euclaise/mathqa_programs huggingface dataset:
Problem: a sports equipment store sold ping pong rackets for a total of $ 539 . if the average ( arithmetic mean ) price of a pair of rackets is $ 9.8 , how many pairs were sold ?
Options: a ) 55 , b ) 100 , c ) 490 , d ) 500 , e ) 980
Rationale: "average price for a pair of rackets = $ 9.8 total cost = $ 9.8 * x = $ 539 x = 55 pairs were sold . answer : a"
Answer: a
Python program:
a = 539 / 9
Problem: a retailer bought a machine at a wholesale price of $ 80 and later on sold it after a 20 % discount of the retail price . if the retailer made a profit equivalent to 20 % of the wholesale price , what is the retail price of the machine ?
Options: a ) $ 80 , b ) $ 100 , c ) $ 120 , d ) 135 , e ) 160
Rationale: "the price after the discount was 1.2 * 80 = $ 96 let x be the retail price . 0.8 x = $ 96 x = 96 / 0.8 = $ 120 the answer is c ."
Answer: c
Python program:
a = 80 * 20
b = a / 100
c = 80 + b 
d = c * 100
e = 3 * 3
f = e * 20
g = d / f
Problem: there are 7 teams in a certain league and each team plays each of the other teams exactly twice . if each game is played by 2 teams , what is the total number of games played ?
Options: a ) 15 , b ) 16 , c ) 28 , d ) 42 , e ) 64
Rationale: "every team plays with 6 teams . . . so total no of matches = 7 x 6 = 42 . now , each match is played twice = > 42 x 2 but 2 teams play a match = > 42 x 2 / 2 = 42 . answer : d"
Answer: d
Python program:
a = 7 - 1
b = 7 * a
c = b / 2
Problem: in expressing a length of 61.472 km as nearly as possible with the 3 significant digits , find the percentage error ?
Options: a ) 0.35 % , b ) 0.4 % , c ) 0.045 % , d ) 0.6 % , e ) none of these
Rationale: explanation : error = ( 61.5 - 61.472 ) = 0.028 required percentage = 0.028 / 61.472100 = 0.045 answer : c
Answer: c
Python program:
a = 3 + 4 
b = a * 4
c = b / 100
d = c / 61
e = d * 10
Problem: if x + y + z = 1 . then xy + yz + zx is
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6
Rationale: 1 / 2 + 1 / 2 + 0 = 1 xy = 1 / 2 * 1 / 2 = 1 / 4 answer : c
Answer: c
Python program:
a = 1 / 4
Problem: in the storage room of a certain bakery , the ratio of sugar to flour is 5 to 2 , and the ratio of flour to baking soda is 10 to 1 . if there were 60 more pounds of baking soda in the room , the ratio of flour to baking soda would be 8 to 1 . how many pounds of sugar are stored in the room ?
Options: a ) 600 , b ) 1200 , c ) 1500 , d ) 3600 , e ) 6000
Rationale: "sugar : flour = 5 : 2 = 25 : 10 ; flour : soda = 10 : 1 = 10 : 1 ; thus we have that sugar : flour : soda = 25 x : 10 x : 1 x . also given that 10 x / ( 1 x + 60 ) = 8 / 1 - - > x = 240 - - > sugar = 25 x = 6000 answer : e ."
Answer: e
Python program:
a = 5 / 2
b = 8 * 60
c = 10 - 8
d = b / c
e = 10 * d
f = a * e
Problem: machine a can process 6000 envelopes in 3 hours . machines b and c working together but independently can process the same number of envelopes in 2.5 hours . if machines a and c working together but independently process 3000 envelopes in 1 hour , then how many hours would it take machine b to process 9800 envelopes .
