the sum of the croissants eaten on the two previous days , with the exception that if she eats more than 4 croissants on any particular day , the next day she will eat only one croissant . at the end of the week ( which runs from monday through sunday ) , the cycle resets , and marina goes back to eating one croissant on monday , two on tuesday , and so forth . if a particular month begins on a saturday , how many croissants will marina eat on the 30 th of that month ?

Explanation: she eat as follow mon - 1 tue - 2 wed - 3 thr - 5 fri - 1 ( since she had more than 4 previous day ) sat - 6 sunday - 1 ( since she had more than 4 previous day ) so 30 th day of month she will have 1 . answer is a

subtract(subtract(30, multiply(const_4, add(const_3, const_4))), const_1)

<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">4 * 7</gadget>
<output>28</output>
<gadget id="calculator">30 - 28</gadget>
<output>2</output>
<gadget id="calculator">2 - 1</gadget>
<output>1</output>
<result>1</result>


if the sides of a cube are in the ratio 5 : 3 . what is the ratio of their diagonals ?

Explanation: explanation : diagonal of a cube = a √ 3 where a is side a 1 : a 2 = 5 : 3 d 1 : d 2 = 5 : 3 where √ 3 cancelled both side answer : e

<gadget id="calculator">5 / 3</gadget>
<output>5/3 = around 1.666667</output>
<result>5/3 = around 1.666667</result>


the average weight of 26 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg . find the average weights of all the boys in the class .

Explanation: "explanation : average weight of 26 boys = 50.25 total weight of 26 boys = 50.25 × 26 average weight of remaining 8 boys = 45.15 total weight of remaining 8 boys = 45.15 × 8 total weight of all boys in the class = ( 50.25 × 26 ) + ( 45.15 × 8 ) total boys = 26 + 8 = 34 average weight of all the boys = ( 50.25 × 26 ) + ( 45.15 × 8 ) / 34 = 49.05 answer : option a"

<gadget id="calculator">26 * 50.25</gadget>
<output>1_306.5</output>
<gadget id="calculator">8 * 45.15</gadget>
<output>361.2</output>
<gadget id="calculator">1_306.5 + 361.2</gadget>
<output>1_667.7</output>
<gadget id="calculator">26 + 8</gadget>
<output>34</output>
<gadget id="calculator">1_667.7 / 34</gadget>
<output>49.05</output>
<result>49.05</result>


a one - foot stick is marked in 1 / 4 and 1 / 5 portion . how many total markings will there be , including the end points ?

Explanation: lcm of 20 = 20 1 / 4 marking are ( table of 5 ) 0 . . . . . . 5 . . . . . . 10 . . . . . 15 . . . . . . 20 ( total = 5 ) 1 / 5 marking are ( table of 4 ) 0 . . . . . . . 4 . . . . . . 8 . . . . . . 12 . . . . . . . . 16 . . . . . . 20 ( total = 6 ) overlapping markings are 0 . . . . . . . . 20 ( total = 2 ) total markings = 5 + 6 - 2 = 9 answer = d

<gadget id="calculator">4 + 5</gadget>
<output>9</output>
<result>9</result>


find out the c . i on rs . 5000 at 4 % p . a . compound half - yearly for 1 1 / 2 years ?

Explanation: "explanation : a = 5000 ( 51 / 50 ) 3 = 5306.04 5000 - - - - - - - - - - - 306.04 answer : c"

subtract(multiply(5000, power(add(1, divide(4, const_100)), divide(const_3, 2))), 5000)

<gadget id="calculator">4 / 100</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">1 + (1/25)</gadget>
<output>26/25 = around 1.04</output>
<gadget id="calculator">3 / 2</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(26/25) ** (3/2)</gadget>
<output>26*sqrt(26)/125 = around 1.060596</output>
<gadget id="calculator">5_000 * (26*sqrt(26)/125)</gadget>
<output>1040*sqrt(26) = around 5_302.980294</output>
<gadget id="calculator">(1040*sqrt(26)) - 5_000</gadget>
<output>-5000 + 1040*sqrt(26) = around 302.980294</output>
<result>-5000 + 1040*sqrt(26) = around 302.980294</result>


the average score of a cricketer in 2 matches is 30 and in other 3 matches is 40 . then find the average score in all the 5 matches ?

Explanation: average in 5 matches = ( 2 * 30 + 3 * 40 ) / 2 + 3 = 60 + 120 / 5 = 180 / 5 = 36 answer is e

divide(add(multiply(2, 30), multiply(3, 40)), 5)

<gadget id="calculator">2 * 30</gadget>
<output>60</output>
<gadget id="calculator">3 * 40</gadget>
<output>120</output>
<gadget id="calculator">60 + 120</gadget>
<output>180</output>
<gadget id="calculator">180 / 5</gadget>
<output>36</output>
<result>36</result>


in what ratio must tea at rs . 62 per kg be mixed with tea at rs . 72 per kg so that the mixture must be worth rs . 64.50 per kg ?

Explanation: mean price = ( 72 - 64.5 = 7.5 ) ( 64.5 - 62 = 2.5 ) req ratio = 7.5 : 2.5 = 3 : 1 answer a

divide(subtract(72, 64.5), subtract(64.5, 62))

<gadget id="calculator">72 - 64.5</gadget>
<output>7.5</output>
<gadget id="calculator">64.5 - 62</gadget>
<output>2.5</output>
<gadget id="calculator">7.5 / 2.5</gadget>
<output>3</output>
<result>3</result>


a solid metallic spherical ball of diameter 6 cm is melted and recast into a cone with diameter of the base as 12 cm . the height of the cone is :

Explanation: sol . let the height of the cone be h cm . then , 1 / 3 ∏ * 6 * 6 * h = 4 / 3 ∏ * 3 * 3 * 3 ⇒ h = [ 36 * 3 / 36 ] = 3 cm . answer d

divide(multiply(multiply(multiply(const_4, const_3), const_3), const_3), multiply(6, 6))

<gadget id="calculator">4 * 3</gadget>
<output>12</output>
<gadget id="calculator">12 * 3</gadget>
<output>36</output>
<gadget id="calculator">36 * 3</gadget>
<output>108</output>
<gadget id="calculator">6 * 6</gadget>
<output>36</output>
<gadget id="calculator">108 / 36</gadget>
<output>3</output>
<result>3</result>


if x is the median of the set { 8 / 2 , 11 / 3 , 27 / 9 , 21 / 5 , x } , x could be

