euclaise/mathqa_programs huggingface dataset:
Problem: a square and an equilateral triangle have the same perimeter . what is the ratio of the area of the circle circumscribing the square to the area of the circle inscribed in the triangle ?
Options: a ) 9 : 8
b ) 15 : 8
c ) 27 : 8
d ) 8 : 9
e ) 8 : 15
Rationale: let x be side of square perimeter of square = 4 x = perimeter of triangle = 3 * side of triangle so side of eq . triangle = ( 4 / 3 ) * x diameter of circle circumscribing the square = sqrt ( 2 ) * x area of circle circumscribing the square = pi * ( sqrt ( 2 ) * x ) ^ 2 / 4 = ( pi / 2 ) * x ^ 2 - - - - ( 1 ) to find radius of the circle inscribed in the triangle area of triangle = r * s = sqrt ( 3 ) / 4 * ( 4 x / 3 ) ^ 2 now s = ( 4 / 3 ) * x + ( 4 / 3 ) * x + ( 4 / 3 ) * x / 2 = 2 x so sqrt ( 3 ) / 4 * ( 4 x / 3 ) ^ 2 = r * 2 x gives r = { 2 / 3 * ( 3 ^ 1 / 2 ) } * x area of the circle inscribed in the triangle = pi * [ { 2 / 3 * ( 3 ^ 1 / 2 ) } * x ] ^ 2 = pi * ( 4 / 27 ) * x ^ 2 - - - - - - - ( 2 ) so reqd ratio = eqn ( 1 ) / eqn ( 2 ) = [ ( pi / 2 ) * x ^ 2 ] / [ pi * ( 4 / 27 ) * x ^ 2 ] = 27 / 8 so reqd ratio = 27 : 8 answer : c
Answer: c
Python program:
a = 3 * 10
b = a - 3
c = 4 * 2
d = b / c
Problem: 10 is subtracted from 50 % of a number , the result is 25 . find the number ?
Options: a ) 75 , b ) 70 , c ) 35 , d ) 170 , e ) 50
Rationale: "( 50 / 100 ) * x â € “ 10 = 25 5 x = 350 x = 70 answer : b"
Answer: b
Python program:
a = 10 + 25 
b = 50 / 100
c = a / b
Problem: a bag holds 3 red marbles and 3 green marbles . if you removed two randomly selected marbles from the bag , without replacement , what is the probability that both would be red ?
Options: a ) 1 / 10 , b ) 1 / 5 , c ) 3 / 10 , d ) 2 / 5 , e ) 1 / 2
Rationale: "given : 3 r and 3 g marbles required : probability that 2 marbles removed without replacement are both red initially we have to pick one red from a total of 3 red and 3 green marbles after one red has been picked , we need to pick 1 red from a total of 2 red and 3 green marbles . p ( both red ) = ( 3 / 6 ) * ( 2 / 5 ) = 1 / 5 option b"
Answer: b
Python program:
a = math.comb(3, 3)
b = 2 + 0 
c = math.comb(b, 2)
d = a / c
Problem: a cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 5 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 5.2 hrs , b ) 2.9 hrs , c ) 1.9 hrs , d ) 7.5 hrs , e ) 1.4 hrs
Rationale: "net part filled in 1 hour = ( 1 / 3 - 1 / 5 ) = 2 / 15 the cistern will be filled in 15 / 2 hrs i . e . , 7.5 hrs . answer : d"
Answer: d
Python program:
a = 1 / 3
b = 1 / 5
c = a - b
d = 1 / c
Problem: the value of a machine depreciates at 20 % per annum . if its present value is rs . 1 , 50,000 , at what price should it be sold after two years such that a profit of rs . 24,000 is made ?
