euclaise/mathqa_programs huggingface dataset:
Problem: the sum of ages of 5 children born 1 year different each is 50 yrs . what is the age of the elder child ?
Options: a ) 8 , b ) 9 , c ) 16 , d ) 17 , e ) 18
Rationale: "let the ages of children be x , ( x + 1 ) , ( x + 2 ) , ( x + 3 ) and ( x + 4 ) years . then , x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) + ( x + 4 ) = 50 5 x = 40 x = 8 x + 4 = 8 + 1 = 9 answer : b"
Answer: b
Python program:
a = 1 + 4 
b = 1 + 4 
c = a + b 
d = 4 + 4 
e = c + d 
f = e + 50 
g = f / 5
Problem: right now , al and eliot have bank accounts , and al has more money than eliot . the difference between their two accounts is 1 / 12 of the sum of their two accounts . if al ’ s account were to increase by 10 % and eliot ’ s account were to increase by 15 % , then al would have exactly $ 22 more than eliot in his account . how much money does eliot have in his account right now ?
Options: a ) $ 146.6 , b ) $ 120 , c ) $ 180 , d ) $ 220 , e ) $ 260
Rationale: lets assume al have amount a in his bank account and eliot ' s bank account got e amount . we can form an equation from the first condition . a - e = 1 / 12 * ( a + e ) = = > 11 a = 13 e - - - - - - - - - - - - ( 1 ) second condition gives two different amounts , al ' s amount = 1.1 a and eliot ' s amount = 1.2 e 1.1 a = 22 + 1.15 e = = > 11 a = 220 + 11.5 e - - - - - - - ( 2 ) substituting ( 1 ) in ( 2 ) : 13 e = 220 + 11.5 e = = > 1.5 e = 220 or e = 440 / 3 = 146.6 a
Answer: a
Python program:
a = 22 * 100
b = 12 + 1 
c = b * 10
d = 100 + 15 
e = c - d
f = a / e
Problem: an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 20 - meter platform and caught it after it had traveled 52.5 meters . how many times did the ball bounce ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 3 , e ) 2
Rationale: "going down = 20 m going up = 10 - - > total = 30 going down = 10 - - > total = 40 going up = 5 - - > total = 45 going down = 5 - - > total = 50 going up = 2.5 - - > total = 52.5 ( caught ) no of bouncing = 3 answer : d"
Answer: d
Python program:
a = 20 / 2
b = a / 2
Problem: the size of a television screen is given as the length of the screen ' s diagonal . if the screens were flat , then the area of a square 21 - inch screen would be how many square inches greater than the area of a square 17 - inch screen ?
Options: a ) 2 , b ) 4 , c ) 16 , d ) 38 , e ) 76
Rationale: "pythogoras will help here ! let the sides be x and diagonal be d then d ^ 2 = 2 x ^ 2 and area = x ^ 2 now plug in the given diagonal values to find x values and then subtract the areas ans will be 21 ^ 2 / 2 - 17 ^ 2 / 2 = 152 / 2 = 76 ans e ."
Answer: e
Python program:
a = 21 ** 2
b = 17 ** 2
c = a - b
d = c / 2
Problem: in a urban village of india named ` ` owlna ' ' , 80 % people have refrigerator , 82 % people have television , 70 % people got computers and 75 % got air - conditionor . how many people ( minimum ) got all these luxury .
Options: a ) 3 % , b ) 8 % , c ) 7 % , d ) 10 % , e ) 15 %
Rationale: "c 7 % 100 - [ ( 100 - 80 ) + ( 100 - 82 ) + ( 100 - 70 ) + ( 100 - 75 ) ] = 100 - ( 20 + 18 + 30 + 25 ) = 100 - 93"
Answer: c
Python program:
a = 100 - 80
b = 100 - 82
c = a + b 
d = 100 - 70
e = c + d 
f = 100 - 75
g = e + f 
h = 100 - g
Problem: in a certain alphabet , 8 letters contain a dot and a straight line . 24 letters contain a straight line but do not contain a dot . if that alphabet has 40 letters , all of which contain either a dot or a straight line or both , how many letters contain a dot but do not contain a straight line ?
