euclaise/mathqa_programs huggingface dataset:
Problem: if y is the smallest positive integer such that 1260 multiplied by y is the square of an integer , then y must be
Options: a ) 25 , b ) 35 , c ) 60 , d ) 75 , e ) 140
Rationale: "1260 = 2 ^ 2 * 3 ^ 2 * 5 * 7 to be perfect square , we need to multiply by at least 5 * 7 = 35 . the answer is b ."
Answer: b
Python program:
a = 2 + 3 
b = a * 2
Problem: 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 1988 on her 32 nd birthday first be eligible to retire under this provision ?
Options: a ) 2003 , b ) 2004 , c ) 2005 , d ) 2006 , e ) 2007
Rationale: "she must gain at least 70 points , now she has 32 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 - - > 1988 + 19 = 2007 . answer : e ."
Answer: e
Python program:
a = 70 - 32
b = a / 2
c = 1988 + b
Problem: a coin is tossed 3 times . what is the probability of getting exactly 2 heads ?
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 3 / 8 , d ) 5 / 8 , e ) 3 / 16
Rationale: "the number of possible outcomes is 2 ^ 3 = 8 there are 3 ways to get exactly 2 heads . p ( exactly 2 heads ) = 3 / 8 the answer is c ."
Answer: c
Python program:
a = 1 / 2
b = a ** 2
c = math.comb(3, 2)
d = 1 / 2
e = c * d
f = b * e
Problem: 3 , 4.5 , 6.75 , 10.13 , 15.18 , ( . . . )
Options: a ) 60 , b ) 60.75 , c ) 22.78 , d ) 32.52 , e ) 88
Rationale: "3 ( 3 ã — 3 ) ã · 2 = 4.5 ( 4.5 ã — 3 ) ã · 2 = 6.75 ( 6.75 ã — 3 ) ã · 2 = 10.13 ( 10.18 ã — 3 ) ã · 2 = 15.18 ( 15.18 ã — 3 ) ã · 2 = 60.75 answer is c"
Answer: c
Python program:
a = negate - (
Problem: a certain protective additive increases from 45 days to 60 days the time between required maintenance checks on an industrial vehicle . by what percent is the time between maintenance checks increased by using the additive ?
Options: a ) 25 % , b ) 33 1 / 3 % , c ) 50 % , d ) 66 2 / 3 % , e ) 75 %
Rationale: "general formula for percent increase or decrease , ( percent change ) : percent = change / original ∗ 100 so , the time between maintenance checks increased by 60 − 45 / 45 ∗ 100 = 33 1 / 3 answer : b ."
Answer: b
Python program:
a = 60 - 45
b = a / 45
c = b * 100
Problem: a can run 4.5 km distance in 1 min 30 seconds , while b can run this distance in 3 min . by how much distance can a beat b ?
Options: a ) 2250 m , b ) 1000 m , c ) 1250 m , d ) 1800 m , e ) 2000 m
Rationale: a takes time 1.30 minutes = 90 sec b takes time 3 minutes = 180 sec diffrence = 180 - 90 = 90 sec now we are to find distance covered in 90 sec by b 180 sec = 4500 m 1 sec = 25 m 90 sec = 25 x 90 = 2250 m answer : a
Answer: a
Python program:
a = 1 * const_60
b = a + 30 
c = 4 * 5
d = 3 * const_60
e = c / d
f = b * e
Problem: a , b and c rents a pasture for rs . 957 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should c pay ?
Options: a ) 270 , b ) 289 , c ) 297 , d ) 255 , e ) 552
Rationale: "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 9 / 29 * 957 = 297 answer : c"
Answer: c
Python program:
a = 12 * 8
b = 16 * 9
c = a + b 
d = 18 * 6
e = c + d 
f = 957 / e
g = 16 * 9
h = f * g
Problem: a student got 74 % in math and 84 % in history . to get an overall average of 75 % , how much should the student get in the third subject ?
Options: a ) 61 % , b ) 63 % , c ) 65 % , d ) 67 % , e ) 69 %
Rationale: 74 + 84 + x = 3 * 75 x = 67 the answer is d .
