euclaise/mathqa_programs huggingface dataset:
Problem: the average speed of a car is 1 4 / 5 times the avg speed of a bike . a tractor covers 575 km in 23 hrs . how much distance will the car cover in 7 hrs if the speed of the bike is twice speed of the tractor ?
Options: a ) 400 km , b ) 500 km , c ) 360 km , d ) 550 km , e ) 630 km
Rationale: "sol . average speed of a tractor = 25 km / h the speed of a bus in an hour = 25 × 2 = 50 km the speed of a car in an hour = 9 / 5 * 50 = 90 km so , the distance covered by car in 7 h is 90 × 7 = 630 km ans . ( e )"
Answer: e
Python program:
a = 4 / 5
b = 1 + a 
c = 575 / 23
d = 2 * c
e = b * d
f = e * 7
Problem: the average of 64 numbers is 48 . if two numbers namely 35 and 45 are discarded , the average of remaining numbers is ?
Options: a ) 35.5 , b ) 37.5 , c ) 39.5 , d ) 34.5 , e ) 47.9
Rationale: total of 50 numbers = 64 * 48 = 3072 average of 62 numbers = 3072 - ( 45 + 55 ) / 62 = 2972 / 62 = 47.9 answer is e .
Answer: e
Python program:
a = 64 + 35 
b = a / 2
Problem: a caterer ordered 125 ice - cream bars and 125 sundaes . if the total price was $ 250.00 and the price of each ice - cream bar was $ 0.60 , what was the price of each sundae ?
Options: a ) $ 0.60 , b ) $ 0.80 , c ) $ 1.00 , d ) $ 1.20 , e ) $ 1.40
Rationale: "let price of a sundae = s price of ice cream bar = . 6 $ 125 * . 6 + 125 * s = 250 = > 125 * s = 175 = > s = 1.4 answer e"
Answer: e
Python program:
a = 125 * 0
b = 250 - 0
c = b / 125
Problem: the sum of ages of 5 children born at the intervals of 3 years each is 65 years . what is the age of the youngest child ?
Options: a ) 3 years , b ) 4 years , c ) 6 years , d ) 7 years , e ) 8 years
Rationale: "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 65 5 x = 35 x = 7 . age of the youngest child = x = 7 years . d )"
Answer: d
Python program:
a = 65 / 5
b = a - 3
c = b - 3
Problem: a toy train produces at least 10 different tunes when it moves around a circular toy track of radius 5 meters , at 10 meters per minute . however , the toy train is defective and it now produces only two different tunes at random . what is the probability that the toy train produces 3 music tunes of the same type ( 1 in _____ ) ?
Options: a ) 3 , b ) 9 , c ) 8 , d ) 4 , e ) 5
Rationale: 1 / 2 ^ 3 = 1 / 8 but here der r two types of tone and we need to find the odds of d train of two tones to form 3 tones consequently so 2 * 1 / 8 = 1 / 4 so ans is 4 answer : d
Answer: d
Python program:
a = 1 / 2
b = a ** 3
c = b * 2
d = 1/(c)
Problem: evaluate : 56 - 12 * 3 * 2 = ?
Options: a ) 42 , b ) 48 , c ) 62 , d ) 72 , e ) 82
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 56 - 12 * 3 * 2 = 56 - 8 = 48 correct answer b"
Answer: b
Python program:
a = 12 * 2
b = a * 2
c = 56 - b
Problem: if a - b = 3 and a ^ 2 + b ^ 2 = 31 , find the value of ab .
Options: a ) 12 , b ) 15 , c ) 10 , d ) 11 , e ) 13
Rationale: "2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 31 - 9 = 22 ab = 11 . answer is d ."
