euclaise/mathqa_programs huggingface dataset:
Problem: a profit of rs . 20000 is to be distributed among a , b , c in the proportion 2 : 3 : 5 . what will be the difference between b ’ s and c ’ s shares
Options: a ) 4000 , b ) 3000 , c ) 5500 , d ) 4500 , e ) none of these
Rationale: explanation : b ' s share = rs 20000 * ( 3 / 10 ) = rs 6000 c ' s share = rs 20000 * ( 5 / 10 ) = rs 10000 difference in b ' s and c ' s shares = rs 4000 answer : a
Answer: a
Python program:
a = 2 + 3 
b = a + 5 
c = 20000 / b
d = 5 * c
e = 2 + 3 
f = e + 5 
g = 20000 / f
h = 3 * g
i = d - h
Problem: find the first term and the common ratio of a g . p whose fourth term is 250 and seventh term is 31,250
Options: a ) 2 / 5,25 , b ) 4,5 / 2 , c ) 1,16 , d ) 2,5 , e ) 1,5
Rationale: a * r ^ 3 = 250 , a * r ^ 6 = 31,250 , r ^ 3 = 31,250 / 250 = 125 r = 5 , a * 125 = 250 , a = 2 answer : d
Answer: d
Python program:
a = 250 / 2
b = const_0_25 * 100
c = a / b
d = c / 2
Problem: a sum of money deposited at c . i . amounts to rs . 6000 in 6 years and to rs . 7500 in 7 years . find the rate percent ?
Options: a ) 25 % , b ) 20 % , c ) 15 % , d ) 10 % , e ) 5 %
Rationale: "6000 - - - 1500 100 - - - ? = > 25 % answer : a"
Answer: a
Python program:
a = 7500 - 6000
b = a / 6000
c = b * 100
Problem: a dog breeder would like to make the largest profit off of his latest litter of puppies . puppies with more than 4 spots sell for more money . the last litter had 10 puppies ; 6 had 5 spots , 3 had 4 spots , and 1 had 2 spots . what % of puppies can the dog breeder expect to sell for a greater profit ?
Options: a ) 90 % , b ) 65 % , c ) 50 % , d ) 85 % , e ) 80 %
Rationale: number of dogs with profitable spots = ( 6 + 3 ) = 6 + 3 = 9 now , we need to calculate 9 is what percent of 10 . = > 9 / 10 * 100 = 90 % a
Answer: a
Python program:
a = 5 + 4 
b = a + 2 
c = 10 / b
d = c * 100
Problem: paulson spends 75 % of his income . his income is increased by 20 % and he increased his expenditure by 10 % . find the percentage increase in his savings .
Options: a ) 25 , b ) 35 , c ) 50 , d ) 20 , e ) 15
Rationale: let the original income = $ 100 . then , expenditure = $ 75 and savings = $ 25 new income = $ 120 , new expenditure = $ ( ( 110 / 100 ) * 75 ) = rs . 165 / 2 new savings = $ ( 120 - ( 165 / 2 ) ) = $ 75 / 2 increase in savings = $ ( ( 75 / 2 ) - 25 ) = $ 25 / 2 increase % = ( ( 25 / 2 ) * ( 1 / 25 ) * 100 ) % = 50 % . answer c ) 50 .
Answer: c
Python program:
a = 20 / 100
b = 1 + a 
c = 10 / 100
d = 1 + c 
e = 75 / 100
f = d * e
g = b - f
h = 75 / 100
i = 1 - h
j = g - i
k = 75 / 100
l = 1 - k
m = j / l
n = m * 100
Problem: on the average mr . jackson has 2 hours to plan for an long hour meeting he talk to his assistant 7 hours to prepare the paper work needed . how much hours should jackson and assistant has t plan for 30 min meeting ?
Options: a ) 4.5 hr , b ) 4.8 hr , c ) 4.9 hr , d ) 5.5 hr , e ) 6.5 hr
Rationale: for a 1 hour talk he took total of 9 hr time 1 hr = 9 hr ( 2 + 7 ) 30 min = 1 / 2 hr = ? so 9 * 1 / 2 div by 1 4.5 hr answer : a
Answer: a
Python program:
a = 7 / 2
b = 2 / 2
c = a + b
Problem: there are 4 red chips and 2 blue ones . when arranged in a row , they form a certain color pattern , for example rbrrb . how many color patterns ?