Answer: d
Python program:
a = 3 * 75
b = 74 + 84 
c = a - b
Problem: the sector of a circle has radius of 7 cm and central angle 135 o . find its perimeter ?
Options: a ) 91.5 cm , b ) 92.2 cm , c ) 28.9 cm , d ) 30.5 cm , e ) 98.2 cm
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 135 / 360 * 2 * 22 / 7 * 7 ) + 2 ( 7 ) = 16.5 + 14 = 30.5 cm answer : d"
Answer: d
Python program:
a = 7 - 3
b = a * 2
c = 4 + 3 
d = b / c
e = 2 * d
f = e * 7
Problem: the width of a rectangular hall is ½ of its length . if the area of the hall is 128 sq . m , what is the difference between its length and breadth ?
Options: a ) 8 m , b ) 10 m , c ) 12 m , d ) 15 m , e ) 17 m
Rationale: "let the length of the hall be x m breadth of the hall = 1 x / 2 m area of the hall = length * breadth 128 = x * 1 x / 2 x ² = 256 x = 16 difference between the length and breadth of the hall = x - 1 x / 2 = x / 2 = 16 / 2 = 8 m answer : a"
Answer: a
Python program:
a = 1 / 2
b = 128 / a
c = math.sqrt(b)
d = c / 2
Problem: two trains running in opposite directions cross a man standing on the platform in 47 seconds and 38 seconds respectively and they cross each other in 40 seconds . the ratio of their speeds is :
Options: a ) 3 : 1 , b ) 3 : 2 , c ) 2 : 7 , d ) 3 : 25 , e ) 3 : 4
Rationale: "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 47 x meters , and length of the second train = 38 y meters . ( 47 x + 37 y ) / ( x + y ) = 40 = = > 47 x + 38 y = 40 x + 40 y = = > 7 x = 2 y = = > x / y = 2 / 7 answer : option c"
Answer: c
Python program:
a = 47 - 40
b = 40 - 38
c = a / b
Problem: a train 200 m long running at 80 kmph crosses a platform in 22 sec . what is the length of the platform ?
Options: a ) 338 , b ) 277 , c ) 350 , d ) 288 , e ) 271
Rationale: "d = 80 * 5 / 18 = 22 = 488 – 200 = 288 answer : d"
Answer: d
Python program:
a = 80 * const_0_2778
b = 22 * a
c = b - 200
Problem: a fruit seller sells mangoes at the rate of rs . 9 per kg and thereby loses 20 % . at what price per kg , he should have sold them to make a profit of 5 % ?
Options: a ) rs . 11.81 , b ) rs . 12 , c ) rs . 12.25 , d ) rs . 12.31 , e ) none
Rationale: "solution 85 : 9 = 105 : x x = ( 9 × 105 / 80 ) = rs . 11.81 hence , s . p per kg = rs . 11.81 answer a"
Answer: a
Python program:
a = 100 + 5 
b = 9 * a
c = 100 - 20
d = b / c
Problem: if the simple interest on a certain sum of money for 8 years is one – fifth of the sum , then the rate of interest per annum is
Options: a ) 4.1 % , b ) 7 % , c ) 2.5 % , d ) 2.8 % , e ) 3 %
Rationale: explanation : let the principal ( p ) be x then , simple interest ( si ) = x / 5 time ( t ) = 8 years rate of interest per annum ( r ) = ( 100 × si ) / pt = ( 100 × ( x / 5 ) / ( x × 8 ) = 20 / 8 = 2.5 % answer : option c
Answer: c
Python program:
a = 1 + 4 
b = 100 / a
c = b / 8
Problem: two pipes a and b can fill a tank in 20 and 30 minutes respectively . if both the pipes are used together , then how long will it take to fill the tank ?