Explanation: the median is the middle number once all the numbers are arranged in increasing / decreasing order . we see that 11 / 3 = 3 . something , 28 / 9 = 3 . something 21 / 5 = 4 . something 9 / 2 = 4 . something so x should greater than the smallest two numbers and smaller than the greatest two numbers . we can see that x = 4 is possible . ( first look at the simplest option or the middle option since options are usually arranged in increasing / decreasing order ) answer ( a )

add(add(divide(add(add(add(divide(8, 2), divide(11, 3)), divide(27, 9)), divide(21, 5)), const_4), divide(const_10, const_100)), divide(const_10, const_100))

<gadget id="calculator">8 / 2</gadget>
<output>4</output>
<gadget id="calculator">11 / 3</gadget>
<output>11/3 = around 3.666667</output>
<gadget id="calculator">4 + (11/3)</gadget>
<output>23/3 = around 7.666667</output>
<gadget id="calculator">27 / 9</gadget>
<output>3</output>
<gadget id="calculator">(23/3) + 3</gadget>
<output>32/3 = around 10.666667</output>
<gadget id="calculator">21 / 5</gadget>
<output>21/5 = around 4.2</output>
<gadget id="calculator">(32/3) + (21/5)</gadget>
<output>223/15 = around 14.866667</output>
<gadget id="calculator">(223/15) / 4</gadget>
<output>223/60 = around 3.716667</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(223/60) + (1/10)</gadget>
<output>229/60 = around 3.816667</output>
<gadget id="calculator">(229/60) + (1/10)</gadget>
<output>47/12 = around 3.916667</output>
<result>47/12 = around 3.916667</result>


how many seconds will a train 100 meters long take to cross a bridge 140 meters long if the speed of the train is 36 kmph ?

Explanation: "explanation : d = 100 + 140 = 240 s = 36 * 5 / 18 = 10 mps t = 240 / 10 = 24 sec answer : option b"

<gadget id="calculator">140 + 100</gadget>
<output>240</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">36 * (5/18)</gadget>
<output>10</output>
<gadget id="calculator">240 / 10</gadget>
<output>24</output>
<result>24</result>


while working alone at their constant rates , computer x can process 240 files in 12 hours , and computer y can process 240 files in 6 hours . if all files processed by these computers are the same size , how many hours would it take the two computers , working at the same time at their respective constant rates , to process a total of 240 files ?

Explanation: "both computers together process files at a rate of 240 / 12 + 240 / 6 = 20 + 40 = 60 files per hour . the time required to process 240 files is 240 / 60 = 4 hours the answer is c ."

<gadget id="calculator">240 / 12</gadget>
<output>20</output>
<gadget id="calculator">240 / 6</gadget>
<output>40</output>
<gadget id="calculator">20 + 40</gadget>
<output>60</output>
<gadget id="calculator">240 / 60</gadget>
<output>4</output>
<result>4</result>


in town x , 64 percent of the population are employed , and 46 percent of the population are employed males . what percent of the employed people in town x are females ?

Explanation: we are asked to find the percentage of females in employed people . total employed people 64 % , out of which 46 are employed males , hence 18 % are employed females . ( employed females ) / ( total employed people ) = 18 / 64 = 28 % answer : c .

multiply(divide(subtract(64, 46), 64), const_100)

<gadget id="calculator">64 - 46</gadget>
<output>18</output>
<gadget id="calculator">18 / 64</gadget>
<output>9/32 = around 0.28125</output>
<gadget id="calculator">(9/32) * 100</gadget>
<output>225/8 = around 28.125</output>
<result>225/8 = around 28.125</result>


the lcm of two numbers is 2310 and hcf is 55 . if one of the numbers is 210 . then what is the other number ?

Explanation: "first number * second number = lcm * hcf other number = 2310 * 55 / 210 = 11 * 55 = 605 answer : d"

<gadget id="calculator">2_310 * 55</gadget>
<output>127_050</output>
<gadget id="calculator">127_050 / 210</gadget>
<output>605</output>
<result>605</result>


a and b invests rs . 2500 and rs . 4000 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ?

Explanation: "( 2.5 * 6 + 5 * 6 ) : ( 4 * 12 ) 45 : 48 = > 15 : 16 answer : b"

divide(add(multiply(2500, 6), multiply(multiply(2500, const_2), 6)), multiply(4000, add(6, 6)))

<gadget id="calculator">2_500 * 6</gadget>
<output>15_000</output>
<gadget id="calculator">2_500 * 2</gadget>
<output>5_000</output>
<gadget id="calculator">5_000 * 6</gadget>
<output>30_000</output>
<gadget id="calculator">15_000 + 30_000</gadget>
<output>45_000</output>
<gadget id="calculator">6 + 6</gadget>
<output>12</output>
<gadget id="calculator">4_000 * 12</gadget>
<output>48_000</output>
<gadget id="calculator">45_000 / 48_000</gadget>
<output>15/16 = around 0.9375</output>
<result>15/16 = around 0.9375</result>


a car traveled from san diego to san francisco at an average speed of 54 miles per hour . if the journey back took twice as long , what was the average speed of the trip ?

Explanation: let the time taken be = x one way distance = 54 x total distance traveled = 2 * 54 x = 108 x total time taken = x + 2 x = 3 x average speed = 108 x / 3 x = 36 answer : c

<gadget id="calculator">1 / 54</gadget>
<output>1/54 = around 0.018519</output>
<gadget id="calculator">(1/54) / 2</gadget>
<output>1/108 = around 0.009259</output>
<gadget id="calculator">(1/54) + (1/108)</gadget>
<output>1/36 = around 0.027778</output>
<gadget id="calculator">1 / (1/36)</gadget>
<output>36</output>
<result>36</result>


a runner runs the 40 miles from marathon to athens at a constant speed . halfway through the run she injures her foot , and continues to run at half her previous speed . if the second half takes her 8 hours longer than the first half , how many hours did it take the runner to run the second half ?

Explanation: "the runner runs the first 20 miles at speed v and the second 20 miles at speed v / 2 . the time t 2 to run the second half must be twice the time t 1 to run the first half . t 2 = 2 * t 1 = t 1 + 8 t 1 = 8 and so t 2 = 16 . the answer is c ."

divide(40, divide(divide(40, const_2), 8))

<gadget id="calculator">40 / 2</gadget>
<output>20</output>
<gadget id="calculator">20 / 8</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">40 / (5/2)</gadget>
<output>16</output>
<result>16</result>


a pump will fill a tank in 3 hours . because of a leak in the tank , it took 3 hours 30 min to fill the tank . in what time the leak can drain out all the water of the tank and will make tank empty ?