Options: a ) a ) 10 , b ) b ) 12 , c ) c ) 24 , d ) d ) 50 , e ) e ) 100
Rationale: using anagram method : 6 _ 5 _ 4 _ 3 _ 2 _ 1 r _ r _ r _ r _ b _ b so . . 6 ! / number of repeated letters ( 4 ! ) ( 2 ! ) = 5 ans : d
Answer: d
Python program:
a = math.factorial(4)
b = math.factorial(2)
c = a * b
Problem: the sum of the first 50 positive even integers is 2550 . what is the sum t of even integers from 102 to 200 inclusive ?
Options: a ) 5100 , b ) 7550 , c ) 10100 , d ) 15500 , e ) 20100
Rationale: "my solution is : first 50 even integers : 2 4 6 8 < . . . > integers from 102 to 200 102 104 106 108 < . . . > we notice that each integer from the second set is 100 more than the respective integer in the first set . since we have 50 even integers from 102 to 200 , then : t = 2550 + ( 100 * 50 ) = 7550 . b"
Answer: b
Python program:
a = 200 + 102 
b = a / 2
c = 200 - 102
d = c / 2
e = d + 1 
f = b * e
Problem: what should be added to 4440 so that it may become a perfect square ?
Options: a ) 44
b ) 45
c ) 46
d ) 47
e ) 49
Rationale: 67 x 67 = 4489 4489 - 4440 = 49 if added to 49 get perfect square answer = e
Answer: e
Python program:
a = 10 + 10 
b = 10 + 10 
c = a + b 
d = 10 + 10 
e = c + d 
f = 4 + 3 
g = e + f 
h = 10 + 10 
i = 10 + 10 
j = h + i 
k = 10 + 10 
l = j + k 
m = 4 + 3 
n = l + m 
o = g * n
p = o - 4440
Problem: a chemist mixes one liter of pure water with x liters of a 50 % salt solution , and the resulting mixture is a 10 % salt solution . what is the value of x ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 1 , e ) 3
Rationale: concentration of salt in pure solution = 0 concentration of salt in salt solution = 50 % concentration of salt in the mixed solution = 10 % the pure solution and the salt solution is mixed in the ratio of - - > ( 50 - 10 ) / ( 10 - 0 ) = 4 / 1 1 / x = 4 / 1 x = 1 / 4 answer : a
Answer: a
Python program:
a = 50 - 10
b = 10 / a
Problem: how many positive even integers less than 100 contain digits 3 or 9 ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 10
Rationale: "two digit numbers : 3 at tens place : 30 , 32,34 , 36,38 9 at tens place : 90 , 92,94 , 96,98 if 3 and 7 is at units place , the number cant be even total : 5 + 5 = 10 answer e"
Answer: e
Python program:
a = 3 * 2
Problem: a can contains a mixture of two liquids a and b in 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 litres of liquid a was contained by the can initially ?
Options: a ) 25 , b ) 21 , c ) 20 , d ) 10 , e ) 15
Rationale: suppose the can initially contains 7 x and 5 x litres mixtures a and b respectively quantity of a in mix . left = [ 7 x – 7 / 12 * 9 ] = [ 7 x – 21 / 4 ] quantity of b in mix . left = [ 5 x – 5 / 12 * 9 ] = [ 5 x - 15 / 4 ] therefore [ 7 x - 21 / 4 ] = 7 / 9 or 28 x - 21 = 7 / 9 [ 5 x - 15 / 4 ] + 9 20 x + 21 252 x - 189 = 140 x + 147 or 112 x = 336 , x = 3 . quantity of a in the can initially = 7 * 3 = 21 answer : b
Answer: b
Python program:
a = math.sqrt(9)
b = a * 7
Problem: in a company of 12 employees , 5 employees earn $ 36,000 , 4 employees earn $ 45,000 , and the 3 highest - paid employees earn the same amount . if the average annual salary for the 12 employees is $ 47,500 , what is the annual salary for each of the highest - paid employees ?