Options: a ) 12 min , b ) 15 min , c ) 25 min , d ) 50 min , e ) 55 min
Rationale: "part filled by a in 1 min = 1 / 20 part filled by b in 1 min = 1 / 30 part filled by ( a + b ) in 1 min = ( 1 / 20 + 1 / 30 ) = 1 / 12 so both pipes can fill the tank in 12 minutes . answer : a"
Answer: a
Python program:
a = 20 * 100
b = 1 / 20
c = 1 / 30
d = b + c 
e = d * 2
f = 1 - e
g = f * 20
h = g * const_60
i = a + h
Problem: the captain of a cricket team of 11 members is 24 years old and the wicket keeper is 3 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 20 years , b ) 21 years , c ) 22 years , d ) 23 years , e ) 24 years
Rationale: "explanation : let the average age of the whole team by x years . 11 x â € “ ( 24 + 27 ) = 9 ( x - 1 ) 11 x â € “ 9 x = 42 2 x = 42 x = 21 . so , average age of the team is 21 years . answer b"
Answer: b
Python program:
a = 24 + 3 
b = 24 + a 
c = 3 * 3
d = b - c
e = d / 2
Problem: the sum of 111 consecutive integers is 11211 . what is the greatest integer in the set ?
Options: a ) 148 , b ) 150 , c ) 152 , d ) 154 , e ) 156
Rationale: "let x be the first integer in the set , then x + 110 is the largest integer . the sum is : x + ( x + 1 ) + ( x + 2 ) + . . . + ( x + 110 ) = 111 x + 110 * 111 / 2 = 111 ( x + 55 ) then x + 55 = 101 x = 46 the largest integer in the set is 46 + 110 = 156 the answer is e ."
Answer: e
Python program:
a = 111 - 10
b = a - 2
c = b / 4
d = c + 2 
e = d + 2 
f = e ** 2
g = 111 - 10
h = g - 2
i = h / 4
j = i + 2 
k = j + 2 
l = k + 2 
m = l ** 2
n = f + m 
o = 111 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 111 - 10
t = s - 2
u = t / 4
v = u + 2 
w = v ** 2
x = r + w 
y = n + x
Problem: according to the formula f = 9 / 5 ( c ) + 32 , if the temperature in degrees farenheit ( f ) increases by 28 , by how much does the temperature in degrees celsius ( c ) increase ?
Options: a ) 9 , b ) 15.55 , c ) 47 , d ) 48 3 / 5 , e ) 59
Rationale: you can plug in values . c = 5 / 9 * ( f - 32 ) f = 32 - - > c = 0 ; f = 32 + 28 = 60 - - > c = 5 / 9 * 28 = 15.55 . increase = 15.55 degrees . answer : b .
Answer: b
Python program:
a = 28 * 5
b = a / 9
Problem: how many positive integers less than 24 are prime numbers , odd multiples of 5 , or the sum of a positive multiple of 2 and a positive multiple of 4 ?
Options: a ) 19 , b ) 25 , c ) 24 , d ) 22 , e ) 20
Rationale: "9 prime numbers less than 28 : { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 } 2 odd multiples of 5 : { 5 , 15 } 9 numbers which are the sum of a positive multiple of 2 and a positive multiple of 4 : { 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 , 22 } notice , that 5 is in two sets , thus total # of integers satisfying the given conditions is 9 + 2 + 9 - 1 = 19 . answer : a ."
Answer: a
Python program:
a = 24 - 2
b = a - 1
c = b - 1
Problem: without stoppages , a train travels certain distance with an average speed of 250 km / h , and with stoppages , it covers the same distance with an average speed of 125 km / h . how many minutes per hour the train stops ?
Options: a ) 25 , b ) 30 , c ) 35 , d ) 40 , e ) 45
Rationale: "due to stoppages , it covers 125 km less . time taken to cover 125 km = 125 â  „ 250 h = 1 â  „ 2 h = 1 â  „ 2 ã — 60 min = 30 min answer b"
Answer: b
Python program:
a = 125 / 250
b = a * const_60
c = const_60 - b
Problem: cara took out a charge account at the general store and agreed to pay 5 % simple annual interest . if she charges $ 54 on her account in january , how much will she owe a year later , assuming she does not make any additional charges or payments ?
Options: a ) $ 55.70 , b ) $ 56.20 , c ) $ 56.70 , d ) $ 57.20 , e ) $ 57.70
Rationale: 1.05 * $ 54 = $ 56.70 the answer is c .
Answer: c
Python program:
a = 5 / 100
b = 1 + a 
c = b * 54
Problem: a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 9 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter t of liquid a was contained by the can initially ?