Answer: d
Python program:
a = math.sqrt(31)
b = a - 3
c = b / 2
d = 3 + c 
e = math.sqrt(31)
f = e - 3
g = f / 2
h = d * g
i = h * 2
Problem: if x , y , and z are positive real numbers such that x ( y + z ) = 132 , y ( z + x ) = 152 , and z ( x + y ) = 180 , then xyz is
Options: a ) 40 , b ) 60 , c ) 160 , d ) 100 , e ) 120
Rationale: xy + xz = 132 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 1 ) yz + yx = 152 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2 ) xz + zy = 180 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 3 ) re - writing equation 3 as follows : xz + zy = 152 + 28 xz + zy = yz + yx + 28 xz = yx + 28 . . . . . . . . . . . . . . . ( 4 ) adding ( 1 ) ( 4 ) 2 xz = 160 xz = 80 xyz has to be multiple of 80 , only 160 fits in answer = c
Answer: c
Python program:
a = 152 - 132
b = 180 - a
Problem: a polling company surveyed a certain country , and it found that 35 % of that country ’ s registered voters had an unfavorable impression of both of that state ’ s major political parties and that 20 % had a favorable impression only of party q . if one registered voter has a favorable impression of both parties for every two registered voters who have a favorable impression only of party b , then what percentage of the country ’ s registered voters have a favorable impression of both parties ( assuming that respondents to the poll were given a choice between favorable and unfavorable impressions only ) ?
Options: a ) 15 , b ) 20 , c ) 30 , d ) 35 , e ) 45
Rationale: s = 100 not ( q and b ) = 35 only q = 20 ( q and b ) / b = 1 / 2 let ( q and b ) = x only b = 2 x so now , 20 + 35 + x + 2 x = 100 x = 15 a ans
Answer: a
Python program:
a = 35 + 20 
b = 100 - a
c = b / 3
Problem: there is enough provisions for 100 girls in a hostel for 50 days . if there were 20 men less , how long will the provision last ?
Options: a ) 250 , b ) 255 , c ) 260 , d ) 265 , e ) 270
Rationale: we have , m 1 d 1 = m 2 d 2 100 * 50 = 20 * d 2 d 2 = 100 * 50 / 20 = 250 days . answer : a
Answer: a
Python program:
a = 100 * 20
b = a / 10
c = b + 50
Problem: at present the ratio between the ages of arun and deepak is 4 : 3 . after 6 years arun ' s age will be 26 years . what is the age of the deepak ?
Options: a ) 15 , b ) 20 , c ) 18 , d ) 22 , e ) 35
Rationale: "let the present age of arun and deepak be 4 x and 3 x 4 x + 6 = 26 4 x = 20 x = 5 deepak ' s age = 3 x = 15 years answer is a"
Answer: a
Python program:
a = 26 - 6
b = a * 3
c = b / 4
Problem: what is the greatest integer m for which the number 40 ! / 14 ^ m is an integer ?
Options: a ) 8 , b ) 7 , c ) 6 , d ) 5 , e ) 4
Rationale: 14 ^ m = 2 ^ m * 7 ^ m . let ' s figure out how many 7 ' s are in the prime factorization of 40 ! the multiples of 7 are : 7 , 14 , 21 , 28 , 35 . thus 7 ^ 5 will divide 40 ! but 7 ^ 6 will not . clearly 2 ^ 5 will divide 40 ! so m = 5 is the largest possible integer . the answer is d .
Answer: d
Python program:
a = 14 / 2
b = 40 / a
c = math.floor(b)
Problem: the price of a book is increased from $ 300 to $ 480 . what is the % of increase in its price ?
Options: a ) 10 % , b ) 20 % , c ) 40 % , d ) 50 % , e ) 60 %
Rationale: "explanation : change in the price = rs 480 â € “ rs 300 = rs 180 percentage of increase = change in the price initial price * 100 . percentage increase in price = ( 180 300 ) * 100 = 60 % e"
Answer: e
Python program:
a = 480 - 300
b = a / 300
c = b * 100
Problem: m and n are the x and y coordinates , respectively , of a point in the coordinate plane . if the points ( m , n ) and ( m + p , n + 21 ) both lie on the line defined by the equation x = ( y / 7 ) - ( 2 / 5 ) , what is the value of p ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: x = ( y / 7 ) - ( 2 / 5 ) , and so y = 7 x + 14 / 5 . the slope is 7 . ( n + 21 - n ) / ( m + p - m ) = 7 p = 3 the answer is c .
Answer: c
Python program:
a = 21 / 7
Problem: let a be the event that a randomly selected two digit number is divisible by 10 and let b be the event that a randomly selected two digit number is divisible by 5 . what is p ( a and b ) ?