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 7
Rationale: "you can either take the amount of work done as the same as karishma has done or take the work done by each in the same time . i will do the latter 1 . work done in 1 hr by a is 2000 envelopes 2 . work done in 1 hr by a and c is 3000 envelopes 3 . so work done in 1 hr by c is 1000 envelopes 4 . work done in 1 hr by b and c is 2400 envelopes 5 . so work done in 1 hr by b is 1400 envelopes 6 . so to process 9800 envelopes b will take 9800 / 1400 hrs = 7 hrs so the answer is choice e"
Answer: e
Python program:
a = 6000 / 2
b = 3000 / 1
c = 6000 / 3
d = b - c
e = a - d
f = 9800 / e
Problem: difference between two numbers is 5 , 6 times of the smaller lacks by 8 from the 4 times of the greater . find the numbers ?
Options: a ) 5,1 , b ) 7,3 , c ) 9,8 , d ) 11,6 , e ) 13,7
Rationale: explanation : x – y = 5 4 x – 6 y = 8 x = 11 y = 6 d )
Answer: d
Python program:
a = 8 - 4
b = a - 1
Problem: angelina walked 600 meters from her home to the grocery at a constant speed . she then walked 480 meters to the gym at double the speed . she spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery . what was angelina ' s speed , in meters per second , from the grocery to the gym ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 9 , e ) 12
Rationale: "let the speed be x . . . so time taken from home to grocery = 600 / x . . the speed to gym = 2 x . . so time taken = 480 / 2 x = 240 / x . . its given 600 / x - 240 / x = 40 . . 360 / x = 40 . . x = 9 m / secs . . so grocery to gym = 2 * 9 = 18 m / s . . . d"
Answer: d
Python program:
a = 480 / 2
b = 600 - a
c = b / 40
d = c * 2
Problem: a train running at the speed of 180 km / hr crosses a pole in 36 seconds . what is the length of the train ?
Options: a ) 450 m , b ) 500 m , c ) 550 m , d ) 600 m , e ) 650 m
Rationale: "speed = ( 180 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec length of the train = ( speed x time ) = ( 50 / 3 * 36 ) m = 600 m . answer : d"
Answer: d
Python program:
a = 180 * 1000
b = a / 3600
c = b * 36
Problem: two brothers took the gmat exam , the higher score is x and the lower one is y . if the difference between the two scores 1 / 4 , what is the value of y / x ?
Options: a ) 3 . , b ) 2 . , c ) 1 / 5 , d ) 1 / 3 . , e ) there is n ' t enough data to answer the question .
Rationale: "answer is c : 1 / 5 x - y = ( x + y ) / 4 solving for y / x = 1 / 5"
Answer: c
Python program:
a = 4 * 1
b = a / 4
c = 4 + b
Problem: walking 3 / 2 of his usual rate , a boy reaches his school 4 min early . find his usual time to reach the school ?
Options: a ) 12 , b ) 99 , c ) 27 , d ) 28 , e ) 20
Rationale: "speed ratio = 1 : 3 / 2 = 2 : 3 time ratio = 3 : 2 1 - - - - - - - - 3 4 - - - - - - - - - ? 12 m . answer : a"
Answer: a
Python program:
a = 4 * 3
Problem: when 5 is added to half of one - third of one - fifth of a number , the result is one - fifteenth of the number . find the number ?
Options: a ) 32 , b ) 150 , c ) 60 , d ) 27 , e ) 11
Rationale: "explanation : let the number be 5 + 1 / 2 [ 1 / 3 ( a / 5 ) ] = a / 15 = > 5 = a / 30 = > a = 150 answer : b"
Answer: b
Python program:
a = 2 + 5 
b = 3 * a
c = 1 / b
d = c / 2
e = 5 / d
Problem: in a certain game , a large bag is filled with blue , green , purple and red chips worth 1 , 5 , x and 11 points each , respectively . the purple chips are worth more than the green chips , but less than the red chips . a certain number of chips are then selected from the bag . if the product of the point values of the selected chips is 440 , how many purple chips were selected ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "440 = 1 * 5 * 8 * 11 the factor of 8 must come from the purple point value , so there is 1 purple chip . the answer is a ."
Answer: a
Python program:
a = 5 - 2
Problem: 9 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?