Options: a ) 10 , b ) 20 , c ) 21 , d ) 25 , e ) 27
Rationale: "as a : b : : 7 : 5 - - - > only option c is a multiple of 7 and hence it is a good place to start . also a : b : : 7 : 5 means that , a = ( 712 ) * total and b = ( 5 / 12 ) * total if a = 21 , b = 15 - - - > remove 9 litres - - - > you remove ( 7 / 12 ) * 9 of a - - - > a remaining = 21 - ( 7 / 12 ) * 9 = 63 / 4 similarly , for b , you remove ( 5 / 12 ) * 9 - - - > b remaining = 15 - ( 5 / 12 ) * 9 = 45 / 4 and then add 9 more litres of b - - - > 9 + 45 / 4 = 81 / 4 thus a / b ( final ratio ) = ( 45 / 4 ) / ( 81 / 4 ) = 7 : 9 , the same as the final ratio mentioned in the question . hence c is the correct answer . a / b = 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) , where 7 x and 5 x are initial quantities of a and b respectively . thus , 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) - - - > giving you x = 3 . thus a ( original ) t = 7 * 3 = 21 . c"
Answer: c
Python program:
a = 7 + 9 
b = 7 + 5 
c = 5 / b
d = c * 9
e = 9 - d
f = a * e
g = 9 * 7
h = 7 * 5
i = g - h
j = f / i
k = 7 * j
Problem: the length of a rectangle is double its width . if the length is diminished by 5 cm and the width is increased by 5 cm then its area is increased by 75 cm square . what is the length of the rectangle ?
Options: a ) 20
b ) 30
c ) 40
d ) 56
e ) 65
Rationale: sol . according to question ( l - 5 ) ( b + 5 ) - lb = 75 and l = 2 b so , b = 20 , l = 40 ans . ( c )
Answer: c
Python program:
a = 5 * 5
b = a + 75 
c = b / 5
d = 2 * c
Problem: a and b go around a circular track of length 1500 m on a cycle at speeds of 36 kmph and 54 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 120 sec , b ) 165 sec , c ) 300 sec , d ) 167 sec , e ) 168 sec
Rationale: "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 1500 / ( 36 * 5 / 18 ) , 1500 / ( 54 * 5 / 18 ) } = lcm ( 150 , 100 ) = 300 sec . answer : c"
Answer: c
Python program:
a = 54 * const_0_2778
b = 36 * const_0_2778
c = a - b
d = 1500 / c
Problem: a train 300 m long takes 9 sec to cross a man walking at 3 kmph in a direction opposite to that of the train . find the speed of the train ?
Options: a ) 100 kmph , b ) 90 kmph , c ) 120 kmph , d ) 117 kmph , e ) 125 kmph
Rationale: "let the speed of the train be x kmph speed of the train relative to man = x + 3 = ( x + 3 ) * 5 / 18 m / sec 300 / [ ( x + 3 ) * 5 / 18 ] = 9 9 ( x + 3 ) = 1080 x = 117 kmph answer is d"
Answer: d
Python program:
a = 300 / 9
b = a / const_0_2778
c = b - 3
Problem: if there are 210 workers in a factory , and on a certain day , 198 were present . calculate the percentage that showed up for work ? ( round to the nearest tenth ) .
Options: a ) 94.3 % , b ) 95.3 % , c ) 93.3 % , d ) 92.3 % , e ) 91.3 %
Rationale: 198 / 210 * 100 = 94.28 94.3 % correct answer a
Answer: a
Python program:
a = 198 / 210
b = a * 100
Problem: a car gets 40 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 210 kilometers ?
Options: a ) 8.25 gallons , b ) 7.5 gallons , c ) 6.55 gallons , d ) 5.25 gallons , e ) 4.5 gallons
Rationale: "each 40 kilometers , 1 gallon is needed . we need to know how many 40 kilometers are there in 210 kilometers ? 210 / 40 = 5.25 * 1 gallon = 5.25 gallons correct answer d"
Answer: d
Python program:
a = 210 / 40
Problem: on a certain farm the ratio of horses to cows is 4 : 1 . if the farm were to sell 15 horses and buy 15 cows , the ratio of horses to cows would then be 7 : 3 . after the transaction , how many more horses than cows would the farm own ?