Explanation: work done for 1 hr without leak = 1 / 3 work done with leak = 31 / 2 = = > 7 / 2 work and leak in 1 hr = 2 / 7 work leak in 1 hr = 1 / 3 - 2 / 7 = 1 / 21 so 21 hrs answer b

divide(multiply(divide(add(multiply(3, const_60), 30), 30), multiply(3, const_60)), const_60)

<gadget id="calculator">3 * 60</gadget>
<output>180</output>
<gadget id="calculator">180 + 30</gadget>
<output>210</output>
<gadget id="calculator">210 / 30</gadget>
<output>7</output>
<gadget id="calculator">7 * 180</gadget>
<output>1_260</output>
<gadget id="calculator">1_260 / 60</gadget>
<output>21</output>
<result>21</result>


the area of a square garden is q square feet and the perimeter is p feet . if q = p + 21 , what is the perimeter of the garden in feet ?

Explanation: let x be the length of one side of the square garden . x ^ 2 = 4 x + 21 x ^ 2 - 4 x - 21 = 0 ( x - 7 ) ( x + 3 ) = 0 x = 7 , - 3 p = 4 ( 7 ) = 28 the answer is b .

multiply(divide(21, subtract(const_4, const_1)), const_4)

<gadget id="calculator">4 - 1</gadget>
<output>3</output>
<gadget id="calculator">21 / 3</gadget>
<output>7</output>
<gadget id="calculator">7 * 4</gadget>
<output>28</output>
<result>28</result>


how many multiples of 3 are there between 10 and 100 , exclusive ?

Explanation: "3 * 4 = 12 3 * 33 = 99 total multiples = ( 33 - 4 ) + 1 = 30 exclude 10 and 100 = 30 answer is a"

add(divide(subtract(100, 10), 3), const_1)

<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">90 / 3</gadget>
<output>30</output>
<gadget id="calculator">30 + 1</gadget>
<output>31</output>
<result>31</result>


an empty fuel tank with a capacity of 200 gallons was filled partially with fuel a and then to capacity with fuel b . fuel a contains 12 % ethanol by volume and fuel b contains 16 % ethanol by volume . if the full fuel tank contains 28 gallons of ethanol , how many gallons of fuel a were added ?

Explanation: "say there are a gallons of fuel a in the tank , then there would be 200 - a gallons of fuel b . the amount of ethanol in a gallons of fuel a is 0.12 a ; the amount of ethanol in 200 - a gallons of fuel b is 0.16 ( 200 - a ) ; since the total amount of ethanol is 28 gallons then 0.12 a + 0.16 ( 200 - a ) = 28 - - > a = 100 . answer : c ."

divide(subtract(multiply(200, divide(16, const_100)), 28), subtract(divide(16, const_100), divide(12, const_100)))

<gadget id="calculator">16 / 100</gadget>
<output>4/25 = around 0.16</output>
<gadget id="calculator">200 * (4/25)</gadget>
<output>32</output>
<gadget id="calculator">32 - 28</gadget>
<output>4</output>
<gadget id="calculator">12 / 100</gadget>
<output>3/25 = around 0.12</output>
<gadget id="calculator">(4/25) - (3/25)</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">4 / (1/25)</gadget>
<output>100</output>
<result>100</result>


maxwell leaves his home and walks toward brad ' s house . one hour later , brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 14 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h . what is the total time it takes maxwell before he meets up with brad ?

Explanation: total distance = 14 kms maxwell speed = 4 kms / hr maxwell travelled for 1 hour before brad started , therefore maxwell traveled for 4 kms in 1 hour . time taken = total distance / relative speed total distance after brad started = 10 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken to meet brad after brad started = 10 / 10 = 1 hrs distance traveled by maxwell = maxwell ' s speed * time taken = 4 * 1 = 4 + 4 = 8 kms . . . therefore total time taken by maxwell to meet brad = distance travelled by maxwell / maxwell ' s speed = 8 / 4 = 2 hrs . . . answer a

<gadget id="calculator">14 + 6</gadget>
<output>20</output>
<gadget id="calculator">4 + 6</gadget>
<output>10</output>
<gadget id="calculator">20 / 10</gadget>
<output>2</output>
<result>2</result>


lloyd normally works 7.5 hours per day and earns $ 3.50 per hour . for each hour he works in excess of 7.5 hours on a given day , he is paid 1.5 times his regular rate . if lloyd works 10.5 hours on a given day , how much does he earn for that day ?

Explanation: "daily working hour * regular rate + overtime * increased rate 7.5 * 3.5 + 3 * 3.5 * 1.5 = 42 answer b"

<gadget id="calculator">7.5 * 3.5</gadget>
<output>26.25</output>
<gadget id="calculator">10.5 - 7.5</gadget>
<output>3</output>
<gadget id="calculator">3 * 1.5</gadget>
<output>4.5</output>
<gadget id="calculator">4.5 * 3.5</gadget>
<output>15.75</output>
<gadget id="calculator">26.25 + 15.75</gadget>
<output>42</output>
<result>42</result>


tammy climbed a mountain in two days . she spent a total of 14 hours climbing the mountain . on the second day , she walked at an average speed that was half a kilometer per hour faster , but 2 hours less than what she walked on the first day . if the total distance she climbed during the two days is 52 kilometers , how many e kilometers per hour did tammy walk on the second day ?

Explanation: ans : c total time = 14 hrs let time traveled during 1 st day = x let time traveled during 2 nd day = x - 2 total time = 14 x + x - 2 = 14 x = 8 speed * time = distance s * 8 + ( s + 0.5 ) ( 8 - 2 ) = 52 solving s = 4.5 now speed for 2 nd day is 0.5 less than the 1 st day which is 4.5 thus speed for 2 nd day = 4 its simple algebra for s * 8 + ( s + 0.5 ) ( 8 - 2 ) = 52 but for some reason im getting 3.5 and not 4.5 . 8 s + 6 s + 3 = 52 14 s = 49 s = 3.5

add(divide(subtract(52, divide(subtract(divide(add(14, 2), const_2), 2), const_2)), add(subtract(divide(add(14, 2), const_2), 2), divide(add(14, 2), const_2))), divide(const_1, const_2))

<gadget id="calculator">14 + 2</gadget>
<output>16</output>
<gadget id="calculator">16 / 2</gadget>
<output>8</output>
<gadget id="calculator">8 - 2</gadget>
<output>6</output>
<gadget id="calculator">6 / 2</gadget>
<output>3</output>
<gadget id="calculator">52 - 3</gadget>
<output>49</output>
<gadget id="calculator">6 + 8</gadget>
<output>14</output>
<gadget id="calculator">49 / 14</gadget>
<output>7/2 = around 3.5</output>
<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(7/2) + (1/2)</gadget>
<output>4</output>
<result>4</result>


the l . c . m of two numbers is 2310 and their h . c . f is 30 . if one number is 462 the other is

Explanation: "the other number = l . c . m * h . c . f / given number = 2310 * 30 / 462 = 150 answer is d ."