Options: a ) $ 60,000 , b ) $ 65,000 , c ) $ 70,000 , d ) $ 75,000 , e ) $ 80,000
Rationale: 5 * 36,000 + 4 * 45,000 + 3 x = 12 * 47,500 3 x = 570,000 - 180,000 - 180,000 3 x = 210,000 x = 70,000 the answer is c .
Answer: c
Python program:
a = 3 * 3
b = 4 + 1 
c = a * b
d = c + 2 
e = 1 / 2
f = d + e 
g = f * 12
h = 12 * 3
i = 4 + 1 
j = h * i
k = g - j
l = 3 * 3
m = 4 + 1 
n = l * m
o = n * 4
p = k - o
q = p / 3
r = q * 1000
s = r / 1000
t = s - 5
Problem: if y is 75 % greater than x , than x is what % less than y ?
Options: a ) 30.6 % , b ) 34.4 % , c ) 38.7 % , d ) 42.9 % , e ) 46.5 %
Rationale: "y = 1.75 x x = y / 1.75 = 100 y / 175 = 4 y / 7 x is 3 / 7 less which is about 42.9 % less than y . the answer is d ."
Answer: d
Python program:
a = 75 + 100 
b = 75 / a
c = b * 100
Problem: a 250 m long train is running at a speed of 55 km / hr . it crossed a platform of length 300 m in ?
Options: a ) 41.1 sec , b ) 20.2 sec , c ) 36 sec , d ) 50.4 sec , e ) none of the above
Rationale: "speed = 55 km / hr ( to convert km / hr in to m / s ) = 55 x 5 / 18 m / s distance = 250 m + 300 m ( if questions is about train crossing a post you need to consider only the length of train , ) = 550 m time = distance / speed = 550 x 18 / ( 5 x 55 ) = 36 sec ans is : c"
Answer: c
Python program:
a = 250 + 300 
b = 55 * const_0_2778
c = a / b
Problem: arjun started a business with rs . 20,000 and is joined afterwards by anoop with rs . 40 , 000 . after how many months did anoop join if the profits at the end of the year are divided equally ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: suppose anoop joined after 3 months . then , 20000 * 12 = 40000 * ( 12 – x ) = > = > x = 6 . answer : d
Answer: d
Python program:
a = 4 * 100
b = a * 100
c = b * 12
d = 2 * 100
e = d * 100
f = e * 12
g = c - f
h = 40 * 100
i = h * 10
j = g / i
Problem: when positive integer n is divided by 5 , the remainder is 1 . when n is divided by 7 , the remainder is 3 . what is the smallest positive integer k such that k + n is a multiple of 36 ?
Options: a ) 3 , b ) 4 , c ) 12 , d ) 32 , e ) 5
Rationale: "n = 5 p + 1 = 6,11 , 16,21 , 26,31 n = 7 q + 3 = 3 , 10,17 , 24,31 = > n = 36 m + 31 to get this , we need to take lcm of co - efficients of p and q and first common number in series . so we need to add 5 more to make it 36 m + 36 answer - e"
Answer: e
Python program:
a = 36 - reminder
Problem: a cubical block of metal weighs 5 pounds . how much will another cube of the same metal weigh if its sides are twice as long ?
Options: a ) 48
b ) 40
c ) 24
d ) 18
e ) 12
Rationale: for example our cube have a side 1 meter , so we have 1 cubical meter in this cube and this cubical meter weigth 5 pounds if we take cube with side 2 meters we will have 8 cubical meters in this cube 8 meters * 5 pounds = 40 pounds so answer is b and similar but more theoretical approach : if we have sides a and b than they have equal ration with their areas : a / b = a ^ 2 / b ^ 2 and they have equal ration with their volumes : a / b = a ^ 3 / b ^ 3 we have two sides 1 / 2 so their volume will be in ratio 1 / 8 weight of one cube * volume of another cube 5 * 8 = 40 so answer is b
Answer: b
Python program:
a = 2 * 4
b = 5 * a
Problem: a box contains 3 red balls and 3 black balls . one by one , every ball is selected at random without replacement . what is the probability that the fourth ball selected is black ?