Options: a ) 20 , b ) 40 , c ) 50 , d ) 60 , e ) 80
Rationale: "originally , there were 4 k horses and k cows . 3 ( 4 k - 15 ) = 7 ( k + 15 ) 12 k - 7 k = 105 + 45 5 k = 150 k = 30 the difference between horses and cows is ( 4 k - 15 ) - ( k + 15 ) = 3 k - 30 = 60 the answer is d ."
Answer: d
Python program:
a = 15 * 7
b = 15 * 3
c = a + b 
d = 4 * 3
e = d - 7
f = c / e
g = 4 * f
h = g - 15
i = 15 * 7
j = 15 * 3
k = i + j 
l = 4 * 3
m = l - 7
n = k / m
o = n + 15 
p = h - o
Problem: two pipes p and q can fill a cistern in 11 and 15 minutes respectively . both are opened together , but at the end of 3 minutes the first is turned off . how much longer will the cistern take to fill ?
Options: a ) 1 / 8 , b ) 1 / 4 , c ) 2 / 4 , d ) 10 / 11 , e ) 1 / 4
Rationale: "3 / 11 + x / 15 = 1 x = 10 10 / 11 answer : d"
Answer: d
Python program:
a = 1 / 11
b = 1 / 15
c = a + b 
d = c * 3
e = 1 - d
f = e * 15
Problem: rani bought more apples than oranges . she sells apples at ₹ 23 apiece and makes 15 % profit . she sells oranges at ₹ 10 apiece and makes 25 % profit . if she gets ₹ 653 after selling all the apples and oranges , find her profit percentage q .
Options: a ) 16.8 % , b ) 17.4 % , c ) 17.9 % , d ) 18.5 % , e ) 19.1 %
Rationale: given : selling price of an apple = 23 - - > cost price = 23 / 1.15 = 20 selling price of an orange = 10 - - > cost price = 10 / 1.25 = 8 a > o 23 * ( a ) + 10 * ( o ) = 653 653 - 23 * ( a ) has to be divisible by 10 - - > units digit has to be 0 values of a can be 1 , 11 , 21 , 31 , . . . . - - > 1 can not be the value between 11 and 21 , if a = 11 , o = 30 - - > not possible if a = 21 , o = 17 - - > possible cost price = 20 * 21 + 8 * 17 = 420 + 136 = 556 profit = 653 - 556 = 97 profit % q = ( 97 / 556 ) * 100 = 17.4 % answer : b
Answer: b
Python program:
a = 2 * 10
b = 2 * 10
c = b + 1 
d = a * c
e = 25 / 100
f = e + 1 
g = 10 / f
h = 15 + 2 
i = g * h
j = d + i 
k = 653 - j
l = 2 * 10
m = 2 * 10
n = m + 1 
o = l * n
p = 25 / 100
q = p + 1 
r = 10 / q
s = 15 + 2 
t = r * s
u = o + t 
v = k / u
w = v * 100
Problem: at a summer camp with 1,800 participants , 1 / 2 of the campers are aged 8 to 12 . next year , the number of campers aged 8 to 12 will increase by 1 / 3 . after this change , what percentage of the total 1,800 campers will the 8 - to 12 - year - olds represent ?
Options: a ) 68 % , b ) 66 % , c ) 66 2 / 3 % , d ) 60 % , e ) 70 %
Rationale: total - 1,800 participants campers are aged 8 to 12 = ( 1 / 2 ) * 1800 = 900 next year , campers are aged 8 to 12 = ( 4 / 3 ) * 900 = 1200 percentage = ( 1200 / 1800 ) * 100 = 66 2 / 3 % answer : option c
Answer: c
Python program:
a = 8 * 100
b = 1000 + a 
c = b / 2
d = 1 / 3
e = d + 1 
f = c * e
g = 8 * 100
h = 1000 + g 
i = f / h
j = i * 100
k = j * 3
l = 8 * 100
m = 1000 + l 
n = m / 2
o = 1 / 3
p = o + 1 
q = n * p
r = 8 * 100
s = 1000 + r 
t = q / s
u = t * 100
v = u * 3
w = v / 10
x = k + w
Problem: village p ’ s population is 800 greater than village q ' s population . if village q ’ s population were reduced by 500 people , then village p ’ s population would be 3 times as large as village q ' s population . what is village q ' s current population ?