Options: a ) 4 , b ) 8 , c ) 14 , d ) 20 , e ) 28
Rationale: "we are told that all of the letters contain either a dot or a straight line or both , which implies that there are no letters without a dot and a line ( no line / no dot box = 0 ) . first we find the total # of letters with lines : 8 + 24 = 32 ; next , we find the total # of letters without line : 40 - 32 = 8 ; finally , we find the # of letters that contain a dot but do not contain a straight line : 8 - 0 = 8 . b"
Answer: b
Python program:
a = 8 + 24 
b = 40 - a
Problem: ( 18 ) 7 x ( 5832 ) - 2 ÷ ( 324 ) - 1 = ( 18 ) 7
Options: a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1
Rationale: "explanation : ( 18 ) 7 x ( 183 ) - 2 ÷ ( 182 ) - 1 ( 18 ) 7 x ( 18 ) - 6 ÷ ( 18 ) - 2 ( 18 ) 7 - 6 + 2 = ( 18 ) 3 answer : option c"
Answer: c
Python program:
a = 4 * 2
b = a - 7
Problem: if a , b , c , d , e and f are integers and ( ab + cdef ) < 0 , then what is the maximum number w of integers that can be negative ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "minimuum should be 1 maximum should be 4 : 1 out of a or b to make the multiplication negative 3 out of c , d , e or f to make the multiplication negative . negative + negative < 0 answer : c maximum will be 5 . . you dont require both the multiplicatin to be negative for entire equation to be negative . . . any one a or b can be negative to make ab negative and it can still be more ( away from 0 ) than the multiplication of 4 other - ve numbers . . . actually by writing minimum required as 1 out of 6 , you are actually meaning 5 out of 6 also possible as you will see w = 5 or 1 will give you same equation . . ans d"
Answer: d
Python program:
a = 10 / 2
b = a + 0
Problem: rajan is sixth from the left end and vinay is tenth from the right end in a row of boys . if there are 8 boys between rajan and vinay , how many boys are there in the row ?
Options: a ) 24 , b ) 66 , c ) 88 , d ) 27 , e ) 91
Rationale: explanation : number of boys in the row = ( 6 + 10 + 8 ) = 24 answer : a ) 24
Answer: a
Python program:
a = 3 * 2
b = a + 8 
c = b + 10
Problem: a man can row 6 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 . how far is the place ?
Options: a ) 2.98 , b ) 2.88 , c ) 2.82 , d ) 2.86 , e ) 2.81
Rationale: "m = 6 s = 1.2 ds = 6 + 1.2 = 7.2 us = 6 - 1.2 = 4.8 x / 7.2 + x / 4.8 = 1 x = 2.88 answer : b"
Answer: b
Python program:
a = 6 + 1 
b = 6 - 1
c = a * b
d = 6 + 1 
e = 6 - 1
f = d + e 
g = c / f
h = g * 2
Problem: find k if 64 / k = 8 .
Options: a ) 6 , b ) 7 , c ) 8 , d ) 4 , e ) 3
Rationale: "since 64 / k = 8 and 64 / 8 = 8 , then k = 8 correct answer c"
Answer: c
Python program:
a = 64 / 8
Problem: the unit digit in the product ( 445 * 534 * 999 * 234 ) is :
Options: a ) 2 , b ) 0 , c ) 6 , d ) 5 , e ) 1
Rationale: "explanation : unit digit in the given product = unit digit in ( 5 * 4 * 9 * 4 ) = 0 answer : b"
Answer: b
Python program:
a = 445 * 534
b = a * 999
c = b * 234
d = 445 * 534
e = d * 999
f = e * 234
g = 4 + 4 
h = f - g
i = c - h
Problem: the difference of two numbers is 1097 . on dividing the larger number by the smaller , we get 10 as quotient and the 17 as remainder . what is the smaller number ?