Options: a ) 144 , b ) 131 , c ) 99 , d ) 90 , e ) 45
Rationale: there are 9 business exec and in each handshake 2 business execs are involved . hence 9 c 2 = 36 also , each of 9 exec will shake hand with every 7 other chairmen for total of 63 handshake . total = 36 + 63 = 99 ans : c
Answer: c
Python program:
a = 9 - 1
b = 9 * a
c = b / 2
d = 9 * 7
e = c + d
Problem: from a pack of cards , two cards are drawn one after the other , with replacement . what is the probability that the first card is a club and the second card is a king or queen ?
Options: a ) 2 / 13 , b ) 3 / 13 , c ) 1 / 26 , d ) 1 / 52 , e ) 3 / 52
Rationale: "p ( club ) = 1 / 4 p ( king or queen ) = 2 / 13 p ( club then a king / queen ) = 1 / 4 * 2 / 13 = 1 / 26 the answer is c ."
Answer: c
Python program:
a = 3 * 4
b = a + 1 
c = b / const_52
d = 2 / const_52
e = c * d
Problem: a container has 40 l milk . 4 l milk is taken out and replaced with water , the process done 3 times . what is the amount of milk now left ?
Options: a ) 29.16 l , b ) 29.19 l , c ) 29.12 l , d ) 29.11 l , e ) 29.14 l
Rationale: explanation : in regard to the problem let after n times liquid in the container is x and liquid removed is y = > liquid in container = x = > liquid removed = y after one trial , quantity of pure liquid = x - ( 1 - y / x ) after n trials quantity of pure liquid = x - ( 1 - y / x ) n therefore , putting the values ( x = 40 l y = 4 l n = 3 ) and solving = > 40 - ( 1 - 4 / 40 ) 3 = 29.16 l answer : a
Answer: a
Python program:
a = 4 * 3
b = 40 - a
Problem: if the length of rectangle is three times of its breadth . if the area of rectangle is 6075 sq . m , then calculate the length ?
Options: a ) 145
b ) 135
c ) 75
d ) 140
e ) none of these
Rationale: let breadth = x , length = 3 x . area of rectangle = length * breadth = 3 x ^ 2 = 6075 x ^ 2 = 2025 , x = √ 2025 = 45 m length = 135 m answer b
Answer: b
Python program:
a = 6075 / 3
b = math.sqrt(a)
c = b * 3
Problem: the average of 9 observations was 9 , that of the 1 st of 4 being 10 and that of the last 4 being 8 . what was the 5 th observation ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "1 to 9 = 9 * 9 = 81 1 to 4 = 4 * 10 = 40 4 to 9 = 6 * 8 = 48 5 th = 48 + 40 = 88 – 81 = 7 answer : d"
Answer: d
Python program:
a = 10 * 4
b = 9 * 4
c = a + b 
d = 9 * 9
e = c - d
Problem: how much water must be added to 48 litres of milk at 1 1 ⁄ 2 litres for 20 so as to have a mixture worth 10 2 ⁄ 3 a litre ?
Options: a ) 10 litres , b ) 12 litres , c ) 15 litres , d ) 18 litres , e ) none of these
Rationale: "c . p . of 1 litre of milk = ( 20 × 2 ⁄ 3 ) = 40 ⁄ 3 ∴ ratio of water and milk = 8 ⁄ 3 : 32 ⁄ 3 = 8 : 32 = 1 : 4 ∴ quantity of water to be added to 48 litres of milk = ( 1 ⁄ 4 × 48 ) litres = 12 litres . answer b"
Answer: b
Python program:
a = 1 / 2
b = 1 + a 
c = 20 / b
Problem: a salesman â € ™ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1000 plus 2.5 % commission on all sales exceeding rs . 4,000 . if his remuneration as per new scheme was rs . 100 more than that by the previous schema , his sales were worth ?