Options: a ) 1 / 50 , b ) 1 / 30 , c ) 1 / 15 , d ) 1 / 10 , e ) 1 / 5
Rationale: p ( a and b ) = 1 / 10 * 1 / 5 = 1 / 50 the answer is a .
Answer: a
Python program:
a = 10 - 1
b = 10 - 1
c = b * 10
d = a / c
e = 10 - 1
f = e * 2
g = 10 - 1
h = g * 10
i = f / h
j = d * i
Problem: in a group of cows and hens , the number of legs are 12 more than twice the number of heads . the number of cows is :
Options: a ) 5 , b ) 6 , c ) 7 , d ) 10 , e ) 12
Rationale: "let no of cows be x , no of hens be y . so heads = x + y legs = 4 x + 2 y now , 4 x + 2 y = 2 ( x + y ) + 12 2 x = 12 x = 6 . answer : b"
Answer: b
Python program:
a = 12 - 4
Problem: find the least number which when divided by 12,24 , 36,42 leaves remainder 9,21 , 33,39 respectively .
Options: a ) 499 , b ) 501 , c ) 452 , d ) 365 , e ) 325
Rationale: "the difference of 12 - 9 = 3 , 24 - 21 = 3 , 36 - 33 = 3 , 42 - 39 = 3 lcm of 12,24 , 36,42 = 504 required number = 504 - 3 = 501 answer is b"
Answer: b
Python program:
a = math.lcm(12, 24)
b = 9 + 21
Problem: the difference between a 6 digit number and the number formed by reversing its digit is not a multiple of
Options: a ) 3 , b ) 92439 , c ) 30813 , d ) 10271 , e ) 10272
Rationale: another approach is to test a number . let ' s say the original number is 123004 so , the reversed number is 400321 the difference = 400321 - 123004 no check the answer choices 277317 is a multiple of 3,92439 , 30813,10271 10272 is not a multiple of 277317 answer : e
Answer: e
Python program:
a = 6 + 4 
b = a ** 4
Problem: sandy is younger than molly by 12 years . if their ages are in the respective ratio of 7 : 9 , how old is molly ?
Options: a ) 36 , b ) 45 , c ) 54 , d ) 63 , e ) 72
Rationale: "s = m - 12 s / m = 7 / 9 9 s = 7 m 9 ( m - 12 ) = 7 m m = 54 the answer is c ."
Answer: c
Python program:
a = 9 - 7
b = 7 / a
c = b * 12
Problem: two pipes can fill a tank in 20 minutes and 15 minutes . an outlet pipe can empty the tank in 45 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ?
Options: a ) 5 minutes , b ) 17 minutes , c ) 15 minutes , d ) 10 minutes , e ) 12 minutes
Rationale: "part of the filled by all the three pipes in one minute = 1 / 20 + 1 / 15 - 1 / 45 = ( 9 + 12 - 4 ) / 180 = 17 / 180 so , the tank becomes full in 5 minutes . answer : a"
Answer: a
Python program:
a = 1 / 20
b = 1 / 15
c = a + b 
d = 1 / 45
e = c - d
Problem: the output of a factory was increased by 10 % to keep up with rising demand . to handle the holiday rush , this new output was increased by 10 % . by approximately what percent would the output now have to be decreased in order to restore the original output ?
Options: a ) 20 % , b ) 24 % , c ) 30 % , d ) 32 % , e ) 17 %
Rationale: "the original output increases by 10 % and then 10 % . total % change = a + b + ab / 100 total % change = 10 + 10 + 10 * 10 / 100 = 21 % now , you want to change it to 0 , so , 0 = 21 + x + 21 x / 100 x = - 21 ( 100 ) / 121 = 17 % approximately answer is e"
Answer: e
Python program:
a = 100 + 10 
b = 100 + 10 
c = 10 / 100
d = b * c
e = a + d 
f = e - 100
g = f * 100
h = 100 + 10 
i = 100 + 10 
j = 10 / 100
k = i * j
l = h + k 
m = g / l
Problem: a company recently conducted a survey and found that 25,000 of its customers live in rural areas . if the number of customers who live in urban areas is 120 percent greater than the number of customers who live in rural areas , how many customers live in urban areas ?