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 1 / 2 , d ) 2 , e ) 2 / 3
Rationale: "my complicated version of your simple approach let the 3 black balls be bbb and 3 red balls be rrr they can be arranged in 8 slots _ _ _ _ _ _ _ _ in ( 6 ! ) / ( 3 ! x 3 ! ) if the fourth slot is black ball then the arrangement will be to fill _ _ _ b _ _ _ _ we have 5 slots and 2 black ( bb ) and 3 red ( rrr ) they can be arranged in ( 5 ! ) / ( 2 ! x 3 ! ) hence required probability = [ ( 6 ! ) / ( 3 ! x 3 ! ) ] / [ ( 5 ! ) / ( 2 ! x 3 ! ) ] = 2 d"
Answer: d
Python program:
a = 3 + 3 
b = a / 3
Problem: 3 candidates in an election and received 1136 , 5636 and 11628 votes respectively . what % of the total votes did the winning candidate gotin that election ?
Options: a ) 40 % , b ) 55 % , c ) 57 % , d ) 63.2 % , e ) 62 %
Rationale: "total number of votes polled = ( 1136 + 5636 + 11628 ) = 18400 so , required percentage = 11628 / 18400 * 100 = 63.2 % d"
Answer: d
Python program:
a = 1136 + 5636 
b = a + 11628 
c = 11628 / b
d = c * 100
Problem: the population of a town increased from 1 , 75,000 to 2 , 62,500 in a decade . the average percent increase of population per year is
Options: a ) 4.37 % , b ) 5 % , c ) 6 % , d ) 8.75 % , e ) none
Rationale: "solution increase in 10 years = ( 262500 - 175000 ) = 87500 . increase % = ( 87500 / 175000 × 100 ) % = 50 % . required average = ( 50 / 10 ) % = 5 % . answer b"
Answer: b
Python program:
a = 10 * 1000
b = a * 10
c = b - 1000
d = c - 1000
e = 2 + 3 
f = e * 100
g = d - f
h = 3 + 4 
i = h * 10
j = 2 + 3 
k = i + j 
l = k * 1000
m = g / l
n = m - 1
o = n / 10
p = o * 100
q = p + 4
Problem: there are 14 teams in a soccer league and each team plays each of the other teams once . how many games will be played in total ?
Options: a ) 87 , b ) 91 , c ) 95 , d ) 99 , e ) 103
Rationale: "14 c 2 = 91 the answer is b ."
Answer: b
Python program:
a = math.factorial(14)
b = 14 - 2
c = math.factorial(b)
d = math.factorial(2)
e = c * d
f = a / e
Problem: the decimal 0.1 is how many times greater than the decimal ( 0.0001 ) ^ 3 ?
Options: a ) 10 ^ 9 , b ) 10 ^ 10 , c ) 10 ^ 11 , d ) 10 ^ 12 , e ) 10 ^ 13
Rationale: "0.1 = 10 ^ - 1 ( 0.0001 ) ^ 3 = ( 10 ^ - 4 ) ^ 3 = 10 ^ - 12 10 ^ 11 * 10 ^ - 12 = 10 ^ - 1 the answer is c ."
Answer: c
Python program:
a = 0 ** 1
b = 0 / 1
Problem: when 52416 is divided by 312 , the quotient is 168 . what will be the quotient when 52.416 is divided by 0.168 ?
Options: a ) 5 , b ) 6 , c ) 4 , d ) 3 , e ) 8
Rationale: "for the 1 st no . there are 2 digits after decimal for the 2 nd no . there are 4 digits after decimal total no . of decimals = 6 req . no . of digits = ( n - 1 ) = ( 6 - 1 ) = 5 answer : a"
Answer: a
Python program:
a = 52 / 416
Problem: two employees a and b are paid a total of rs . 450 per week by their employer . if a is paid 150 percent of the sum paid to b , how much is b paid per week ?
Options: a ) 130 , b ) 140 , c ) 150 , d ) 170 , e ) 180
Rationale: "let the amount paid to a per week = x and the amount paid to b per week = y then x + y = 450 but x = 150 % of y = 150 y / 100 = 15 y / 10 ∴ 15 y / 10 + y = 450 ⇒ y [ 15 / 10 + 1 ] = 450 ⇒ 25 y / 10 = 450 ⇒ 25 y = 4500 ⇒ y = 4500 / 25 = rs . 180 e"
Answer: e
Python program:
a = 150 / 100
b = a + 1 
c = 450 / b
Problem: what is the probability of getting only 1 head in a single throw of four fair coins ?