Options: a ) 230 , b ) 120 , c ) 95 , d ) 310 , e ) 320
Rationale: "solution : let the smaller number be x . then larger number = ( x + 1097 ) x + 1097 = 10 x + 17 9 x = 1080 x = 120 answer b"
Answer: b
Python program:
a = 1097 + 17 
b = 10 - 1
c = a / b
Problem: a boat running downstream covers a distance of 20 km in 2 hours while for covering the same distance upstream , it takes 5 hours . what is the speed of the boat in still water ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 1
Rationale: explanation : rate downstream = ( 20 / 2 ) kmph = 10 kmph ; rate upstream = ( 20 / 5 ) kmph = 4 kmph speed in still water = 1 / 2 ( 10 + 4 ) kmph = 7 kmph answer : b
Answer: b
Python program:
a = 20 / 2
b = 20 / 5
c = a + b 
d = c / 2
Problem: a gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same . if there are 4 rows or 5 rows or 6 rows , then no tree will be left . find the least number of trees required .
Options: a ) 30 , b ) 60 , c ) 120 , d ) 240 , e ) 480
Rationale: "the least number of trees that are required = lcm ( 4 , 5 , 6 ) = 60 . answer : b"
Answer: b
Python program:
a = 6 * 5
b = a * 4
c = b / 2
Problem: a and b can together finish a work in 40 days . they worked together for 10 days and then b left . after another 6 days , a finished the remaining work . in how many days a alone can finish the job ?
Options: a ) 10 , b ) 25 , c ) 60 , d ) 8 , e ) 20
Rationale: "a + b 10 days work = 10 * 1 / 40 = 1 / 4 remaining work = 1 - 1 / 4 = 3 / 4 3 / 4 work is done by a in 6 days whole work will be done by a in 6 * 4 / 3 = 8 days answer is d"
Answer: d
Python program:
a = 6 * 40
b = 40 - 10
c = a / b
Problem: what distance will be covered by a bus moving at 72 kmph in 30 seconds ?
Options: a ) 877 m , b ) 600 m , c ) 167 m , d ) 176 m , e ) 546 m
Rationale: "explanation : 72 kmph = 72 * 5 / 18 = 20 mps d = speed * time = 20 * 30 = 600 m . answer : b"
Answer: b
Python program:
a = 72 * const_0_2778
b = a * 30
Problem: steve traveled the first 2 hours of his journey at 40 mph and the last 2 hours of his journey at 80 mph . what is his average speed of travel for the entire journey ?
Options: a ) 53.33 mph , b ) 56.67 mph , c ) 60 mph , d ) 64 mph , e ) 66.67 mph
Rationale: "average speed = total distance / total time = ( 40 * 2 + 80 * 2 ) / ( 2 + 2 ) = 240 / 4 = 60 answer : c"
Answer: c
Python program:
a = 80 * 2
b = 40 * 2
c = a + b 
d = 2 + 2 
e = c / d
f = 100 / 2
g = f - const_0_33
h = e + g
Problem: a rectangular field is to be fenced on three sides leaving a side of 10 feet uncovered . if the area of the field is 600 sq . ft , how many feet of fencing will be required ?
Options: a ) 130 feet , b ) 22 feet , c ) 20 feet , d ) 15 feet , e ) 10 feet
Rationale: "explanation : we are given with length and area , so we can find the breadth . as length * breadth = area = > 10 * breadth = 600 = > breadth = 60 feet area to be fenced = 2 b + l = 2 * 60 + 10 = 130 feet answer : option a"
Answer: a
Python program:
a = 600 / 10
b = a * 2
c = b + 10
Problem: find the greatest number which leaves the same remainder when it divides 20 , 40 and 90 .
Options: a ) 18 , b ) 8 , c ) 12 , d ) 10 , e ) none of these
Rationale: "90 - 40 = 50 40 - 20 = 20 90 - 20 = 70 the h . c . f of 20 , 50 and 70 is 10 . answer : d"
Answer: d
Python program:
a = 40 - 20
b = a / 2
Problem: what will be the compound interest on a sum of rs . 25,000 after 3 years at the rate of 12 p . c . p . a ?