Options: a ) 50,000 , b ) 55,000 , c ) 60,000 , d ) 65,000 , e ) 70,000
Rationale: "the number of customers in urban areas is 25,000 + 1.2 * 25,000 = 55,000 . the answer is b ."
Answer: b
Python program:
a = 4 * 2
b = 100 - a
Problem: how long does a train 110 m long running at the speed of 72 km / hr takes to cross a bridge 142 m length ?
Options: a ) 82.1 sec . , b ) 12.6 sec , c ) 19.1 sec . , d ) 17.1 sec . , e ) 42.1 sec .
Rationale: "speed = 72 * 5 / 18 = 20 m / sec total distance covered = 110 + 142 = 252 m . required time = 252 / 20 = 12.6 sec . answer : b"
Answer: b
Python program:
a = 110 + 142 
b = 72 * const_0_2778
c = a / b
Problem: 150 ml of 30 % sulphuric acid was added to approximate 400 ml of 12 % sulphuric acid solution . find the approximate concentration q of the acid in the mixture ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 6 , e ) 1 / 5
Rationale: "do not need any computation 30 % - - - - - - - - - - - 21 % - - - - - - - - - 12 % if volume of both sol . were equal the concentration q would be 21 % = 1 / 5 , but 12 % is more than 3 times only possibility is 1 / 6 d"
Answer: d
Python program:
a = 150 * 30
b = a / 100
c = 400 * 12
d = c / 100
e = b + d 
f = 150 + 400 
g = e / f
Problem: in measuring the sides of a rectangle , one side is taken 10 % in excess and other 5 % in deficit . find the error percentage in the area calculated from these measurements .
Options: a ) 3.5 % , b ) 2.4 % , c ) 3 % , d ) 4.5 % , e ) 2.6 %
Rationale: "say both sides of the rectangle are equal to 100 ( so consider that we have a square ) . in this case the area is 100 * 100 = 10,000 . now , the area obtained with wrong measurements would be 110 * 95 = 10,450 , which is 4.5 % greater than the actual area . answer : d ."
Answer: d
Python program:
a = 10 - 5
b = 10 * 5
c = b / 100
d = a - c
Problem: if 2 x + y = 7 and x + 2 y = 5 , then 4 xy / 3 = ?
Options: a ) a ) 1 , b ) b ) 2 , c ) c ) 17 / 5 , d ) d ) 18 / 5 , e ) e ) 4
Rationale: "2 * ( x + 2 y = 5 ) equals 2 x + 4 y = 10 2 x + 4 y = 10 - 2 x + y = 7 = 3 y = 3 therefore y = 1 plug and solve . . . 2 x + 1 = 7 2 x = 6 x = 3 ( 4 * 3 * 1 ) / 3 = 12 / 3 = 4 e"
Answer: e
Python program:
a = 7 * 2
b = a - 5
c = 2 * 2
d = c - 1
e = b / d
f = 7 * 2
g = f - 5
h = 2 * 2
i = h - 1
j = g / i
k = 2 * j
l = 7 - k
m = e + l 
n = m / 4
Problem: rates for having a manuscript typed at a certain typing service are $ 5 per page for the first time a page is typed and $ 4 per page each time a page is revised . if a certain manuscript has 100 pages , of which 30 were revised only once , 20 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ?
Options: a ) $ 760 , b ) $ 750 , c ) $ 810 , d ) $ 800 , e ) $ 780
Rationale: 50 pages typed 1 x 30 pages typed 2 x ( original + one revision ) 20 pages typed 3 x ( original + two revisions ) 50 ( 5 ) + 30 ( 5 + 4 ) + 20 ( 5 + 4 + 4 ) = 250 + 270 + 260 = 780 answer - e
Answer: e
Python program:
a = 100 * 5
b = 30 * 4
c = a + b 
d = 20 * 4
e = d * 2
f = c + e
Problem: 0.2 x 0.7 = ?