Options: a ) s . 14,000 , b ) s . 12,000 , c ) s . 32,000 , d ) s . 40,000 , e ) s . 50,000
Rationale: "[ 1000 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 100 x = 32000 answer : c"
Answer: c
Python program:
a = 5 * 4
b = a - 12
Problem: two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 24 seconds . the ratio of their speeds is ?
Options: a ) 3 / 6 , b ) 3 / 2 , c ) 7 / 3 , d ) 3 / 5 , e ) 5 / 2
Rationale: "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 27 x meters , and length of the second train = 17 y meters . ( 27 x + 17 y ) / ( x + y ) = 24 = = > 27 x + 17 y = 24 x + 24 y = = > 3 x = 7 y = = > x / y = 7 / 3 . answer : c"
Answer: c
Python program:
a = 27 - 24
b = 24 - 17
c = a / b
Problem: 32 % of employees are women with fair hair . 40 % of fair - haired employees are women . what percent of employees have fair hair ?
Options: a ) 25 , b ) 30 , c ) 50 , d ) 55 , e ) 80
Rationale: "i came up with ( e ) 80 think of 100 people total : from the first fact , 32 of these are women with fair hair . from the second fact , these 30 women make up 40 % of the total fair haired population . we can then make a ratio of 60 : 40 fair haired men to fair haired women . this means that ( 60 / 40 ) * 32 equals the number of fair haired men , which is 48 men with fair hair . add this 48 to the 32 women and get 80 fair haired men and women out of 100 total men and women . 80 % e"
Answer: e
Python program:
a = 32 / 40
b = a * 100
Problem: while visiting a small town in the united states , i lost my overcoat in a bus . when i reported the matter to the bus company i was asked the number of the bus . though i did not remember the exact number i did remember that the bus number bad a certain peculiarity about it . the number plate showed the bus number as a perfect square and also if the plate was turned upside down . ? the number would still be a perfect square — of course it was not ? i came to know from the bus company they had only 5 100 buses numbered from 1 to 500 . from this i was able to deduce the bus number . can you tell what was the other number .
Options: a ) 127 , b ) 196 , c ) 116 , d ) 140 , e ) 234
Rationale: b 196 the only numbers that can be turned upside down and still read as a number are 0 , 1 , 6 , 8 and 9 . the numbers 0 , 1 and 8 remain 0 , 1 and 8 when turned over , but 6 becomes 9 and 9 becomes 6 . therefore the possible numbers on the bus were 9 , 16 , 81 , 100 , 169 or 196 . however , the number 196 is the only number which becomes a perfect square when turned over because 961 is the perfect square of 31 . therefore 196 is the correct answer .
Answer: b
Python program:
a = 100 - 4
b = a + 100
Problem: a car traveled from san diego to san francisco at an average speed of 51 miles per hour . if the journey back took twice as long , what was the average speed of the trip ?
Options: a ) 24 . , b ) 34 . , c ) 36 . , d ) 42 . , e ) 44 .
Rationale: "let the time taken be = x one way distance = 51 x total distance traveled = 2 * 51 x = 102 x total time taken = x + 2 x = 3 x average speed = 102 x / 3 x = 34 answer : b"
Answer: b
Python program:
a = 1/(51)
b = 1/(51)
c = b / 2
d = a + c 
e = 1/(d)
Problem: in what time will a train 150 metres long cross an electric pole , if its speed be 122 km / hr ?
Options: a ) 2.42 , b ) 6.42 , c ) 5.42 , d ) 4.42 , e ) 3.42
Rationale: "solution speed = ( 122 x 5 / 18 ) m / sec = 33.88 m / sec time taken = ( 150 / 33.88 ) sec = 4.42 sec . answer d"
Answer: d
Python program:
a = 122 * const_0_2778
b = 150 / a
Problem: what is the sum of the greatest common factor and the lowest common multiple of 16 and 36 ?