Options: a ) rs . 10111.00 , b ) rs . 10123.20 , c ) rs . 10123.00 , d ) rs . 10100.00 , e ) rs . 10110.00
Rationale: "= rs . ( 25000 x ( 1 + 12 / 100 ) ³ = rs . ( 25000 x 28 / 25 x 28 / 25 x 28 / 25 ) = rs . 35123.20 . c . i = rs ( 35123.20 - 25000 ) = rs . 10123.20 answer : b"
Answer: b
Python program:
a = 4 * 100
b = a * 100
c = 12 / 100
d = 1 + c 
e = d ** 3
f = b * e
g = 4 * 100
h = g * 100
i = f - h
Problem: a bag contains 2 white marbles and 2 black marbles . if each of 2 girls and 2 boys randomly selects and keeps a marble , what is the probability that all of the girls select the same colored marble ?
Options: a ) 1 / 35 , b ) 1 / 10 , c ) 1 / 3 , d ) 1 / 4 , e ) 1 / 5
Rationale: "first , total ways to select for all boys and girls , i . e 4 ! / ( 2 ! * 2 ! ) = 4 * 3 * 2 * 1 / 2 * 1 * 2 * 1 = 6 then there are one two way girls can have all same colors , either white or black . the number of ways in which 2 girls can select 2 white balls = 2 c 2 = 1 the number of ways in which 2 girls can select 2 black balls = 2 c 2 = 1 therefore , total favorable outcomes / total outcomes = 2 / 6 = 1 / 3 c"
Answer: c
Python program:
a = 2 + 2 
b = math.comb(a, 2)
c = 2 / b
Problem: a started a business with an investment of rs . 70000 and after 6 months b joined him investing rs . 100000 . if the profit at the end of a year is rs . 108000 , then the share of b is ?
Options: a ) 40000 , b ) 50000 , c ) 70000 , d ) 60000 , e ) 80000
Rationale: "ratio of investments of a and b is ( 70000 * 12 ) : ( 100000 * 6 ) = 7 : 20 total profit = rs . 108000 share of b = 20 / 27 ( 108000 ) = rs . 80000 answer : e"
Answer: e
Python program:
a = const_60 * 100
b = 108000 - a
Problem: matt and peter can do together a piece of work in 20 days . after they have worked together for 10 days matt stops and peter completes the remaining work in 10 days . in how many days peter complete the work separately .
Options: a ) 21 , b ) 20 , c ) 22 , d ) 23 , e ) 24
Rationale: "together they complete the job in 20 days means they complete 10 / 20 of the job after 10 days . peter completes the remaining ( 10 / 20 ) of the job in 10 days which means that the whole job ( 1 ) can be completed in x days . < = > 8 / 20 - > 10 < = > x = 10 / ( 10 / 20 ) = 20 b"
Answer: b
Python program:
a = 1 / 20
b = 10 * a
c = 1 - b
d = 10 / c
Problem: a grocer has a sale of rs . 7435 , rs . 7927 , rs . 7855 , rs . 8230 and rs . 7562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 7500 ?
Options: a ) rs . 1991 , b ) rs . 2991 , c ) rs . 3991 , d ) rs . 4991 , e ) rs . 5991
Rationale: "explanation : total sale for 5 months = rs . ( 7435 + 7927 + 7855 + 8230 + 7562 ) = rs . 39009 . required sale = rs . [ ( 7500 x 6 ) â € “ 39009 ] = rs . ( 45000 â € “ 39009 ) = rs . 5991 . answer e"
Answer: e
Python program:
a = 5 + 1 
b = a * 7500
c = 7435 + 7927 
d = c + 7855 
e = d + 8230 
f = e + 7562 
g = b - f
Problem: how many seconds will a 150 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 12 sec , b ) 30 sec , c ) 86 sec , d ) 15 sec , e ) 18 sec
Rationale: "speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 150 * 3 / 50 = 15 sec . answer : d"
Answer: d
Python program:
a = 63 - 3
b = a * const_0_2778
c = 150 / b
Problem: in a certain supermarket , a triangular display of cans is arranged in 10 rows , numbered 1 through 10 from top to bottom . each successively numbered row contains 3 more cans than the row immediately above it . if there are fewer than 150 cans in the entire display , how many cans are in the fifth row ?