Options: a ) 0.0001 , b ) 0.001 , c ) 0.01 , d ) 0.14 , e ) none of these
Rationale: "explanation : 2 x 7 = 14 . sum of decimal places = 2 0.2 x 0.7 = 0.14 answer - d"
Answer: d
Python program:
a = 0 / 2
b = a * 100
Problem: the cost price of a radio is rs . 1860 and it was sold for rs . 1340 , find the loss % ?
Options: a ) 18 % , b ) 12 % , c ) 22 % , d ) 27 % , e ) 21
Rationale: "1860 - - - - 520 100 - - - - ? = > 27 % answer : d"
Answer: d
Python program:
a = 1860 - 1340
b = a / 1860
c = b * 100
Problem: in a kilometer race , a beats b by 16 meters or 10 seconds . what time does a take to complete the race ?
Options: a ) 167 sec , b ) 190 sec , c ) 176 sec , d ) 716 sec , e ) 615 sec
Rationale: "time taken by b run 1000 meters = ( 1000 * 10 ) / 16 = 625 sec . time taken by a = 625 - 10 = 615 sec . answer : e"
Answer: e
Python program:
a = 1 * 1000
b = 16 / 10
c = a / b
d = c - 10
Problem: if 15 students in a class average 75 % on an exam and 10 students average 95 % on the same exam , what is the average in percent for all 25 students ?
Options: a ) 81 % , b ) 82 % , c ) 83 % , d ) 84 % , e ) 85 %
Rationale: "( 15 * 75 + 10 * 95 ) / 25 = 83 % the answer is c ."
Answer: c
Python program:
a = 15 * 75
b = 10 * 95
c = a + b 
d = c / 25
Problem: a boat crossed a lake from north to west at the speed of 5 km / h , entered a river and covered twice as much distance going upstream at 4 km / h . it then turned around and stopped at the south shore of the lake . if it averaged 3.6 km / h that day , what was its approximate downstream speed ?
Options: a ) 2 , b ) 3 , c ) 6 , d ) 7 , e ) 8
Rationale: one way of solving this is : speed of boat on still water ( lake ) = 5 kmph speed upstream = 4 kmph = speed in still water - speed of river = > speed of river = 1 kmph = > speed downstream = speed in still water + speed of river = 5 + 1 = 6 kmph ans is c
Answer: c
Python program:
a = 5 * 2
b = a - 4
Problem: fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 9 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discounts rates is 50 percent , what is the discount rate on pony jeans ?
Options: a ) 9 % , b ) 10 % , c ) 110 % , d ) 120 % , e ) 150 %
Rationale: "x discount on pony jeans , ( 0.5 - x ) discount on fox jeans . set the equation : 3 * 15 ( 0.5 - x ) + 2 * 18 x = 9 - - > x = 1.5 = 150 % answer : e ."
Answer: e
Python program:
a = 50 / 100
b = 50 / 100
c = 18 * 2
d = b * c
e = 9 - d
f = 15 * 3
g = 18 * 2
h = f - g
i = e / h
j = a - i
k = j * 100
Problem: a shopkeeper forced to sell at cost price , uses a 750 grams weight for a kilogram . what is his gain percent ?
Options: a ) 10 % , b ) 9 % , c ) 33.33 % , d ) 12 % , e ) none of these
Rationale: shopkeeper sells 750 g instead of 1000 g . so , his gain = 1000 - 750 = 250 g . thus , % gain = ( 250 * 100 ) / 750 = 33.33 % . answer : option c
Answer: c
Python program:
a = 2 * 100
b = 100 / 2
c = a + b 
d = c / 750
e = d * 100
Problem: uba capital recently bought brand new vehicles for office use . uba capital only went for toyota and honda and bought more of toyota than honda at the ratio of 9 : 1 . if 90 % of the toyota bought and 10 % of the honda bought were suv ã ¢ â ‚ ¬ â „ ¢ s . how many suv ã ¢ â ‚ ¬ â „ ¢ s did uba capital buy in the aforementioned purchase ?