<gadget id="calculator">30 * 2_310</gadget>
<output>69_300</output>
<gadget id="calculator">69_300 / 462</gadget>
<output>150</output>
<result>150</result>


a person incurs a loss of 5 % be selling a watch for rs . 1140 . at what price should the watch be sold to earn 5 % profit .

Explanation: explanation : let the new s . p . be x , then . ( 100 - loss % ) : ( 1 st s . p . ) = ( 100 + gain % ) : ( 2 nd s . p . ) = > ( 951 / 140 = 105 / x ) = > x = 1260 answer is c

multiply(divide(1140, divide(subtract(const_100, 5), const_100)), divide(add(const_100, 5), const_100))

<gadget id="calculator">100 - 5</gadget>
<output>95</output>
<gadget id="calculator">95 / 100</gadget>
<output>19/20 = around 0.95</output>
<gadget id="calculator">1_140 / (19/20)</gadget>
<output>1_200</output>
<gadget id="calculator">100 + 5</gadget>
<output>105</output>
<gadget id="calculator">105 / 100</gadget>
<output>21/20 = around 1.05</output>
<gadget id="calculator">1_200 * (21/20)</gadget>
<output>1_260</output>
<result>1_260</result>


patanjali walked for 3 days . she walked 18 miles on the first day , walking 3 miles per hour . on the second day she walked for one less hour but she walked one mile per hour , faster than on the first day . on the third day she walked the same number of hours as on the first day , but at the same speed as on the second day . how many miles in total did she walk ?

Explanation: patanjali walked 18 miles on the first day , walking 3 miles per hour i . e . total time of walk on day - 1 = 18 / 3 = 6 hours second day time of walk = 6 - 1 = 5 hours and speed = 3 + 1 = 4 miles per hour i . e . distance walked on second day = 5 * 4 = 20 miles third day time of walk = 6 hours and speed = 4 miles per hour i . e . distance walked on second day = 6 * 4 = 24 miles total distance travelled on three days = 18 + 20 + 24 = 62 answer : option e

add(add(18, multiply(add(const_2, const_3), add(3, const_1))), multiply(add(add(const_2, const_3), const_1), add(3, const_1)))

<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">3 + 1</gadget>
<output>4</output>
<gadget id="calculator">5 * 4</gadget>
<output>20</output>
<gadget id="calculator">18 + 20</gadget>
<output>38</output>
<gadget id="calculator">5 + 1</gadget>
<output>6</output>
<gadget id="calculator">6 * 4</gadget>
<output>24</output>
<gadget id="calculator">38 + 24</gadget>
<output>62</output>
<result>62</result>


the current in a river is 10 mph . a boat can travel 50 mph in still water . how far up the river can the boat travel if the round trip is to take 5 hours ?

Explanation: upstream speed = 50 - 10 = 40 mph downstream speed = 50 + 10 = 60 mph d / 40 + d / 60 = 5 hours solving for d we get d = 120 answer : a

divide(multiply(multiply(subtract(50, 10), add(50, 10)), 5), add(add(50, 10), subtract(50, 10)))

<gadget id="calculator">50 - 10</gadget>
<output>40</output>
<gadget id="calculator">50 + 10</gadget>
<output>60</output>
<gadget id="calculator">40 * 60</gadget>
<output>2_400</output>
<gadget id="calculator">2_400 * 5</gadget>
<output>12_000</output>
<gadget id="calculator">60 + 40</gadget>
<output>100</output>
<gadget id="calculator">12_000 / 100</gadget>
<output>120</output>
<result>120</result>


60 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780 . the bigger part is :

Explanation: "explanation : let the two parts be ( 60 - x ) and x . then , 10 ( 60 - x ) + 22 x = 780 = > 12 x = 180 = > x = 15 . bigger part = ( 60 - x ) = 45 . answer : b ) 45"

subtract(60, divide(subtract(780, multiply(60, 10)), subtract(22, 10)))

<gadget id="calculator">60 * 10</gadget>
<output>600</output>
<gadget id="calculator">780 - 600</gadget>
<output>180</output>
<gadget id="calculator">22 - 10</gadget>
<output>12</output>
<gadget id="calculator">180 / 12</gadget>
<output>15</output>
<gadget id="calculator">60 - 15</gadget>
<output>45</output>
<result>45</result>


a library branch originally contained 18360 volumes , 30 % of which were fiction novels . 1 / 3 of the volumes were transferred to another location and 1 / 5 of the volumes transferred were fiction novels . what percent of the remaining collection was fiction novels ?

Explanation: fiction novels = 5,508 transferred to another location = 6,120 transferred fiction novels = 1,101 non transferred fiction novels = 4,407 percent of the remaining collection was fiction novels = 4,407 / ( 18360 - 6120 ) * 100 = > 36.004 . . . % hence answer will be ( d )

multiply(divide(multiply(divide(30, const_100), subtract(const_1, divide(1, 5))), subtract(const_1, divide(const_1, const_3))), const_100)

<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(3/10) * (4/5)</gadget>
<output>6/25 = around 0.24</output>
<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">(6/25) / (2/3)</gadget>
<output>9/25 = around 0.36</output>
<gadget id="calculator">(9/25) * 100</gadget>
<output>36</output>
<result>36</result>


there is one 4 - digit whole number n , such that the last 4 digits of n 2 are in fact the original number n

Explanation: c 9376 looking at the last digit , the last digit must be either 0 , 1 , 5 or 6 . then looking at the last two digits , the last two digits must be either 0001 , 25 or 76 . then looking at the last three digits , the last three digits must be either 00001 , 625 or 376 . then looking at the last four digits , the last four digits must be either 0000001 , 0625 or 9376 . out of those , only 9376 is a 4 digit number

add(multiply(subtract(const_12, const_3), const_1000), add(multiply(const_3, const_100), multiply(subtract(multiply(const_12, const_4), const_10), 2)))

<gadget id="calculator">12 - 3</gadget>
<output>9</output>
<gadget id="calculator">9 * 1_000</gadget>
<output>9_000</output>
<gadget id="calculator">3 * 100</gadget>
<output>300</output>
<gadget id="calculator">12 * 4</gadget>
<output>48</output>
<gadget id="calculator">48 - 10</gadget>
<output>38</output>
<gadget id="calculator">38 * 2</gadget>
<output>76</output>
<gadget id="calculator">300 + 76</gadget>
<output>376</output>
<gadget id="calculator">9_000 + 376</gadget>
<output>9_376</output>
<result>9_376</result>


when two dice are tossed , what is the probability that the total score is a prime number ?