Options: a ) 10 , b ) 11 , c ) 13 , d ) 14 , e ) 16
Rationale: "let x be the number of cans in row 1 . the total number of cans is x + ( x + 3 ) + . . . + ( x + 27 ) = 10 x + 3 ( 1 + 2 + . . . + 9 ) = 10 x + 3 ( 9 ) ( 10 ) / 2 = 10 x + 135 since the total is less than 150 , x must equal 1 . the number of cans in the 5 th row is 1 + 3 ( 4 ) = 13 the answer is c ."
Answer: c
Python program:
a = 3 + 3 
b = a * 3
c = 10 - 1
d = 3 * c
e = d / 2
f = e * 10
g = 150 - f
h = g / 10
i = math.floor(h)
j = b + i
Problem: an order was placed for a carpet whose length and width were in the ratio of 3 : 2 . subsequently , the dimensions of the carpet were altered such that its length and width were in the ratio 2 : 1 but were was no change in its perimeter . what is the ratio of the areas of the carpets ?
Options: a ) 7 : 5 , b ) 12 : 11 , c ) 17 : 15 , d ) 22 : 17 , e ) 27 : 25
Rationale: "let the length and width of one carpet be 3 x and 2 x . let the length and width of the other carpet be 2 y and y . 2 ( 3 x + 2 x ) = 2 ( 2 y + y ) 5 x = 3 y ( 5 / 3 ) * x = y the ratio of the areas of the carpet in both cases : = 3 x * 2 x : 2 y * y = 6 x ^ 2 : 2 y ^ 2 = 6 x ^ 2 : 2 * ( 25 / 9 ) * x ^ 2 = 54 : 50 = 27 : 25 the answer is e ."
Answer: e
Python program:
a = rectangle_area / (
Problem: mixture contains alcohol and water in the ratio 4 : 3 . if 6 liters of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture .
Options: a ) 10 , b ) 6.8 , c ) 27 , d ) 22 , e ) 29
Rationale: "let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 24 x = 4 ( 3 x + 5 ) 12 x = 20 x = 1.7 quantity of alcohol = ( 4 x 1.7 ) litres = 6.8 litres . answer : b"
Answer: b
Python program:
a = 4 * 5
b = 6 * 4
c = 3 * 4
d = b - c
e = a / d
f = e * 4
Problem: a cistern is filled by pipe a in 8 hours and the full cistern can be leaked out by an exhaust pipe b in 12 hours . if both the pipes are opened , in what time the cistern is full ?
Options: a ) 24 hrs , b ) 60 hrs , c ) 70 hrs , d ) 80 hrs , e ) 90 hrs
Rationale: time taken to full the cistern = ( 1 / 8 - 1 / 12 ) hrs = 1 / 24 = 24 hrs answer : a
Answer: a
Python program:
a = 1 / 8
b = 1 / 12
c = a - b
d = 1 / c
Problem: a and b put in rs . 300 and rs . 400 respectively into a business . a reinvests into the business his share of the first year ' s profit of rs . 238 where as b does not . in what ratio should they divide the second year ' s profit ?
Options: a ) 220 : 113 , b ) 201 : 200 , c ) 210 : 201 , d ) 100 : 99 , e ) 113 : 77
Rationale: "explanation : 3 : 4 a = 3 / 7 * 238 = 102 402 : 400 201 : 200 answer : b"
Answer: b
Python program:
a = 400 - 100
b = a + 300 
c = 300 / b
d = 3 + 2 
e = 2 * d
f = 238 + e 
g = c * f
h = 300 + g 
i = 400 - 100
j = h / i
Problem: it costs $ 2 for the first 1 / 6 hour to use the laundry machine at the laundromat . after the first ¼ hour it costs $ 15 per hour . if a certain customer uses the laundry machine for 2 hours and 25 minutes , how much will it cost him ?