Options: a ) 1100 , b ) 1150 , c ) 1200 , d ) 1250 , e ) 1300
Rationale: "p = q + 800 . p = 3 ( q - 500 ) . 3 ( q - 500 ) = q + 800 . 2 q = 2300 . q = 1150 . the answer is b ."
Answer: b
Python program:
a = 500 * 3
b = 800 + a 
c = b / 3
Problem: the sale price of a trolley bag including the sale tax is rs . 420 . the rate of sale tax is 12 % . if the shopkeeper has made a profit of 25 % , the cost price of the trolley bag is :
Options: a ) rs 625 , b ) rs 300 , c ) rs 350 , d ) rs 375 , e ) none of these
Rationale: explanation : 112 % of s . p . = 420 s . p . = rs . ( 420 x 100 / 112 ) = rs . 375 . c . p . = rs ( 100 / 125 x 375 ) = rs 300 answer : b
Answer: b
Python program:
a = 12 / 100
b = 420 * a
c = 420 - b
d = 25 / 100
e = d + 1 
f = c / e
Problem: how many bricks each measuring 20 cm x 13.25 cm x 8 cm , will be needed to build a wall 7 m x 8 m x 15.5 m
Options: a ) 5600 , b ) 4600 , c ) 4094 , d ) 7200 , e ) none of these
Rationale: "explanation : no . of bricks = volume of the wall / volume of 1 brick = ( 700 x 800 x 15.5 ) / ( 20 x 13.25 x 8 ) = 4094 answer : c"
Answer: c
Python program:
a = 7 * 8
b = a * 15
c = 20 * 13
d = c * 8
e = d / 100
f = e / 100
g = b / f
Problem: one - tenth of the students at a nursery school are 4 years old or older . if 20 students have not yet reached their third birthday , and a total of 50 students are not between 3 years old and 4 years old , how many children are in the nursery school ?
Options: a ) 150 , b ) 300 , c ) 450 , d ) 490 , e ) 620
Rationale: x / 10 students are > 4 yrs 20 students are < 3 yrs x / 10 + 20 = 50 x / 10 = 30 x = 300 answer : b
Answer: b
Python program:
a = 50 - 20
b = a * 10
Problem: if p / q = 3 / 4 then 3 p + 4 q = ?
Options: a ) 25 / 4 , b ) 25 / 2 , c ) 20 / 4 , d ) 35 / 4 , e ) 25 / 3
Rationale: 3 p + 4 q = ? divided by q , 3 ( p / q ) + 4 = x 3 * ( 3 / 4 ) + 4 = 25 / 4 answer : a
Answer: a
Python program:
a = 4 / 3
b = 3 * a
c = 4 / 3
d = 3 * c
e = b * d
f = 3 * 3
g = e + f 
h = 4 / 3
i = 3 * h
j = g / i
Problem: x and y started a business by investing rs . 36000 and rs . 42000 respectively after 4 months z joined in the business with an investment of rs . 48000 , then find share of z in the profit of rs . 13970 ?
Options: a ) 3200 , b ) 4064 , c ) 3250 , d ) 3825 , e ) 3985
Rationale: "ratio of investment , as investments is for different time . investment x number of units of time . ratio of investments x : y : z = 36000 : 42000 : 48000 = > 6 : 7 : 8 . x = 6 x 12 months = 72 , y = 7 x 12 = 84 , z = 8 x 8 = 64 = > 18 : 21 : 16 . ratio of investments = > x : y : z = 18 : 21 : 16 . investment ratio = profit sharing ratio . z = 13970 ã — 16 / 55 = rs . 4064 . share of z in the profit is rs . 4064 . option b"
Answer: b
Python program:
a = 3 * 4
b = a - 4
c = 48000 * b
d = 3 * 4
e = 36000 * d
f = 3 * 4
g = 42000 * f
h = e + g 
i = 3 * 4
j = i - 4
k = 48000 * j
l = h + k 
m = 13970 / l
n = c * m
Problem: the banker â € ™ s discount of a certain sum of money is rs . 42 and the true discount on the same sum for the same time is rs . 36 . the sum due is
Options: a ) 252 , b ) 280 , c ) 360 , d ) 450 , e ) none
Rationale: "sol . sum = b . d . * t . d . / b . d . - t . d . = rs . [ 42 * 36 / 42 - 36 ] = rs . [ 42 * 36 / 6 ] = rs . 252 answer a"
Answer: a
Python program:
a = 42 * 36
b = 42 - 36
c = a / b
Problem: the cost of 20 pens and 12 pencils is rs . 400 and the cost of 6 pens and 4 pencils is rs . 100 . find the cost of each pen ?