Explanation: total number of outcomes possible = 36 probability of total score is a prime number = 15 p ( e ) = 15 / 36 = 5 / 12 answer : c

divide(add(multiply(const_6, const_2), const_3), multiply(const_6, const_6))

<gadget id="calculator">6 * 2</gadget>
<output>12</output>
<gadget id="calculator">12 + 3</gadget>
<output>15</output>
<gadget id="calculator">6 * 6</gadget>
<output>36</output>
<gadget id="calculator">15 / 36</gadget>
<output>5/12 = around 0.416667</output>
<result>5/12 = around 0.416667</result>


running at the same constant rate , 6 identical machines can produce a total of 420 bottles per minute . at this rate , how many bottles could 10 such machines produce in 4 minutes ?

Explanation: "let the required number of bottles be x . more machines , more bottles ( direct proportion ) more minutes , more bottles ( direct proportion ) machines 6 : 10 : : 420 : x time ( in minutes ) 1 : 4 6 x 1 x x = 10 x 4 x 420 x = ( 10 x 4 x 420 ) / ( 6 ) x = 2800 . answer : c"

multiply(multiply(divide(420, 6), 4), 10)

<gadget id="calculator">420 / 6</gadget>
<output>70</output>
<gadget id="calculator">70 * 4</gadget>
<output>280</output>
<gadget id="calculator">280 * 10</gadget>
<output>2_800</output>
<result>2_800</result>


there is food for 760 men for 22 days . how many more men should join after two days so that the same food may last for 5 days more ?

Explanation: "760 - - - - 22 760 - - - - 20 x - - - - - 5 x * 5 = 760 * 20 x = 3040 760 - - - - - - - 2280 answer : a"

subtract(divide(multiply(760, subtract(22, const_2)), 5), 760)

<gadget id="calculator">22 - 2</gadget>
<output>20</output>
<gadget id="calculator">760 * 20</gadget>
<output>15_200</output>
<gadget id="calculator">15_200 / 5</gadget>
<output>3_040</output>
<gadget id="calculator">3_040 - 760</gadget>
<output>2_280</output>
<result>2_280</result>


the ratio of the volumes of two cubes is 216 : 343 . what is the ratio of their total surface areas ?

Explanation: "ratio of the sides = ³ √ 216 : ³ √ 343 = 6 : 7 ratio of surface areas = 62 : 72 = 31 : 36 answer : b"

power(divide(216, 343), divide(const_1, const_3))

<gadget id="calculator">216 / 343</gadget>
<output>216/343 = around 0.629738</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(216/343) ** (1/3)</gadget>
<output>6/7 = around 0.857143</output>
<result>6/7 = around 0.857143</result>


the length and breadth of a rectangle is increased by 10 % and 30 % respectively . what is the increase in the area ?

Explanation: "100 * 100 = 10000 110 * 130 = 14300 - - - - - - - - - - 4300 10000 - - - - - - - 4300 100 - - - - - - - 43.00 answer a"

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

<gadget id="calculator">10 + 100</gadget>
<output>110</output>
<gadget id="calculator">30 + 100</gadget>
<output>130</output>
<gadget id="calculator">110 * 130</gadget>
<output>14_300</output>
<gadget id="calculator">100 * 100</gadget>
<output>10_000</output>
<gadget id="calculator">14_300 - 10_000</gadget>
<output>4_300</output>
<gadget id="calculator">4_300 * 100</gadget>
<output>430_000</output>
<gadget id="calculator">430_000 / 10_000</gadget>
<output>43</output>
<result>43</result>


if k is the greatest positive integer such that 3 ^ k is a divisor of 15 ! then k =

Explanation: for solving this type of tasks we can use such approach 15 / 3 = 5 15 / 3 ^ 2 = 1 and remainder and 3 ^ 3 is more than 15 so we stop on second exponent 5 + 1 = 6 so maximum value of k = 6 and answer is d

<gadget id="calculator">15 / 3</gadget>
<output>5</output>
<gadget id="calculator">1 + 5</gadget>
<output>6</output>
<result>6</result>


how many of the integers between 15 and 55 are even ?

Explanation: "number start between 15 to 55 is 40 numbers half of them is even . . which is 20 answer : b"

<gadget id="calculator">55 - 15</gadget>
<output>40</output>
<gadget id="calculator">40 / 2</gadget>
<output>20</output>
<result>20</result>


if ryan and smith car ratio is 5 : 8 . ryan bought 6 new car and smith bought 2 new car . now , smith has 18 car . what is their car ratio now ?

Explanation: current no . of smith car = 8 x + 2 = 18,8 x = 16 , x = 2 . current car ratio = 10 + 6 / 18 = 16 / 18 = 8 : 9 . answer c

divide(add(multiply(divide(5, 8), subtract(18, 2)), 6), 18)

<gadget id="calculator">5 / 8</gadget>
<output>5/8 = around 0.625</output>
<gadget id="calculator">18 - 2</gadget>
<output>16</output>
<gadget id="calculator">(5/8) * 16</gadget>
<output>10</output>
<gadget id="calculator">10 + 6</gadget>
<output>16</output>
<gadget id="calculator">16 / 18</gadget>
<output>8/9 = around 0.888889</output>
<result>8/9 = around 0.888889</result>


the grade point average of one third of the classroom is 45 ; the grade point average of the rest is 60 . what is the grade point average of the whole class ?

Explanation: let n = total students in class total points for 1 / 3 class = 45 n / 3 = 15 n total points for 2 / 3 class = 60 * 2 n / 3 = 40 n total points for whole class = 15 n + 40 n = 55 n 63 n total class points / n total students = 55 grade point average for total class answer : b

add(multiply(divide(60, const_3), const_2), divide(45, const_3))

<gadget id="calculator">60 / 3</gadget>
<output>20</output>
<gadget id="calculator">20 * 2</gadget>
<output>40</output>
<gadget id="calculator">45 / 3</gadget>
<output>15</output>
<gadget id="calculator">40 + 15</gadget>
<output>55</output>
<result>55</result>


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

Explanation: "according to the chain rule , m 1 x t 1 = m 2 x t 2 therefore , 63 x 12 x 5 = 30 x 6 x x x = 21 hence , the number of days = 21 . answer : a"

divide(multiply(multiply(63, 12), 5), multiply(30, 6))

<gadget id="calculator">63 * 12</gadget>
<output>756</output>
<gadget id="calculator">756 * 5</gadget>
<output>3_780</output>
<gadget id="calculator">30 * 6</gadget>
<output>180</output>
<gadget id="calculator">3_780 / 180</gadget>
<output>21</output>
<result>21</result>


marcella has 24 pairs of shoes . if she loses 9 individual shoes , what is the greatest number of matching pairs she could have left ?