Options: a ) $ 42.25 . , b ) $ 40.25 . , c ) $ 38.25 . , d ) $ 36.25 . , e ) $ 34.25
Rationale: "2 hrs 25 min = 145 min first 10 min - - - - - - > $ 2 time left is 135 min . . . now , 60 min costs $ 15 1 min costs $ 15 / 60 145 min costs $ 15 / 60 * 145 = > $ 36.25 so , total cost will be $ 36.25 + $ 2 = > $ 38.25 hence answer will be c"
Answer: c
Python program:
a = 15 * 2
b = a + 2 
c = 15 / const_60
d = 25 / 6
e = c * d
f = b + e
Problem: when positive integer x is divided by positive integer y , the remainder is 9 . if x / y = 86.12 , what is the value of y ?
Options: a ) 96 , b ) 87 , c ) 75 , d ) 25 , e ) 12
Rationale: "by the definition of a remainder , the remainder here is equal to 9 / y . the remainder in decimal form is given as . 12 therefore , 9 / y = . 12 solve for y and get 75 . c"
Answer: c
Python program:
a = math.floor(86, 12)
b = 86 - 12
c = 9 / b
Problem: a truck driver starts with the speed of 70 kmph with the truck driver decreasing speed every two hours by 10 kmph . the truck driver ' s speed does not drop below 50 kmph . in how many hours will it take the truck driver to travel 500 kms ?
Options: a ) 480 minutes , b ) 492 minutes , c ) 504 minutes , d ) 528 minutes , e ) 540 minutes
Rationale: distance covered in first two hours = 70 ã — 2 = 140 km distance covered in next two hours = 60 ã — 2 = 120 km distance covered in next two hours = 50 ã — 2 = 100 km distance covered in next two hours = 50 ã — 2 = 100 km distance covered in first eight hours 140 + 120 + 100 + 100 = 460 km remaining distance = 500 â € “ 460 = 40 km . now , this distance will be covered at the speed of 50 km / hr . â ˆ ´ time taken = 40 â  „ 50 = 4 â  „ 5 hour . total time = 8 + 4 â  „ 5 = 8 4 â  „ 5 hour answer d
Answer: d
Python program:
a = 10 / 2
b = a / 2
c = 70 / b
d = c ** 2
Problem: a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 57.76 , the number of the member is the group is :
Options: a ) 57 , b ) 76 , c ) 77 , d ) 87 , e ) 97
Rationale: "money collected = ( 57.76 x 100 ) paise = 5776 paise numbers of members = 5776 squareroot = 76 answer b"
Answer: b
Python program:
a = 57 * 76
b = math.sqrt(a)
Problem: an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 16 - meter platform and caught it after it had traveled 44 meters . how many times did the ball bounce ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 3 , e ) 9
Rationale: "going down = 16 m going up = 8 - - > total = 24 going down = 8 - - > total = 32 going up = 4 - - > total = 36 going down = 4 - - > total = 40 going up = 2 - - > total = 42 going down = 2 - - > total = 44 ( caught ) no of bounce = 3 . . answer : d"
Answer: d
Python program:
a = 16 / 2
b = a / 2
Problem: how many cubes of edge 2 dm can be cut out of a meter cube ?
Options: a ) 296
b ) 289
c ) 270
d ) 125
e ) 278
Rationale: 1 * 1 * 1 = 2 / 10 * 2 / 10 * 2 / 10 * x x = 125 answer : d
Answer: d
Python program:
a = volume_cube / (
Problem: length of a rectangular plot is 20 mtr more than its breadth . if the cost of fencing the plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
Options: a ) 59 m , b ) 60 m , c ) 80 m , d ) 82 m , e ) 84 m
Rationale: "let breadth = x metres . then , length = ( x + 18 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 18 ) + x ] = 200 2 x + 18 = 100 2 x = 82 x = 41 . hence , length = x + 18 = 59 m a"
Answer: a
Python program:
a = 5300 / 26
b = 2 * 20
c = a + b 
d = c / 4
Problem: a cistern is filled by pipe a in 16 hours and the full cistern can be leaked out by an exhaust pipe b in 20 hours . if both the pipes are opened , in what time the cistern is full ?