Options: a ) 148 , b ) 222 , c ) 144 , d ) 157 , e ) 164
Rationale: "prime factorization of the given numbers 16 = 2 ^ 4 36 = 2 ^ 2 * 3 * 2 greatest common factor = 2 ^ 2 = 4 lowest common multiple = 2 ^ 4 * 3 ^ 2 = 144 sum = 4 + 144 = 148 answer a"
Answer: a
Python program:
a = 16 * 36
b = a / 4
Problem: x is a positive integer less than 100 . when x is divided by 7 , the remainder is 1 ; when x is divided by 3 , the remainder is 2 . how many x are there ?
Options: a ) 14 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "the nubmer which when divided by 7 leaves remainder 1 should be of the form 7 k + 1 this number when divided by 3 leaves remainder 2 . so , ( 7 k + 1 ) - 2 should be divisible by 3 or 7 k - 1 should be divisible by 3 . we now put the values of k starting from 0 to find first number divisible by 3 we find 1 st number at k = 1 thus smallest number will be 7 ( 1 ) + 1 = 8 now , next number will be = 8 + lcm of 37 i . e 29 now we will find number of all such values less than 500 by using the formula for last term of an a . p 8 + ( n - 1 ) 21 = 100 n = 14.42 or n = 14 answer : - a"
Answer: a
Python program:
a = reminder * (
b = a + 3 
c = b - reminder
Problem: a student has to obtain 33 % of the total marks to pass . he got 125 marks and failed by 40 marks . the maximum mark is
Options: a ) 600 , b ) 500 , c ) 400 , d ) 300 , e ) 800
Rationale: "the student got 125 marks and still failed by 40 marks = 125 + 40 = 165 therefore 33 % of the total marks = 165 100 % of the total = 165 * 100 / 33 = 55 max mark = 500 answer b"
Answer: b
Python program:
a = 125 + 40 
b = 33 / 100
c = a / b
Problem: the number of boxes in a warehouse can be divided evenly into 9 equal shipments by boat or 24 equal shipments by truck . what is the smallest number of boxes that could be in the warehouse ?
Options: a ) 27 , b ) 33 , c ) 72 , d ) 81 , e ) 162
Rationale: "answer is the lcm of 9 and 24 = 72 answer c"
Answer: c
Python program:
a = 2 * 2
b = a * 2
c = b * 3
d = c * 9
Problem: an outlet pipe empties a tank which is full in 5 hours . if the inlet pipe is kept open , which lets water in at the rate of 8 litres / min then outlet pipe would take 3 hours longer . find the capacity of the tank .
Options: a ) 8600 litres , b ) 200 litres , c ) 12800 litres , d ) 6400 litres , e ) 13200 litres
Rationale: "let the rate of outlet pipe be x liters / hour ; rate of inlet pipe is 8 litres / min , or 8 * 60 = 480 liters / hour ; net outflow rate when both pipes operate would be x - 480 liters / hour . capacity of the tank = x * 5 hours = ( x - 480 ) * ( 5 + 3 ) hours 5 x = ( x - 480 ) * 8 - - > x = 1280 - - > capacity = 5 x = 6400 liters . answer : d"
Answer: d
Python program:
a = 8 * const_60
b = 5 + 3 
c = a * b
d = c / 3
e = d * 5
Problem: a can do a piece of work in 3 hours ; b and c together can do it in 2 hours , which a and b together can do it in 2 hours . how long will c alone take to do it ?
Options: a ) 2 hours , b ) 5 hours , c ) 6 hours , d ) 4 hours , e ) 3 hours
Rationale: "a ' s 1 hour work = 1 / 3 ; ( b + c ) ' s 1 hour work = 1 / 2 ; ( a + b ) ' s 1 hour work = 1 / 2 ( a + b + c ) ' s 1 hour work = ( 1 / 3 + 1 / 2 ) = 5 / 6 c ' s 1 hour work = ( 5 / 6 - 1 / 2 ) = 1 / 3 c alone will take 3 hours to do the work . answer : e"
Answer: e
Python program:
a = 1 / 2
b = 1 / 2
c = 1 / 3
d = b - c
e = a - d
f = 1 / e
Problem: tony alone can paint a wall in 7 days and his friend roy alone can paint the same wall in 9 days . in how many days they can paint the wall working together ? round off the answer to the nearest integer .