Explanation: "marcella has 24 pairs of shoes and loses 9 shoes . to minimize the loss of identical pairs of shoes we want marcella to lose as many identical pairs as possible . this would yield 4 identical pairs and 1 additional shoe ( destroying 5 pairs of shoes ) . the 24 pairs of shoes minus the 5 ' destroyed ' pairs yields 19 pairs that still fulfill the requirements . answer : c"

subtract(24, add(floor(divide(9, const_2)), const_1))

<gadget id="calculator">9 / 2</gadget>
<output>9/2 = around 4.5</output>
<gadget id="calculator">floor(9/2)</gadget>
<output>4</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">24 - 5</gadget>
<output>19</output>
<result>19</result>


two trains are approaching each other at 60 mph each . the length of each train is 1 / 6 miles . when the two locomotives ( engines ) meet , how many seconds will it take for them to pass each other completely ?

Explanation: total distance to cover = 2 * ( 1 / 6 ) = 2 / 6 miles relative speed = 60 + 60 = 120 mph time taken = ( 2 / 6 ) / 120 * 3600 = 10 sec . answer : d

multiply(60, multiply(60, divide(multiply(divide(1, 6), const_2), multiply(60, const_2))))

<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/6) * 2</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">60 * 2</gadget>
<output>120</output>
<gadget id="calculator">(1/3) / 120</gadget>
<output>1/360 = around 0.002778</output>
<gadget id="calculator">60 * (1/360)</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">60 * (1/6)</gadget>
<output>10</output>
<result>10</result>


a courtyard is 25 meter long and 15 meter board is to be paved with bricks of dimensions 20 cm by 10 cm . the total number of bricks required is ?

Explanation: "number of bricks = courtyard area / 1 brick area = ( 2500 × 1500 / 20 × 10 ) = 18750 answer : c"

divide(multiply(multiply(25, const_100), multiply(15, const_100)), multiply(20, 10))

<gadget id="calculator">25 * 100</gadget>
<output>2_500</output>
<gadget id="calculator">15 * 100</gadget>
<output>1_500</output>
<gadget id="calculator">2_500 * 1_500</gadget>
<output>3_750_000</output>
<gadget id="calculator">20 * 10</gadget>
<output>200</output>
<gadget id="calculator">3_750_000 / 200</gadget>
<output>18_750</output>
<result>18_750</result>


a certain elevator has a safe weight limit of 1950 pounds . what is the greatest possible number of people who can safely ride on the elevator at one time with the average ( arithmetic mean ) weight of half the riders being 190 pounds and the average weight of the others being 200 pounds ?

Explanation: "lets assume there are 2 x people . half of them have average weight of 190 and other half has 200 . maximum weight is = 1950 so 190 * x + 200 * x = 1950 = > 390 x = 1950 = > x is approximately equal to 5 . so total people is 2 * 5 = 10 answer d ."

multiply(divide(multiply(const_10, 190), add(190, 200)), const_2)

<gadget id="calculator">10 * 190</gadget>
<output>1_900</output>
<gadget id="calculator">190 + 200</gadget>
<output>390</output>
<gadget id="calculator">1_900 / 390</gadget>
<output>190/39 = around 4.871795</output>
<gadget id="calculator">(190/39) * 2</gadget>
<output>380/39 = around 9.74359</output>
<result>380/39 = around 9.74359</result>


a and b invests rs . 8000 and rs . 12000 in a business . after 4 months , a withdraws half of his capital and 2 months later , b withdraws one - third of his capital . in what ratio should they share the profits at the end of the year ?

Explanation: a : b ( 8000 * 4 ) + ( 4000 * 8 ) : ( 12000 * 6 ) + ( 9000 * 6 ) 64000 : 120000 8 : 15 answer : c

divide(add(multiply(8000, 4), multiply(divide(12000, const_3), multiply(const_2, const_4))), add(multiply(12000, multiply(const_2, const_3)), multiply(subtract(12000, divide(12000, const_3)), multiply(const_2, const_3))))

<gadget id="calculator">8_000 * 4</gadget>
<output>32_000</output>
<gadget id="calculator">12_000 / 3</gadget>
<output>4_000</output>
<gadget id="calculator">2 * 4</gadget>
<output>8</output>
<gadget id="calculator">4_000 * 8</gadget>
<output>32_000</output>
<gadget id="calculator">32_000 + 32_000</gadget>
<output>64_000</output>
<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">12_000 * 6</gadget>
<output>72_000</output>
<gadget id="calculator">12_000 - 4_000</gadget>
<output>8_000</output>
<gadget id="calculator">8_000 * 6</gadget>
<output>48_000</output>
<gadget id="calculator">72_000 + 48_000</gadget>
<output>120_000</output>
<gadget id="calculator">64_000 / 120_000</gadget>
<output>8/15 = around 0.533333</output>
<result>8/15 = around 0.533333</result>


the height of the wall is 6 times its width and length of the wall is 7 times its height . if the volume of the wall be 86436 cu . m . its width is

Explanation: "explanation : let width = x then , height = 6 x and length = 42 x 42 x ã — 6 x ã — x = 86436 x = 7 answer : d"

power(divide(86436, multiply(multiply(6, 7), 6)), divide(const_1, const_3))

<gadget id="calculator">6 * 7</gadget>
<output>42</output>
<gadget id="calculator">42 * 6</gadget>
<output>252</output>
<gadget id="calculator">86_436 / 252</gadget>
<output>343</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">343 ** (1/3)</gadget>
<output>7</output>
<result>7</result>


money invested at x % , compounded annually , triples in value in approximately every 112 / x years . if $ 2000 is invested at a rate of 8 % , compounded annually , what will be its approximate worth in 28 years ?