Options: a ) 1 / 2 , b ) 3 / 8 , c ) 1 / 4 , d ) 1 / 5 , e ) 5 / 8
Rationale: "one possible case is httt . p ( httt ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 16 there are 4 c 1 = 4 possible cases . p ( 1 head ) = 4 * 1 / 16 = 1 / 4 the answer is c ."
Answer: c
Python program:
a = 3 + 3 
b = math.comb(a, 3)
c = 2 / b
Problem: a jogger running at 9 km / hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 3.6 sec , b ) 18 sec , c ) 36 sec , d ) 72 sec , e ) none
Rationale: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 240 + 120 = 360 m . time taken = 360 / 10 = 36 sec answer : c"
Answer: c
Python program:
a = 240 + 120 
b = 45 - 9
c = 10 / 2
d = 45 - 9
e = d / 2
f = c / e
g = b * f
h = a / g
Problem: 4 is what percent of 50 ?
Options: a ) 0.2 % , b ) 8 % , c ) 10 % , d ) 20 % , e ) 500 %
Rationale: "4 = x * 50 / 100 x = 8 % ans ; b"
Answer: b
Python program:
a = 4 / 50
b = a * 100
Problem: the ratio of the radius of two circles is 2 : 3 , and then the ratio of their areas is ?
Options: a ) 1 : 7
b ) 2 : 9
c ) 4 : 9
d ) 3 : 7
e ) 3 : 4
Rationale: r 1 : r 2 = 2 : 3 î r 1 ^ 2 : î r 2 ^ 2 r 1 ^ 2 : r 2 ^ 2 = 4 : 9 answer : c
Answer: c
Python program:
a = circle_area / (
Problem: the profit earned by selling an article for $ 832 is equal to the loss incurred when the same article is sold for $ 448 . what should be the sale price for making 55 % profit ?
Options: a ) $ 480 , b ) $ 450 , c ) $ 992 , d ) $ 870 , e ) $ 660
Rationale: "c let c . p . = $ x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 155 % of $ 640 = 150 / 100 * 640 = $ 992 ."
Answer: c
Python program:
a = 832 + 448 
b = a / 2
c = b * 55
d = c / 100
e = 832 + 448 
f = e / 2
g = d + f
Problem: what is the units digit of the expression 14 ^ 7 − 18 ^ 4 ?
Options: a ) 0 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: "units digit of 14 ^ 7 − 18 ^ 4 : consider the following unit digits : 4 ^ 1 : 4 4 ^ 2 : 6 4 ^ 3 : 4 4 ^ 4 : 6 ⇒ unit digit of 4 ^ 7 is : 4 the unit digit of 14 ^ 7 will also be 4 also : 8 ^ 1 : 8 8 ^ 2 : 4 8 ^ 3 : 2 8 ^ 4 : 6 ⇒ unit digit of 8 ^ 4 is : 6 the unit digit of 18 ^ 4 will also be 6 finally , 4 - 6 ( or 14 - 6 ) = 8 answer : e )"
Answer: e
Python program:
a = 4 + 3 
b = a + 2
Problem: for 6 - digit integer 46 x , y 12 , when x and y are drawn at random from { 3 , 58 } , what is the probability w that the integer drawn is divisible by 8 ? * a solution will be posted in two days .
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Rationale: in general , the remainder divided by integer n is the same as the remainder that up to tens of n is divided by 8 . thus , in order for 46 , x , y 12 to be divided by 8 , y 12 should be divided by 8 . amongst 3 , 5,8 , 3 and 5 can be divided by 8 . therefore , w = two out of three can be divided and the answer is d .
Answer: d
Python program:
a = 58 - 46
b = a / 6
c = b / 3
Problem: the average of 10 numbers is calculated as 46 . it is discovered later on that while calculating the average , the number 75 was incorrectly read as 25 , and this incorrect number was used in the calculation . what is the correct average ?
Options: a ) 48 , b ) 51 , c ) 60 , d ) 71 , e ) 96
Rationale: "the total sum of the numbers should be increased by 50 . then the average will increase by 50 / 10 = 5 . the correct average is 51 . the answer is b ."