Options: a ) 2 , b ) 4 , c ) 6 , d ) 7 , e ) 9
Rationale: sol . use formula ( xy / x + y ) so nearest value for 3.93 = 4 answer : option b
Answer: b
Python program:
a = 7 * 9
b = 7 + 9 
c = a / b
Problem: when the number 9 y 30012 is exactly divisible by 11 , what is the smallest whole number that can replace y ?
Options: a ) 1 , b ) 2 , c ) 5 , d ) 6 , e ) 8
Rationale: "the given number = 9 y 30012 sum of the odd places = 2 + 0 + 3 + 9 = 14 sum of the even places = 1 + 0 + y ( sum of the odd places ) - ( sum of even places ) = number ( exactly divisible by 11 ) 14 - ( 1 + y ) = divisible by 11 13 � y = divisible by 11 . y must be 2 , to make given number divisible by 11 . b"
Answer: b
Python program:
a = 9 - 9
Problem: a worker ' s daily wage is increased by 40 % and the new wage is $ 35 per day . what was the worker ' s daily wage before the increase ?
Options: a ) $ 20 , b ) $ 21 , c ) $ 24 , d ) $ 25 , e ) $ 28
Rationale: "let x be the daily wage before the increase . 1.4 x = $ 35 x = $ 25 the answer is d ."
Answer: d
Python program:
a = 40 / 100
b = 1 + a 
c = 35 / b
Problem: for the past n days , the average ( arithmetic mean ) daily production at a company was 60 units . if today ' s production of 90 units raises the average to 65 units per day , what is the value of n ?
Options: a ) 30 , b ) 18 , c ) 10 , d ) 9 , e ) 5
Rationale: "( average production for n days ) * n = ( total production for n days ) - - > 60 n = ( total production for n days ) ; ( total production for n days ) + 90 = ( average production for n + 1 days ) * ( n + 1 ) - - > 60 n + 90 = 65 * ( n + 1 ) - - > n = 5 . or as 30 extra units increased the average for n + 1 days by 5 units per day then 30 / ( n + 1 ) = 5 - - > n = 5 . answer : e ."
Answer: e
Python program:
a = 90 - 60
b = 65 - 60
c = a / b
d = c - 1
Problem: a 7 - digit combination lock on a safe has zero exactly 3 times , does not have the digit 1 at all . what is the probability that exactly 3 of its digits are odd ?
Options: a ) 9 / 16 , b ) 1 / 2 , c ) 1 / 3 , d ) 1 / 4 , e ) 1 / 6
Rationale: remaining number of digits after three ' 0 ' digits = 4 constraint - no more ' 0 ' and no more ' 1 ' well , these four digits can be odd or even 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 16 ways to choose 3 odd digits out of total 4 digits = 4 c 3 = 4 4 * 1 / 16 = 1 / 4 d is the answer hi ! since we are talking about remaining 4 digits . each digit can either be odd or even ( total ways to select = 2 . desired outcome = 1 ) so let ' s say we want to choose first 3 digits as odd digits and last digit as even . the probability will be : - 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 16 but out of remaining 4 digit , any 3 can be odd and one even as there are no constraints in the question . therefore , total ways of choosing 3 odd digits out of 4 total digits = 4 c 3 so , the probability = 4 * 1 / 16 = 1 / 4 answer is d
Answer: d
Python program:
a = 7 - 3
b = 1 / a
Problem: area of a square is 1 / 2 hectare . the diagonal of the square is ?