Options: a ) 50 hrs , b ) 60 hrs , c ) 70 hrs , d ) 80 hrs , e ) 90 hrs
Rationale: "time taken to full the cistern = ( 1 / 16 - 1 / 20 ) hrs = 1 / 80 = 80 hrs answer : d"
Answer: d
Python program:
a = 1 / 16
b = 1 / 20
c = a - b
d = 1 / c
Problem: village x has a population of 76000 , which is decreasing at the rate of 1200 per year . village y has a population of 42000 , which is increasing at the rate of 800 per year . in how many years will the population of the two villages be equal ?
Options: a ) 15 , b ) 17 , c ) 11 , d ) 18 , e ) 13
Rationale: "let the population of two villages be equal after p years then , 76000 - 1200 p = 42000 + 800 p 2000 p = 34000 p = 17 answer is b ."
Answer: b
Python program:
a = 76000 - 42000
b = 800 + 1200 
c = a / b
Problem: average of 10 matches is 34 , how many runs one should should score to increase his average by 5 runs .
Options: a ) a ) 70 , b ) b ) 76 , c ) c ) 78 , d ) d ) 89 , e ) e ) 88
Rationale: "explanation : average after 11 innings should be 39 so , required score = ( 11 * 39 ) - ( 10 * 34 ) = 429 - 340 = 89 answer : option d"
Answer: d
Python program:
a = 34 + 5 
b = 10 + 1 
c = a * b
d = 10 * 34
e = c - d
Problem: two pipes can fill a cistern in 14 and 16 hours respectively . the pipes are opened simultaneously and it is found that due to leakage in the bottom , 32 minutes extra are taken for the cistern to be filled up . if the cistern is full , in what time would the leak empty it ?
Options: a ) 110 hours , b ) 112 hours , c ) 115 hours , d ) 100 hours , e ) none of these
Rationale: cistern filled by both pipes in one hour = 1 ⁄ 14 + 1 ⁄ 16 = 15 ⁄ 112 th ∴ both pipes filled the cistern in 112 ⁄ 15 hrs . now , due to leakage both pipes filled the cistern in 112 ⁄ 15 + 32 ⁄ 60 = 8 hrs . ∴ due to leakage , filled part in one hour 1 ⁄ 8 ∴ part of cistern emptied , due to leakage in one hour = 15 ⁄ 112 - 1 ⁄ 8 = 1 ⁄ 112 th ∴ in 112 hr , the leakage would empty the cistern . answer b
Answer: b
Python program:
a = 14 * 16
b = a / 2
c = 14 + 16 
d = c / 2
e = 16 / 2
f = d * e
g = 14 * 16
h = g / 2
i = f - h
j = b * i
k = 14 + 16 
l = k / 2
m = 16 / 2
n = l * m
o = 14 * 16
p = o / 2
q = n - p
r = j / q
Problem: the cost price of a radio is rs . 1500 and it was sold for rs . 1110 , find the loss % ?
Options: a ) 18 , b ) 16 , c ) 26 , d ) 17 , e ) 11
Rationale: explanation : 1500 - - - - 390 100 - - - - ? = > 26 % answer : c
Answer: c
Python program:
a = 1500 - 1110
b = a / 1500
c = b * 100
Problem: a restaurant spends one quarter of its monthly budget for rent and quarter of the rest for food and beverages . what percentage of the budget does the restaurant spend for food and beverages ?
Options: a ) 23.5 % , b ) 32.5 % , c ) 35 % , d ) 18.75 % , e ) 20 %
Rationale: spend on rent = 1 / 4 spend on food and beverage = 1 / 4 of remaining = 1 / 4 * 3 / 4 = 3 / 16 so 3 / 16 = 18.75 % d is the answer
Answer: d
Python program:
a = 1 / 4
b = 1 - a
c = 1 / 4
d = b * c
e = d * 100