Answer: b
Python program:
a = 46 * 10
b = a - 25
c = b + 75 
d = c / 10
Problem: a certain car can travel 40 minutes on a gallon of gasoline at 60 miles per hour . if the car had started with a full tank and had 8 gallons of gasoline left in its tank at the end , then what percent of the tank was used to travel 80 miles at 60 mph ?
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 40 %
Rationale: "otal time for travelling 80 miles @ 60 mph = 80 / 60 = 4 / 3 hour = 80 minutes . given , the car uses 1 gallon for every 40 minutes of driving @ 60 mph . thus in 80 minutes it will use = 2 gallons . thus , full tank = 2 + 8 = 10 gallons - - - > 2 / 10 = 20 % of the fuel used . b is the correct answer ."
Answer: b
Python program:
a = 40 * 60
b = 80 * 60
c = a / b
d = 40 * 60
e = 80 * 60
f = d / e
g = f + 8 
h = c / g
Problem: all the students of class are told to sit in circle shape . here the boy at the 10 th position is exactly opposite to 40 th boy . total number of boys in the class ?
Options: a ) 50 , b ) 45 , c ) 60 , d ) 55 , e ) 53
Rationale: "as half the circle shape consist of 40 - 10 = 30 boys , so total number of boys in full circle = 2 * 30 = 60 answer : c"
Answer: c
Python program:
a = 40 - 10
b = a * 2
Problem: in what time will a train 120 metres long cross an electric pole , if its speed be 72 km / hr ?
Options: a ) 7 sec , b ) 6 sec , c ) 8 sec , d ) 9 sec , e ) 5 sec
Rationale: "solution speed = ( 72 x 5 / 18 ) m / sec = 20 m / sec time taken = ( 120 / 20 ) sec = 6 sec . answer b"
Answer: b
Python program:
a = 72 * const_0_2778
b = 120 / a
Problem: a , b and c completed a piece of work , a worked for 6 days , b for 9 days and c for 4 days . their daily wages were in the ratio of 3 : 4 : 5 . find the daily wages of c , if their total earning was rs . 1850 ?
Options: a ) s . 125 , b ) s . 108 , c ) s . 100 , d ) s . 103 , e ) s . 102
Rationale: "3 x 4 x 5 x 6 9 4 18 x + 36 x + 20 x = 1850 74 x = 1850 = > x = 25 5 x = 125 rs . answer : a"
Answer: a
Python program:
a = 6 * 3
b = 9 * 4
c = a + b 
d = 4 * 5
e = c + d 
f = 1850 / e
g = 5 * f
Problem: a worker ' s daily wage is increased by 50 % and the new wage is $ 42 per day . what was the worker ' s daily wage before the increase ?
Options: a ) $ 22 , b ) $ 24 , c ) $ 28 , d ) $ 32 , e ) $ 36
Rationale: "let x be the daily wage before the increase . 1.5 x = $ 42 x = $ 28 the answer is c ."
Answer: c
Python program:
a = 50 / 100
b = 1 + a 
c = 42 / b
Problem: 5 ltr of water is added with 15 ltr of a solution containing 26 % of alcohol in the water . the % of alcohol in the new mixture is ?
Options: a ) 17.25 % , b ) 19 , c ) 19.5 % , d ) 21.5 % , e ) 22 %
Rationale: we have a 15 litre solution containing 26 % alcohol in water . = > quantity of alcohol in the solution = 15 ã — 26 / 100 now 5 litre of water is added to the solution . = > total quantity of the new solution = 15 + 5 = 20 percentage of alcohol in the new solution = 15 ã — 26 / 100 20 ã — 100 = 15 ã — 26 / 10020 ã — 100 = 15 ã — 1.3 / 100 = 19.5 % c
Answer: c
Python program:
a = 26 / 100
b = a * 15
c = 5 + 15 
d = b / c
e = 100 * d
Problem: a 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds . what is the length of the platform ?
Options: a ) 177 , b ) 166 , c ) 350 , d ) 198 , e ) 161
Rationale: "speed = [ 300 / 18 ] m / sec = 50 / 3 m / sec . let the length of the platform be x meters . then , x + 300 / 39 = 50 / 3 3 ( x + 300 ) = 1950 è x = 350 m . answer : c"
Answer: c
Python program:
a = 300 / 18
b = a * 39
c = b - 300
Problem: anne bought doughnuts for a class breakfast party . she bought 15 chocolate doughnuts , 12 coconut doughnuts , and 14 jam - filled doughnuts . how many doughnuts did anne buy in all ?