Options: a ) 250 meter
b ) 100 meter
c ) 50 √ 2 meter
d ) 50 meter
e ) 35 meter
Rationale: area = 1 / 2 hectare = 10000 / 2 m 2 = 5000 m 2 again area = 1 / 2 x ( diagonal ) 2 so 1 / 2 x ( diagonal ) 2 = 5000 m 2 diagonal 2 = 10000 diagonal = 100 answer : b
Answer: b
Python program:
a = 1 / 2
b = 100 * 100
c = a * b
d = 2 * c
e = math.sqrt(d)
Problem: the ratio of the cost price and the selling price is 4 : 5 . the profit percent is :
Options: a ) 67 % , b ) 45 % , c ) 25 % , d ) 70 % , e ) 50 %
Rationale: "c c . p . = rs . 4 x . then , s . p . = rs . 5 x gain = ( 5 x - 4 x ) = rs . x gain % = ( x * 100 ) / 4 x = 25 % ."
Answer: c
Python program:
a = 5 / 4
b = a - 1
c = b * 100
Problem: pipe a and pipe b fill water into a tank of capacity 5000 litres , at a rate of 200 l / min and 50 l / min . pipe c drains at a rate of 25 l / min . pipe a is open for 1 min and closed , then pipe b is open for 2 min and closed . further the pipe c is opened and drained for another 2 min . this process is repeated until the tank is filled . how long will it take to fill the tank ?
Options: a ) 120 , b ) 100 , c ) 140 , d ) 80 , e ) 90
Rationale: tank capacity : 5000 l , 1 st - 200 l / min for 1 min , volume filled : 200 l 2 nd - 100 l / min for 2 min , volume filled : 100 l 3 rd ( water draining ) : 25 l / min * 2 : 50 l total : ( 200 + 100 ) - 50 = 250 l filled for 1 cycle number of 250 in 5000 l tank : 1000 / 250 = 20 time taken to fill : 20 * total time = 20 * 5 = 100 ( option b )
Answer: b
Python program:
a = 1 + 2 
b = a + 2 
c = 50 * 2
d = 200 + c 
e = 25 * 2
f = d - e
g = 5000 / f
h = b * g
Problem: a can do a piece of work in 10 days and b in 20 days . they began the work together but 5 days before the completion of the work , a leaves . the work was completed in ?
Options: a ) 15 days , b ) 10 days , c ) 12 days , d ) 19 days , e ) 13 days
Rationale: b ( x â € “ 5 ) / 10 + x / 20 = 1 x = 10 days
Answer: b
Python program:
a = 1 / 10
b = 5 * a
c = 1 / 20
d = 5 * c
e = b + d 
f = 1 - e
g = 1 / 20
h = f / g
i = h + 5
Problem: a car gets 20 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 130 kilometers ?
Options: a ) 8.5 gallons , b ) 7.5 gallons , c ) 6.5 gallons , d ) 5.5 gallons , e ) 4.5 gallons
Rationale: "each 20 kilometers , 1 gallon is needed . we need to know how many 20 kilometers are there in 130 kilometers ? 130 / 20 = 6.5 * 1 gallon = 6.5 gallons correct answer c"
Answer: c
Python program:
a = 130 / 20
Problem: the diameter of a garden roller is 1.4 m and it is 2 m long . how much area will it cover in 6 revolutions ? ( use ï € = 22 â  „ 7 )
Options: a ) 40 m 2 , b ) 44 m 2 , c ) 52.8 m 2 , d ) 36 m 2 , e ) none of these
Rationale: "required area covered in 5 revolutions = 6 ã — 2 ï € rh = 6 ã — 2 ã — 22 â  „ 7 ã — 0.7 ã — 2 = 52.8 m 2 answer c"
Answer: c
Python program:
a = 22 / 7
b = 2 * a
c = 1 / 4
d = b * c
e = d * 2
f = 6 * e
Problem: at what price must an article costing rs . 200 be marked in order that after deducting 10 % from the list price . it may be sold at a profit of 20 % on the cost price ?
Options: a ) 62.5 , b ) 62.0 , c ) 266.67 , d ) 62.1 , e ) 62.2
Rationale: "cp = 200 sp = 200 * ( 120 / 100 ) = 240 mp * ( 90 / 100 ) = 240 mp = 266.67 answer : c"
Answer: c
Python program:
a = 200 * 20
b = a / 100
c = 200 + b 
d = c * 100
e = 100 - 10
f = d / e