Options: a ) 328897 , b ) 120000 , c ) 877888 , d ) 277768 , e ) 188871
Rationale: "the value of the machine after two years = 0.8 * 0.8 * 1 , 50,000 = rs . 96,000 sp such that a profit of rs . 24,000 is made = 96,000 + 24,000 = rs . 1 , 20,000 answer : b"
Answer: b
Python program:
a = 20 / 100
b = 1 - a
c = 20 / 100
d = 1 - c
e = b * d
f = 100 * 100
g = math.sqrt(100)
h = f * g
i = math.sqrt(100)
j = i / 2
k = j * 100
l = k * 100
m = h + l 
n = e * m
o = 20 + 2 
p = o * 100
q = math.sqrt(100)
r = p * q
s = n + r
Problem: a tank can supply water to a village for 100 days . if a leak at the bottom of the tank drains out 10 liters per day , the supply lasts for 75 days only . for how many days will the supply last if the leak drains out 20 liters per day ?
Options: a ) 50 , b ) 60 , c ) 65 , d ) 70 , e ) 72
Rationale: "losing 10 liters per day results in a loss of 750 liters in 75 days . so , those 750 liters were for 25 days , making daily consumption of the village 30 liters per day . thus the capacity of the tank is 30 * 100 = 3000 liters . losing 20 liters plus 30 liters gives 50 liters per day . at this rate the supply will last 3000 / 50 = 60 days . the answer is b ."
Answer: b
Python program:
a = 10 * 75
b = 100 - 75
c = a / b
d = c * 100
e = 10 * 75
f = 100 - 75
g = e / f
h = 20 + g 
i = d / h
Problem: if x + y = 2 x + 2 z , x - 2 y = 2 z and x + y + z = 21 , what is the value of y / z ?
Options: a ) - 4 . , b ) - 2 . , c ) - 1.7 . , d ) 3 . , e ) 2.5 .
Rationale: x + y = 2 x + 2 z y = x + 2 z - - - - - - - - - - 1 x - 2 y = 2 z x - 2 z = 2 y - - - - - - - - - 2 subtracting equation 1 from equation 2 - 4 z = y y / z = - 4 a is the answer
Answer: a
Python program:
a = 21 / 10
Problem: a 300 meter long train crosses a platform in 36 seconds while it crosses a signal pole in 18 seconds . what is the length of the platform ?
Options: a ) 300 m , b ) 278 m , c ) 350 m , d ) 228 m , e ) 282 m
Rationale: "speed = [ 300 / 18 ] m / sec = 50 / 3 m / sec . let the length of the platform be x meters . then , x + 300 / 36 = 50 / 3 3 ( x + 300 ) = 1800 è x = 300 m . answer : a"
Answer: a
Python program:
a = 300 / 18
b = a * 36
c = b - 300
Problem: the ratio of pens to pencils is 5 to 6 . there are 9 more pencils than pens . how many pencils are there ?
Options: a ) 36 , b ) 42 , c ) 48 , d ) 54 , e ) 60
Rationale: let the number of pens be 5 x and the number of pencils be 6 x . 6 x - 5 x = 9 x = 9 the number of pencils is 54 . the answer is d .
Answer: d
Python program:
a = 9 * 5
b = a + 9
Problem: the area of a rectangular field is equal to 300 square meters . its perimeter is equal to 70 meters . find the width of this rectangle .
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: "l * w = 300 : area , l is the length and w is the width . 2 l + 2 w = 70 : perimeter l = 35 - w : solve for l ( 35 - w ) * w = 300 : substitute in the area equation w = 15 and l = 20 : solve for w and find l using l = 35 - w . correct answer c"
Answer: c
Python program:
a = 70 / 2
b = 70 / 2
c = 70 / 2
d = b * c
e = 4 * 300
f = d - e
g = math.sqrt(f)
h = a - g
i = h / 2
Problem: if the average of 10 digits is 80 and the average of 6 of them is 58 , calculate the average of the remaining 4 numbers ?