Explanation: "x = 8 % 112 / x years = 112 / 8 = 14 years now , money triples every 14 years therefore , in 14 yrs , if $ 2000 triples to $ 6000 , in 28 years , it will again triple to $ 6000 * 3 = $ 18,000 answer d"

multiply(2000, power(const_3, divide(28, divide(112, 8))))

<gadget id="calculator">112 / 8</gadget>
<output>14</output>
<gadget id="calculator">28 / 14</gadget>
<output>2</output>
<gadget id="calculator">3 ** 2</gadget>
<output>9</output>
<gadget id="calculator">2_000 * 9</gadget>
<output>18_000</output>
<result>18_000</result>


a man buys rs . 44 shares paying 9 % dividend . the man wants to have an interest of 12 % on his money . the market value of each share is :

Explanation: "dividend on rs . 44 = rs . 9 / 100 x 44 = rs . 3.96 . rs . 12 is an income on rs . 100 . rs . 3.96 is an income on rs . 100 / 12 x 3.96 = rs . 33 . answer : option e"

multiply(divide(const_100, 12), multiply(divide(9, const_100), 44))

<gadget id="calculator">100 / 12</gadget>
<output>25/3 = around 8.333333</output>
<gadget id="calculator">9 / 100</gadget>
<output>9/100 = around 0.09</output>
<gadget id="calculator">(9/100) * 44</gadget>
<output>99/25 = around 3.96</output>
<gadget id="calculator">(25/3) * (99/25)</gadget>
<output>33</output>
<result>33</result>


Explanation: 4 ^ 2 : 5 ^ 2 = 16 : 25 answer : e

divide(power(4, const_2), power(5, const_2))

<gadget id="calculator">4 ** 2</gadget>
<output>16</output>
<gadget id="calculator">5 ** 2</gadget>
<output>25</output>
<gadget id="calculator">16 / 25</gadget>
<output>16/25 = around 0.64</output>
<result>16/25 = around 0.64</result>


how many different ways can 2 students be seated in a row of 5 desks , so that there is always at least one empty desk between the students ?

Explanation: "6 ways to seat the students : with two empty seats between 1 empty w / one student on the left most 1 empty . . . . right most two students can be interchanged 6 x 2 = 12 e"

<gadget id="calculator">5 - 1</gadget>
<output>4</output>
<gadget id="calculator">factorial(4) / factorial(4 - 2)</gadget>
<output>12</output>
<result>12</result>


he average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 70 kg . what might be the weight of the new person ?

Explanation: "explanation : total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 70 + 20 ) kg = 90 kg . answer : a"

<gadget id="calculator">2.5 * 8</gadget>
<output>20</output>
<gadget id="calculator">20 + 70</gadget>
<output>90</output>
<result>90</result>


if the function q is defined by the formula q = 5 w / ( 4 h ( z ^ 2 ) ) , by what factor will q be multiplied if w is quadrupled , h is doubled , and z is tripled ?

Explanation: "we just need to find the factor thats all , w - > quadrupled - > 4 w h - > doubled - > 2 h z - > tripled - > 3 z hence , z ^ 2 = 9 z ^ 2 w is in numerator , and h * z in denominator . hence , additional factor being introduced = 4 / 2 * 9 = 4 / 18 = 2 / 9 = b"

divide(4, multiply(2, power(const_3, 2)))

<gadget id="calculator">3 ** 2</gadget>
<output>9</output>
<gadget id="calculator">2 * 9</gadget>
<output>18</output>
<gadget id="calculator">4 / 18</gadget>
<output>2/9 = around 0.222222</output>
<result>2/9 = around 0.222222</result>


the radius of a wheel is 20.4 cm . what is the distance covered by the wheel in making 400 resolutions ?

Explanation: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 400 resolutions . = 400 * 2 * 22 / 7 * 20.4 = 51244.8 cm = 512.448 m answer : a"

divide(multiply(multiply(multiply(divide(add(multiply(add(const_3, const_4), const_3), const_1), add(const_3, const_4)), 20.4), const_2), 400), const_100)

<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">7 * 3</gadget>
<output>21</output>
<gadget id="calculator">21 + 1</gadget>
<output>22</output>
<gadget id="calculator">22 / 7</gadget>
<output>22/7 = around 3.142857</output>
<gadget id="calculator">(22/7) * 20.4</gadget>
<output>64.114286</output>
<gadget id="calculator">64.114286 * 2</gadget>
<output>128.228572</output>
<gadget id="calculator">128.228572 * 400</gadget>
<output>51_291.4288</output>
<gadget id="calculator">51_291.4288 / 100</gadget>
<output>512.914288</output>
<result>512.914288</result>


a particular store purchased a stock of turtleneck sweaters and marked up its cost by 20 % . during the new year season , it further marked up its prices by 25 % of the original retail price . in february , the store then offered a discount of 20 % . what was its profit on the items sold in february ?

Explanation: "assume the total price = 100 x price after 20 % markup = 120 x price after 25 % further markup = 1.25 * 120 x = 150 x price after the discount = 0.8 * 150 x = 120 x hence total profit = 20 % option a"

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

<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">100 + 20</gadget>
<output>120</output>
<gadget id="calculator">100 + 25</gadget>
<output>125</output>
<gadget id="calculator">125 / 100</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">120 * (5/4)</gadget>
<output>150</output>
<gadget id="calculator">(4/5) * 150</gadget>
<output>120</output>
<gadget id="calculator">120 - 100</gadget>
<output>20</output>
<result>20</result>


if the cost price of 50 articles is equal to the selling price of 20 articles , then the gain or loss percent is ?

Explanation: "percentage of profit = 30 / 20 * 100 = 150 % answer : e"

multiply(const_100, divide(subtract(const_100, divide(multiply(const_100, 20), 50)), divide(multiply(const_100, 20), 50)))

<gadget id="calculator">100 * 20</gadget>
<output>2_000</output>
<gadget id="calculator">2_000 / 50</gadget>
<output>40</output>
<gadget id="calculator">100 - 40</gadget>
<output>60</output>
<gadget id="calculator">60 / 40</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">100 * (3/2)</gadget>
<output>150</output>
<result>150</result>


what is rate of interest if principal . amount be 400 , simple interest 160 and time 2 year .

Explanation: s . i = ( p * r * t ) / 100 160 = 800 r / 100 r = 160 / 8 = 20 % answer c

multiply(divide(160, multiply(400, 2)), const_100)

<gadget id="calculator">400 * 2</gadget>
<output>800</output>
<gadget id="calculator">160 / 800</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 100</gadget>
<output>20</output>
<result>20</result>


the radius of a sphere is increased by 50 % . the increase in surface area of the sphere is :

Explanation: "explanation : take radius 100 . then surface area is 4 × π π × 100 × 100 . after increase radius by 50 % the radius becomes 100 + 50 % of 100 = 150 then new surface area is 4 × π π × 150 × 150 then put the values into formula of percentage = 4 π 1502 − 4 π 10024 π 1002 × 1004 π 1502 − 4 π 10024 π 1002 × 100 = 125 % answer : b"

multiply(divide(subtract(surface_sphere(add(const_1, divide(50, const_100))), surface_sphere(const_1)), surface_sphere(const_1)), const_100)

<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 + (1/2)</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">4 * pi * ((3/2) ** 2)</gadget>
<output>9*pi = around 28.274334</output>
<gadget id="calculator">4 * pi * (1 ** 2)</gadget>
<output>4*pi = around 12.566371</output>
<gadget id="calculator">(9*pi) - (4*pi)</gadget>
<output>5*pi = around 15.707963</output>
<gadget id="calculator">(5*pi) / (4*pi)</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">(5/4) * 100</gadget>
<output>125</output>
<result>125</result>


a man can row 4 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?