Options: a ) rs . 50 , b ) rs . 100 , c ) rs . 150 , d ) rs . 25 , e ) rs . 125
Rationale: "20 p + 12 q = 400 - - - ( 1 ) 6 p + 4 q = 100 8 p + 8 q = 192 - - - ( 2 ) ( 1 ) - ( 2 ) = > 8 p = 160 = > p = 50 answer : a"
Answer: a
Python program:
a = 3 * 4
b = 20 + 4 
c = 400 / b
d = a * c
Problem: two trains of equal lengths take 10 sec and 15 sec , respectively , to cross a telegraph post . if the length of each train is 120 m , in what time will they cross each other , travelling in opposite directions ?
Options: a ) 17 sec , b ) 12 sec , c ) 18 sec , d ) 19 sec , e ) 52 sec
Rationale: speed of the first train = 120 / 10 = 12 m / sec . speed of the second train = 120 / 5 = 8 m / sec . relative speed = 12 + 8 = 20 m / sec . required time = ( 120 + 120 ) / 20 = 12 sec . answer : b
Answer: b
Python program:
a = 120 + 120 
b = 120 / 10
c = 120 / 15
d = b + c 
e = a / d
Problem: if there is an equal probability of a child being born a boy or a girl , what is the probability that a couple who have 5 children have two children of the same sex and one of the opposite sex ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 1 / 4 , d ) 5 / 16 , e ) 3 / 5
Rationale: "no of ways of selecting a gender - 2 c 1 no of ways of selecting any 2 children out of 5 = 5 c 2 total possible outcomes - 2 ^ 5 ( each child can be either a girl or a boy ) probability = 2 c 1 * 5 c 2 / 2 ^ 5 = 2 * 5 / 2 * 2 * 2 * 2 * 2 = 10 / 32 = 5 / 16 ans = d"
Answer: d
Python program:
a = 2 / 5
Problem: 2 men and 3 women are lined up in a row . what is the number of cases where they stand with each other in turn ? ( the number of cases in which men ( or women ) do not stand next to each other )
Options: a ) 12 , b ) 15 , c ) 18 , d ) 21 , e ) 24
Rationale: "first arrange 3 women . 3 women can be arranged in 3 places in 3 ! ways . now w blank w blankw we have to fill the two blanks with 2 men . we can arrange 2 persons in 2 places in 2 ! ways . 3 ! * 2 ! = 12 ways . a is the answer"
Answer: a
Python program:
a = math.factorial(2)
b = math.factorial(3)
c = a * b
Problem: a constructor estimates that 3 people can paint mr khans house in 4 days . if he uses 4 people instead of 3 , how long will they take to complete the job ?
Options: a ) 2 , b ) 8 , c ) 1 , d ) 3 , e ) 4
Rationale: explanation : use formula for a work members × days = constant 3 × 4 = 4 × a a = 3 so answer is 3 days answer : d
Answer: d
Python program:
a = 4 * 3
b = 1 / a
c = b * 4
d = 1 / c
Problem: ( 0.82 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.82 ) ( power 2 ) + 0.082 + ( 0.1 ) ( power 2 ) is :
Options: a ) 0.86 , b ) 0.68 , c ) 0.96 , d ) 0.69 , e ) 0.72
Rationale: "given expression = ( 0.82 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.82 ) ( power 2 ) + ( 0.82 x 0.1 ) + ( 0.1 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.82 - 0.1 ) = 0.72 answer is e"
Answer: e
Python program:
a = 0 ** 82
b = 0 ** 1
c = a - b
d = 0 ** 82
e = d + 0 
f = 0 ** 1
g = e + f 
h = c / g