Options: a ) 119 , b ) 117 , c ) 116 , d ) 113 , e ) 115
Rationale: "explanation : total of the 10 digits - 10 * 80 = 800 total of the 6 digits - 6 * 58 = 348 total of the remaining 4 digits - 800 - 348 = 452 average of the remaining 4 numbers = 452 / 4 = 113 answer : d"
Answer: d
Python program:
a = 10 * 80
b = 6 * 58
c = a - b
d = c / 4
Problem: 1 / 2 is what percent of 1 / 3
Options: a ) 150 % , b ) 200 % , c ) 250 % , d ) 300 % , e ) 400 %
Rationale: "explanation : 1 / 2 / 1 / 3 * 100 = 1 / 2 * 3 / 1 * 100 = 150 % answer : option a"
Answer: a
Python program:
a = 1 / 2
Problem: 39 persons can repair a road in 12 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 15 , e ) 14
Rationale: "first codition = total hours to complete the work = 39 persons * 12 days * 5 hr second codition = total hours to complete the work = 30 persons * x days * 6 hr since the work is still the same so 39 * 12 * 5 = 30 * x * 6 x = 13 answer : c"
Answer: c
Python program:
a = 39 * 12
b = a * 5
c = 30 * 6
d = b / c
Problem: 2 : 3 : : 23 : ?
Options: a ) 25 , b ) 28 , c ) 22 , d ) 29 , e ) 30
Rationale: "d 29 3 is the next prime number after 2 . similarly , 29 is the next prime number after 23 ."
Answer: d
Python program:
a = 2 / 3
b = 23 * a
Problem: the product of two numbers is 220 and the sum of their squares is 289 . the sum of the number is ?
Options: a ) a ) 23 , b ) b ) 25 , c ) c ) 27 , d ) d ) 31 , e ) e ) 35
Rationale: "let the numbers be x and y . then , xy = 220 and x 2 + y 2 = 289 . ( x + y ) 2 = x 2 + y 2 + 2 xy = 289 + ( 2 x 220 ) = 729 x + y = 27 . option c"
Answer: c
Python program:
a = 2 * 220
b = 289 - a
c = math.sqrt(b)
d = c ** 2
e = 4 * 220
f = d + e 
g = math.sqrt(f)
Problem: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 300 resolutions .
Options: a ) 421 m , b ) 422 m , c ) 423 m , d ) 424 m , e ) 425 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 300 resolutions . = 300 * 2 * 22 / 7 * 22.4 = 42200 cm = 422 m answer : b"
Answer: b
Python program:
a = 3 + 4 
b = a * 3
c = b + 1 
d = 3 + 4 
e = c / d
f = e * 22
g = f * 2
h = g * 300
i = h / 100
Problem: the ratio between x and y is 7 / 9 ; x is increased by 4 and y is decreased by 4 , what is the ratio between the new values of x and y ?
Options: a ) 7 / 9 , b ) 14 / 9 , c ) 7 / 18 , d ) 11 / 13 , e ) it can not be determined
Rationale: "ratio = 7 k / 9 k = 7 / 9 , 14 / 18 , etc . x is increased by 4 and y is decreased by 4 - - > ( 7 k + 4 ) / ( 9 k - 4 ) new ratio can be 11 / 15 , 18 / 14 , etc . answer : e"
Answer: e
Python program:
a = 7 * 9
b = 9 * 7
c = a / b
Problem: an outlet pipe empties a tank which is full in 10 hours . if the inlet pipe is kept open , which lets liquid in at the rate of 8 litres / min then outlet pipe would take 6 hours longer . find the capacity of the tank .