Options: a ) 82 % , b ) 64 % , c ) 28 % , d ) 69 % , e ) 80 %
Rationale: "let total no of vehicles bought be 100 , toyota 90 and honda 10 , so total number of suv ' s bought for toyota and honda respectively 90 * 90 / 100 = 81 and 10 * 10 / 100 = 1 so total 82 suv ' s were bought out of 100 vehicles bought . . so required % is 82 % answer : a"
Answer: a
Python program:
a = 9 * 1
b = 1 * 9
c = a + b 
d = 100 - c
Problem: if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 171 games will be played during the tournament . find the number of participants .
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "let p be the number of participants . pc 2 = 171 ( p ) ( p - 1 ) = 342 = 19 * 18 p = 19 the answer is e ."
Answer: e
Python program:
a = 171 * 2
b = a * 4
c = b + 1 
d = math.sqrt(c)
e = d + 1 
f = e / 2
Problem: a contest will consist of n questions , each of which is to be answered eithertrueorfalse . anyone who answers all n questions correctly will be a winner . what is the least value of n for which the probability is less than 1 / 10 that a person who randomly guesses the answer to each question will be a winner ?
Options: a ) 5 , b ) 10 , c ) 50 , d ) 100 , e ) 1000
Rationale: a contest will consist of n questions , each of which is to be answered eithertrueorfalse . anyone who answers all n questions correctly will be a winner . what is the least value of n for which the probability is less than 1 / 1000 that a person who randomly guesses the answer to each question will be a winner ? a . 5 b . 10 c . 50 d . 100 e . 1000 soln : ans is b probability that one question is answered right is 1 / 2 . now for minimum number of questions needed to take probability less than 1 / 1000 is = > ( 1 / 2 ) ^ n < 1 / 1000 n = 10 satisfies this . d
Answer: d
Python program:
a = 1 / 10
b = 1000 * a
Problem: a pipe takes a hours to fill the tank . but because of a leakage it took 3 times of its original time . find the time taken by the leakage to empty the tank
Options: a ) 50 min , b ) 60 min , c ) 90 min , d ) 80 min , e ) 70 min
Rationale: "pipe a can do a work 60 min . lets leakage time is x ; then 1 / 60 - 1 / x = 1 / 180 x = 90 min answer : c"
Answer: c
Python program:
a = 1 * 3
b = 10 * a
Problem: the average of 13 numbers is 60 . average of the first 7 of them is 56 and that of the last 7 is 61 . find the 8 th number ?
Options: a ) 39 , b ) 83 , c ) 45 , d ) 53 , e ) 64
Rationale: "sum of all the 13 numbers = 13 * 60 = 780 sum of the first 7 of them = 7 * 56 = 392 sum of the last 7 of them = 7 * 61 = 427 so , the 8 th number = 427 + 392 - 780 = 39 . answer : a"
Answer: a
Python program:
a = 8 * 61
b = 13 * 60
c = 56 * 7
d = b - c
e = a - d
Problem: a student got twice as many sums wrong as he got right . if he attempted 75 sums in all , how many did he solve correctly ?
Options: a ) 25 , b ) 16 , c ) 18 , d ) 24 , e ) 26
Rationale: "explanation : suppose the boy got x sums right and 2 x sums wrong . then , x + 2 x = 75 3 x = 75 x = 25 . answer : a"
Answer: a
Python program:
a = 1 + 2 
b = 75 / a
Problem: how much water should be added to 12 liters of a 20 % - solution of alcohol to reduce the concentration of alcohol in the solution by 75 % ?
Options: a ) 28 liters , b ) 27 liters , c ) 30 liters , d ) 32 liters , e ) 35 liters
Rationale: let x ltr water to be added 2 ltr alcohol to be represented as ( 20 ( 1 - 3 / 4 ( new soln . = 12 + x ) ) ) 2 = 5 % * ( 12 + x ) - - - - - - - - > x = 28 ans a
Answer: a
Python program:
a = 2 * 100
b = 75 / 100
c = b * 20
d = 20 - c
e = a / d
f = e - 12
Problem: a sum of money lent out at s . i . amounts to rs . 710 after 2 years and to rs . 1020 after a further period of 5 years . the sum is ?