Options: a ) 41 , b ) 36 , c ) 39 , d ) 21 , e ) 11
Rationale: add the numbers of doughnuts . 15 + 12 + 14 = 41 . answer is a .
Answer: a
Python program:
a = 15 + 12 
b = a + 14
Problem: following an increase in prices , the price of a candy box was 10 pounds and the price of a can of soda was 6 pounds . if the price of a candy box was raised by 25 % , and the price of a can of soda was raised by 50 % . what was the price of a box of candy plus a can of soda before prices were raised ?
Options: a ) 11 . , b ) 12 , c ) 13 , d ) 14 , e ) 14.5
Rationale: "let the candy and soda before the increase be c and s respectively so increased price of can = c ( 1 + 25 / 100 ) = 10 - - - - - - - - - - - > c = 8 increase price of soda : s ( 1 + 1 / 2 ) = 6 - - - - - - - - - - - > s = 4 hence total = 8 + 4 = 12 . . hence answer : b"
Answer: b
Python program:
a = 10 * 100
b = 100 + 25 
c = a / b
d = 6 * 100
e = 100 + 50 
f = d / e
g = c + f
Problem: if a boat is rowed downstream for 500 km in 5 hours and upstream for 240 km in 6 hours , what is the speed of the boat and the river ?
Options: a ) 70 , 30 , b ) 30 , 70 , c ) 70 , 70 , d ) 30 , 30 , e ) 80 , 50
Rationale: "explanation : if x : speed of boats man in still water y : speed of the river downstream speed ( ds ) = x + y upstream speed ( us ) = x â € “ y x = ( ds + us ) / 2 y = ( ds â € “ us ) / 2 in the above problem ds = 100 ; us = 40 x = ( 100 + 40 ) / 2 = 140 / 2 = 70 km / hr y = ( 100 - 40 ) / 2 = 60 / 2 = 30 km / hr answer : a"
Answer: a
Python program:
a = 240 / 6
b = 500 / 5
c = a + b 
d = c / 2
Problem: the owner of a furniture shop charges his customer 24 % more than the cost price . if a customer paid rs . 8215 for a computer table , then what was the cost price of the computer table ?
Options: a ) 7297 , b ) 6625 , c ) 2871 , d ) 6725 , e ) 2981
Rationale: "explanation : cp = sp * ( 100 / ( 100 + profit % ) ) = 8215 ( 100 / 124 ) = rs . 6625 . answer : b"
Answer: b
Python program:
a = 24 / 100
b = 1 + a 
c = 8215 / b
Problem: set d consists of all the prime numbers between 10 and 25 . what is the range of set d ?
Options: a ) 12 , b ) 13 , c ) 16.6 , d ) 17 , e ) 23
Rationale: answer of set d is 12 = a
Answer: a
Python program:
a = 10 + 2
Problem: an amount of money is to be divided between p , q and r in the ratio of 3 : 7 : 12 . if the difference between the shares of p and q is rs . 2800 , what will be the difference between q and r ' s share ?
Options: a ) 2788 , b ) 3500 , c ) 7282 , d ) 2782 , e ) 2729
Rationale: "4 - - - 2800 5 - - - ? = > 3500 answer : b"
Answer: b
Python program:
a = 12 - 7
b = 7 - 3
c = 2800 / b
d = a * c
Problem: the price of a mobile was increased by 25 percent . the new price was then decreased by 10 percent . a single increase of what percent is equivalent to these two successive changes ?
Options: a ) 10 % , b ) 15 % , c ) 17.5 % , d ) 25 % , e ) 12.5 %
Rationale: "consider base price - $ 100 25 % increase = 1.25 * 100 = $ 125 then a 10 % decrease on new price = 0.9 * 125 = $ 112.5 so final price of radio - $ 112.5 therefore a 12.5 % increase correct option - e"
Answer: e
Python program:
a = 100 + 25 
b = a / 100
c = 100 - 10
d = c / 100
e = b * d
f = e - 1
g = f * 100