Options: a ) 8600 litres , b ) 12800 litres , c ) 12100 litres , d ) 11200 litres , e ) 13200 litres
Rationale: "let the rate of outlet pipe be x liters / hour ; rate of inlet pipe is 8 litres / min , or 8 * 60 = 480 liters / hour ; net outflow rate when both pipes operate would be x - 480 liters / hour . capacity of the tank = x * 10 hours = ( x - 480 ) * ( 10 + 6 ) hours 10 x = ( x - 480 ) * 16 - - > x = 1280 - - > capacity = 10 x = 12800 liters . answer : b"
Answer: b
Python program:
a = 8 * const_60
b = 10 + 6 
c = a * b
d = c / 6
e = d * 10
Problem: karen places a bet with tom that she will beat tom in a car race by 4 miles even if karen starts 4 minutes late . assuming that karen drives at an average speed of 60 mph and tom drives at an average speed of 45 mph , how many y miles will tom drive before karen wins the bet ?
Options: a ) 15 , b ) 18 , c ) 21 , d ) 24 , e ) 27
Rationale: "let k and t be the speeds of karen and tom respectively . t be the time that karen will travel - - - - > t + 4 / 60 will be the total time tom will travel by the time the distance between karen and tom is 4 miles . thus , per the question , k ( t ) - t ( t + 4 / 60 ) = 4 - - - > t = 7 / 15 hours thus the distance traveled by tom when karen is 4 miles ahead of him y : t * ( t + 4 / 60 ) = 45 ( 7 / 15 + 4 / 60 ) = 24 miles . d is the correct answer ."
Answer: d
Python program:
a = 45 / 60
b = a * 4
c = b + 4 
d = 60 / 60
e = 45 / 60
f = d - e
g = c / f
h = g - 4
Problem: ( 3108 + 6160 ) / 28
Options: a ) 380 , b ) 350 , c ) 331 , d ) 310 , e ) none of these
Rationale: "explanation : as per bodmas rule , first we will solve the equation in bracket then we will go for division = ( 9268 ) / 28 = 331 option c"
Answer: c
Python program:
a = 4 + 1 
b = a ** 4
c = 3108 * b
Problem: for a certain art exhibit , a museum sold admission tickets to a group of 30 people every 5 minutes from 9 : 00 in the morning to 5 : 55 in the afternoon , inclusive . the price of a regular admission ticket was $ 8 and the price of a student ticket was $ 4 . if on one day 3 times as many regular admission tickets were sold as student tickets , what was the total revenue from ticket sales that day ?
Options: a ) $ 20960 , b ) $ 21920 , c ) $ 22680 , d ) $ 28500 , e ) $ 29160
Rationale: "from 9 : 00 in the morning to 5 : 55 in the afternoon , inclusive there are 9 * 12 = 108 five - minute intervals , thus total of 108 * 30 tickets were sold . say x student and 3 x regular tickets were sold , then x + 3 x = 108 * 30 - - > x = 27 * 30 and 3 x = 3 * ( 27 * 30 ) = 27 * 90 . therefore , the total revenue from ticket sales that day was 27 * 30 * 4 + 27 * 90 * 8 = $ 22,680 . answer : c ."
Answer: c
Python program:
a = 12 + 5 
b = a - 9
c = b + 1 
d = c * 12
e = d * 30
f = 3 + 1 
g = e / f
h = g * 3
i = h * 8
j = 12 + 5 
k = j - 9
l = k + 1 
m = l * 12
n = m * 30
o = 3 + 1 
p = n / o
q = p * 4
r = i + q
Problem: a train ride from two p to town q costs $ 6.85 more than does a bus ride from town p to town q . together , the cost of one train ride and one bus ride is $ 9.85 . what is the cost of a bus ride from town p to town q ?
Options: a ) $ 1.50 , b ) $ 2.50 , c ) $ 4.10 , d ) $ 4.70 , e ) $ 8.20
Rationale: "let x be the cost of a bus ride . x + ( x + 685 ) = 985 2 x = 300 x = $ 1.50 the answer is a ."
Answer: a
Python program:
a = 9 - 85
b = a / 2
Problem: compound x contains elements a and b at an approximate ratio , by weight , of 2 : 10 . approximately how many grams of element b are there in 222 grams of compound x ?