Options: a ) s . 440 , b ) s . 586 , c ) s . 540 , d ) s . 740 , e ) s . 840
Rationale: "s . i for 5 years = ( 1020 - 710 ) = rs . 310 . s . i . for 2 years = 310 / 5 * 2 = rs . 124 . principal = ( 710 - 124 ) = rs . 586 . answer : b"
Answer: b
Python program:
a = 1020 - 710
b = a / 5
c = b * 2
d = 710 - c
Problem: there is 60 % increase in an amount in 6 years at si . what will be the ci of rs . 15,000 after 3 years at the same rate ?
Options: a ) 2372 , b ) 2572 , c ) 4542 , d ) 4965 , e ) 3972
Rationale: "let p = rs . 100 . then , s . i . rs . 60 and t = 6 years . r = 100 x 60 = 10 % p . a . 100 x 6 now , p = rs . 15000 . t = 3 years and r = 10 % p . a . c . i . = rs . 15000 x 1 + 10 3 - 1 100 = rs . 15000 x 331 1000 = 4965 . d"
Answer: d
Python program:
a = 100 * 100
b = 60 / 6
c = 100 * b
d = c * 3
e = a + d 
f = 60 / 6
g = f / 100
h = 1 + g 
i = 60 / 6
j = i / 100
k = 1 + j 
l = h * k
m = 60 / 6
n = m / 100
o = 1 + n 
p = l * o
q = e * p
r = 100 * 100
s = 60 / 6
t = 100 * s
u = t * 3
v = r + u 
w = q - v
Problem: the overall age of x and y is 10 year greater than the overall age of y and z . z is how many decades younger that x ?
Options: a ) 11 , b ) 10 , c ) 12 , d ) 17 , e ) 19
Rationale: "b 10 ( x + y ) â € “ ( y + z ) = 10 x â € “ z = 10"
Answer: b
Python program:
a = 10 / 1
Problem: a bag contains 15 red jellybeans and 15 blue jellybeans . if 3 jellybeans are removed one at a time , at random and are not replaced , what is the probability that all 3 jellybeans removed from the bag are blue ?
Options: a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 3 / 20 , e ) 3 / 10
Rationale: "method - 1 10 red jellybeans and 10 blue jellybeans total outcomes = no . of ways to choose 3 jelly bean at random out of a total 20 jellybeans = 20 c 3 = 1140 favourable outcomes = no . of ways to choose 3 jelly bean such that they are all blue out of 10 blue = 10 c 3 = 120 probability = favourable outcomes / total outcomes = 10 c 3 / 20 c 3 probability = 120 / 1140 = 2 / 19 answer : option b method - 2 probability of first jelly bean to be blue = 10 / 20 [ total 10 blue out of total 20 jellybeans ] probability of second jelly bean to be blue = 9 / 19 [ total 9 blue remaining out of total 19 jellybeans remaining ] probability of third jelly bean to be blue = 8 / 18 [ total 8 blue remaining out of total 18 jellybeans remaining ] required probability = ( 10 / 20 ) * ( 9 / 19 ) * ( 8 / 18 ) = 3 / 10 answer : option e"
Answer: e
Python program:
a = math.comb(15, 3)
b = 15 + 15 
c = math.comb(b, 3)
d = a / c
Problem: if the simple interest on a sum of money for 6 years at 12 % per annum is rs . 700 , what is the compound interest on the same sum at the rate and for the same time ?
Options: a ) 746.77 , b ) 945.77 , c ) 946.77 , d ) 246.77 , e ) 926.77
Rationale: "sum = ( 700 * 100 ) / ( 6 * 12 ) = rs . 972.22 c . i . on rs . rs . 972.22 for 6 years at 12 % = rs . 1 , 918.99 . = rs . 1 , 918.99 - 972.22 = rs . 946.77 answer : c"
Answer: c
Python program:
a = 12 / 100
b = a * 6
c = 700 / b
d = c * 12
e = d / 100
f = 12 / 100
g = f * 6
h = 700 / g
i = e + h 
j = 12 / 100
k = j * 6
l = 700 / k
m = l * 12
n = m / 100
o = 12 / 100
p = o * 6
q = 700 / p
r = n + q 
s = r * 12
t = s / 100
u = i + t 
v = 12 / 100
w = v * 6
x = 700 / w
y = u - x