Explanation: "m = 4 s = 1.2 ds = 4.8 us = 2.8 x / 4.8 + x / 2.8 = 1 x = 1.77 d = 1.77 * 2 = 3.54 answer : c"

multiply(divide(multiply(add(4, 1.2), subtract(4, 1.2)), add(add(4, 1.2), subtract(4, 1.2))), const_2)

<gadget id="calculator">4 + 1.2</gadget>
<output>5.2</output>
<gadget id="calculator">4 - 1.2</gadget>
<output>2.8</output>
<gadget id="calculator">5.2 * 2.8</gadget>
<output>14.56</output>
<gadget id="calculator">5.2 + 2.8</gadget>
<output>8</output>
<gadget id="calculator">14.56 / 8</gadget>
<output>1.82</output>
<gadget id="calculator">1.82 * 2</gadget>
<output>3.64</output>
<result>3.64</result>


in a certain game , each player scores either 2 points or 5 points . if n players score 2 points and m players score 5 points , and the total number of points scored is 50 , what is the least possible positive difference w between n and m ?

Explanation: "we have equation 2 n + 5 m = 50 we have factor 2 in first number and we have factor 5 in second number . lcm ( 2 , 5 ) = 10 so we can try some numbers and we should start from 5 because it will be less list than for 2 2 * 5 = 10 and n should be equal 20 4 * 5 = 20 and n should be equal 15 6 * 5 = 30 and n should be equal 10 8 * 5 = 40 and n should be equal 5 10 * 5 = 50 and n should be equal 0 third variant give us the mininal difference n - m = 10 - 6 = 4 and there is some mistake in my way of thinking because we do n ' t have such answer ) if we change the task and will seek for difference between m and n than minimal result w will be 8 - 5 = 3 and answer b"

<gadget id="calculator">5 - 2</gadget>
<output>3</output>
<result>3</result>


h is a positive integer and 225 and 216 are both divisors of h . if h = ( 2 ^ a ) * ( 3 ^ b ) * ( 5 ^ c ) , where a , b and c are positive integers , what is the least possible value of a + b + c ?

Explanation: lets make factorization of 225 and 216 . . 225 = 5 x 5 x 3 x 3 x 3 216 = 2 x 2 x 2 x 3 x 3 x 3 h would have to have 3 two ' s , 225 has 3 threes and and so does 216 but they can be the same three threes so we count them only once . . . 225 has 2 fives . . . so we had them together and we get 3 + 3 + 2 = 8 ( b ) ( answer ) . . .

<gadget id="calculator">3 + 3</gadget>
<output>6</output>
<gadget id="calculator">6 + 2</gadget>
<output>8</output>
<result>8</result>


if p and q are both odd prime numbers andp < q , then how many different positive integer factors does 2 pqhave ?

Explanation: p and q are both odd prime numbers - it means either p or q is not 2 and since prime numbers have only two factors - 1 and the number itself p and q each will have ( 1 + 1 ) = 2 factors hence 2 pq will have ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 8 factors d is the answer

<gadget id="calculator">2 ** 3</gadget>
<output>8</output>
<result>8</result>


Explanation: "let y x 12 = 173 x 240 then y = ( 173 x 240 ) / 12 = 3460 answer : a"

<gadget id="calculator">173 * 240</gadget>
<output>41_520</output>
<gadget id="calculator">41_520 / 12</gadget>
<output>3_460</output>
<result>3_460</result>


a man goes to shopkeeper and says that if u give me as much as i have , i will spend rs . 10 / - on ur shop . shopkeeper agrees and man moves to another shopkeeper ans asked same . at 3 rd shop after all the transaction , he was left with no money . find the initial amount with the man

Explanation: man has rs . x he leaves - 1 st shop wid rs . ( 2 x - 10 ) 2 nd shop wid rs . [ 2 ( 2 x - 10 ) - 10 ] 3 rd shop wid rs . { 2 [ 2 ( 2 x - 10 ) - 10 ] - 10 } = 0 ( since he has no money left ) so solving the eqn x = 8.75 answer : d

divide(add(divide(add(divide(10, const_2), 10), const_2), 10), const_2)

<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">5 + 10</gadget>
<output>15</output>
<gadget id="calculator">15 / 2</gadget>
<output>15/2 = around 7.5</output>
<gadget id="calculator">(15/2) + 10</gadget>
<output>35/2 = around 17.5</output>
<gadget id="calculator">(35/2) / 2</gadget>
<output>35/4 = around 8.75</output>
<result>35/4 = around 8.75</result>


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

Explanation: ratio in which profit is divided = 2 : 3 assume that b ' s contribution to the capital = b 3500 × 12 : b × 7 = 2 : 3 ⇒ 3500 × 12 × 3 = 2 × b × 7 ⇒ b = 3500 × 12 × 3 / 2 × 7 = 500 × 6 × 3 = 9000 answer : b

divide(divide(multiply(multiply(3500, const_12), 3), 2), subtract(const_12, 5))

<gadget id="calculator">3_500 * 12</gadget>
<output>42_000</output>
<gadget id="calculator">42_000 * 3</gadget>
<output>126_000</output>
<gadget id="calculator">126_000 / 2</gadget>
<output>63_000</output>
<gadget id="calculator">12 - 5</gadget>
<output>7</output>
<gadget id="calculator">63_000 / 7</gadget>
<output>9_000</output>
<result>9_000</result>


two trains of length 180 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?

Explanation: "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 180 + 280 = 400 m . the time required = d / s = 460 / 20 = 23 sec . answer : b"

<gadget id="calculator">180 + 280</gadget>
<output>460</output>
<gadget id="calculator">42 + 30</gadget>
<output>72</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">72 * (5/18)</gadget>
<output>20</output>
<gadget id="calculator">460 / 20</gadget>
<output>23</output>
<result>23</result>


a train running at the speed of 60 km / hr crosses a pole in 7 sec . what is the length of the train ?

Explanation: "speed = 60 * 5 / 18 = 50 / 3 m / sec length of the train = speed * time = 50 / 3 * 7 = 116.66 answer : e"

multiply(divide(multiply(60, const_1000), const_3600), 7)

<gadget id="calculator">60 * 1_000</gadget>
<output>60_000</output>
<gadget id="calculator">60_000 / 3_600</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">(50/3) * 7</gadget>
<output>350/3 = around 116.666667</output>
<result>350/3 = around 116.666667</result>