Options: a ) 54 , b ) 185 , c ) 250 , d ) 270 , e ) 322
Rationale: "total number of fractions = 2 + 10 = 12 element b constitutes = 10 out of 12 parts of x so in 222 gms of x have 222 * 10 / 12 = 185 gms of b and 222 - 185 = 37 gms of a . cross check : - a / b = 37 / 185 = 2 / 10 ( as given ) ans b"
Answer: b
Python program:
a = 222 * 10
b = 2 + 10 
c = a / b
Problem: a train 100 m long is running at a speed of 68 kmph . how long does it take to pass a man who is running at 8 kmph in the same direction as the train ?
Options: a ) 6 sec , b ) 9 sec , c ) 12 sec , d ) 15 sec , e ) 18 sec
Rationale: "speed of the train relative to man = ( 68 - 8 ) kmph = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec time taken by the train to cross the man = time taken by it to cover 100 m at 50 / 3 m / sec = 100 * 3 / 50 sec = 6 sec answer : a"
Answer: a
Python program:
a = 68 - 8
b = a * const_0_2778
c = 100 / b
Problem: how many multiples of 8 are less than 1600 , and also multiples of 64 ?
Options: a ) 25 , b ) 28 , c ) 62 , d ) 83 , e ) 89
Rationale: the lcm of 8 and 64 is 64 . divide 1600 / 64 = 25 . xxx . so a is your answer .
Answer: a
Python program:
a = 64 - 1600
b = a / 8
c = b + 1
Problem: what is the greatest positive integer n such that 3 ^ n is a factor of 36 ^ 50 ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 600 , e ) 900
Rationale: "36 = 3 ^ 2 * 2 ^ 2 . 36 ^ 50 = 3 ^ 100 * 2 ^ 100 the answer is a ."
Answer: a
Python program:
a = 36 - 50
b = a * 50
Problem: find k if 32 / k = 4 .
Options: a ) 6 , b ) 7 , c ) 8 , d ) 4 , e ) 3
Rationale: "since 32 / k = 4 and 32 / 8 = 4 , then k = 8 correct answer c"
Answer: c
Python program:
a = 32 / 4
Problem: exactly 3 / 7 of the people in the room are under the age of 21 , and exactly 5 / 14 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ?
Options: a ) 21 , b ) 35 , c ) 39 , d ) 42 , e ) 65
Rationale: "the total number of the people in the room must be a multiple of both 7 and 14 ( in order 3 / 7 and 5 / 14 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 7 and 14 , which is 98 . since , the total number of the people in the room is greater than 50 and less than 100 , then there are 98 people in the room . therefore there are 3 / 7 * 98 = 42 people in the room under the age of 21 . answer : d ."
Answer: d
Python program:
a = 7 * 14
b = a * 3
c = b / 7
Problem: in a group of ducks and cows , the total number of legs are 36 more than twice the number of heads . find the total number of cows .
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "let the number of ducks be d and number of cows be c then , total number of legs = 2 d + 4 c = 2 ( d + 2 c ) total number of heads = c + d given that total number of legs are 36 more than twice the number of heads = > 2 ( d + 2 c ) = 36 + 2 ( c + d ) = > d + 2 c = 18 + c + d = > 2 c = 18 + c = > c = 18 i . e . , total number of cows = 18 answer is d ."
Answer: d
Python program:
a = 36 / 2
Problem: the radius of a semi circle is 6.6 cm then its perimeter is ?
Options: a ) 32.7 , b ) 32.4 , c ) 22.4 , d ) 33.9 , e ) 32.1
Rationale: "36 / 7 r = 6.6 = 33.9 answer : d"
Answer: d
Python program:
a = circumface / (
b = a + 2
Problem: the total age of a and b is 12 years more than the total age of b and c . c is how many years younger than a . ?
Options: a ) 16 , b ) 12 , c ) 15 , d ) 20 , e ) 10
Rationale: "( a + b ) - ( b - c ) = 12 a - c = 12 answer is b"
Answer: b
Python program:
a = 12 * 1
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 w . 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 ( w and b ) = 35 only w = 20 ( w and b ) / b = 1 / 2 let ( w 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: pipe a fills a tank in 6 minutes . pipe b can fill the same tank 2 times as fast as pipe a . if both the pipes are kept open when the tank is empty , how many minutes will it take to fill the tank ?
Options: a ) 0.5 , b ) 1.0 , c ) 1.5 , d ) 2.0 , e ) 2.5
Rationale: "a ' s rate is 1 / 6 and b ' s rate is 1 / 3 . the combined rate is 1 / 6 + 1 / 3 = 1 / 2 the pipes will fill the tank in 2 minutes . the answer is d ."
Answer: d
Python program:
a = 1 / 6
b = 2 / 6
c = a + b 
d = 1/(c)
Problem: the average salary of a person for the months of january , february , march and april is rs . 8000 and that for the months february , march , april and may is rs . 8600 . if his salary for the month of may is rs . 6500 , find his salary for the month of january ?
Options: a ) s . 4100 , b ) s . 4270 , c ) s . 4500 , d ) s . 4550 , e ) s . 2500
Rationale: "sum of the salaries of the person for the months of january , february , march and april = 4 * 8000 = 32000 - - - - ( 1 ) sum of the salaries of the person for the months of february , march , april and may = 4 * 8600 = 34400 - - - - ( 2 ) ( 2 ) - ( 1 ) i . e . may - jan = 2400 salary of may is rs . 6500 salary of january = rs . 4100 answer : a"
Answer: a
Python program:
a = 8000 * 4
b = 8600 * 4
c = b - 6500
d = a - c
Problem: what is the tens digit of 7 ^ 545 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 0
Rationale: "7 ^ 1 = 7 7 ^ 2 = 49 7 ^ 3 = 343 7 ^ 4 = 2401 7 ^ 5 = 16807 7 ^ 6 = 117649 we should see this as pattern recognition . we have a cycle of 4 . ( we can multiply the last 2 digits only as we care about ten ' s digit ) 0 , 4 , 4 , 0 . 546 = 4 * 136 + 1 the ten ' s digit will be 0 . answer e"
Answer: e
Python program:
a = 4 + 1 
b = 7 ** reminder
c = reminder / (
d = math.floor(c, 100)
Problem: set a consists of all the prime numbers between 6 and 42 . what is the range of set a ?
Options: a ) 16 , b ) 34 , c ) 16.6 , d ) 17 , e ) 23
Rationale: "the range of a set of data is the difference between the highest and lowest values in the set in this set , highest number = 41 lowest number = 7 range = highest - lowest = 41 - 7 = 34 option b"
Answer: b
Python program:
a = 42 - 2
b = 6 + 4 
c = b + 1 
d = a - c
Problem: a certain elevator has a safe weight limit of 2000 pounds . what is the greatest possible number of people who can safely ride on the elevator at one time with the average ( arithmetic mean ) weight of half the riders being 200 pounds and the average weight of the others being 230 pounds ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: lets assume there are 2 x people . half of them have average weight of 200 and other half has 230 . maximum weight is = 2000 so 200 * x + 230 * x = 2000 = > 430 x = 2000 = > x is approximately equal to 5 . so total people is 2 * 5 = 10 we are not taking 10 as answer because say 10 th person has minimum of 200 weight then 200 * 5 + 230 * 5 = 2150 ( which is more than 2000 ) answer c .
Answer: c
Python program:
a = 200 + 230 
b = 2000 / a
c = b * 2
Problem: a can do a particular work in 6 days . b can do the same work in 8 days . a and b signed to do it for rs . 3360 . they completed the work in 3 days with the help of c . how much is to be paid to c ?
Options: a ) s . 380 , b ) s . 600 , c ) s . 420 , d ) s . 400 , e ) s . 480
Rationale: explanation : amount of work a can do in 1 day = 1 / 6 amount of work b can do in 1 day = 1 / 8 amount of work a + b can do in 1 day = 1 / 6 + 1 / 8 = 7 / 24 amount of work a + b + c can do = 1 / 3 amount of work c can do in 1 day = 1 / 3 - 7 / 24 = 1 / 24 work a can do in 1 day : work b can do in 1 day : work c can do in 1 day = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 amount to be paid to c = 3360 × ( 1 / 8 ) = 420 answer : option c
Answer: c
Python program:
a = 1 / 3
b = 1 / 6
c = 1 / 8
d = b + c 
e = a - d
f = 3 * e
g = f * 3360
Problem: 90 is increased by 50 % . find the final number .
Options: a ) 100 , b ) 110 , c ) 135 , d ) 140 , e ) 160
Rationale: "final number = initial number + 50 % ( original number ) = 90 + 50 % ( 90 ) = 90 + 45 = 135 . answer c"
Answer: c
Python program:
a = 50 / 100
b = 90 * a
c = 90 + b
Problem: rahim bought 55 books for rs . 1500 from one shop and 60 books for rs . 340 from another . what is the average price he paid per book ?
Options: a ) s . 17 , b ) s . 18 , c ) s . 16 , d ) s . 11 , e ) s . 10
Rationale: "average price per book = ( 1500 + 340 ) / ( 55 + 60 ) = 1840 / 115 = rs . 16 answer : c"
Answer: c
Python program:
a = 1500 + 340 
b = 55 + 60 
c = a / b
Problem: the average of 10 numbers was calculated as 16 . it is discovered later on that while calculating the average , one number , namely 46 , was incorrectly read as 26 . what is the correct average ?
Options: a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "10 * 16 - 26 + 46 = 180 180 / 10 = 18 the answer is a ."
Answer: a
Python program:
a = 10 * 16
b = 46 - 26
c = a + b 
d = c / 10
Problem: a taxi company charges $ 1.25 for the first quarter of a mile and fifteen cents for each additional quarter of a mile . what is the maximum distance someone could travel with $ 4.90 ?
Options: a ) 4 miles , b ) 4 1 / 4 miles , c ) 4 3 / 4 miles , d ) 5 1 / 2 miles , e ) 6 1 / 3 miles
Rationale: "if we start out with $ 4.90 and have to spend $ 1.25 for the first quarter - mile , we will have $ 3.65 left to spend on quarter - mile intervals . since $ 3.65 / $ 0.15 = 24.33 we can buy 24.33 more quarter - miles , and will travel 25.33 quarter miles in all : 25.33 × 1 / 4 = 6 1 / 3 miles . the correct answer is choice ( e ) ."
Answer: e
Python program:
a = 4 - 90
b = a * 100
c = b / 3
d = c / 4
Problem: a can complete a project in 20 days and b can complete the same project in 30 days . if a and b start working on the project together and a quits 10 days before the project is completed , in how many days will the project be completed ?
Options: a ) 18 days , b ) 27 days , c ) 26.67 days , d ) 16 days , e ) 12 days
Rationale: "answer a can complete a project in 20 days . so , a will complete 1 / 20 th of the project in a day . b can complete a project in 30 days . so , b will complete 1 / 30 th of the project in a day . let the total number of days taken to complete the project be x days . b worked for all x days . however , a worked for ( x - 10 ) days because a quits 10 days before the project is completed . in a day , a completes 1 / 20 th of the project . therefore , a would have completed x − 10 / 20 th of the project in ( x - 10 ) days . in a day , b completes 130130 th of the project . therefore , b would have completed x / 30 h of the project in x days . ∴ x − 10 / 20 + x / 30 = 1 or x = 18 . choice a"
Answer: a
Python program:
a = 1 / 30
b = a * 10
c = 1 - b
d = 1 / 20
e = 1 / 30
f = d + e 
g = c / f
h = g + 10