euclaise/mathqa_programs huggingface dataset:
Problem: each month a retailer sells 100 identical items . on each item he makes a profit of $ 50 that constitutes 10 % of the item ' s price to the retailer . if the retailer contemplates giving a 5 % discount on the items he sells , what is the least number of items he will have to sell each month to justify the policy of the discount ?
Options: a ) 191 , b ) 213 , c ) 221 , d ) 223 , e ) 226
Rationale: "for this question , we ' ll need the following formula : sell price = cost + profit we ' re told that the profit on 1 item is $ 20 and that this represents 10 % of the cost : sell price = cost + $ 50 sell price = $ 500 + $ 50 thus , the sell price is $ 550 for each item . selling all 100 items gives the retailer . . . 100 ( $ 50 ) = $ 2,000 of profit if the retailer offers a 5 % discount on the sell price , then the equation changes . . . 5 % ( 550 ) = $ 27.5 discount $ 522.5 = $ 500 + $ 22.5 now , the retailer makes a profit of just $ 22.5 per item sold . to earn $ 2,000 in profit , the retailer must sell . . . . $ 22.5 ( x ) = $ 2,000 x = 2,000 / 22.5 x = 222.222222 items you ' ll notice that this is not among the answer choices . . . . 221 and 223 are . selling 221 items would get us 9 ( 221 ) = $ 1989 which is not enough money . to get back to at least $ 2,000 , we need to sell 223 items . final answer : d"
Answer: d
Python program:
a = 100 * 50
b = 100 * 50
c = b / 10
d = c + 50 
e = d * 5
f = e / 100
g = 50 - f
h = a / g
Problem: the perimeter of a square is equal to the perimeter of a rectangle of length 20 cm and breadth 14 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places )
Options: a ) 23.57 , b ) 25.54 , c ) 26.5 , d ) 26.55 , e ) 26.71
Rationale: "let the side of the square be a cm . perimeter of the rectangle = 2 ( 20 + 14 ) = 68 cm perimeter of the square = 68 cm i . e . 4 a = 68 a = 17 diameter of the semicircle = 17 cm circumference of the semicircle = 1 / 2 ( ∏ ) ( 17 ) = 1 / 2 ( 22 / 7 ) ( 17 ) = 26.71 cm to two decimal places answer : e"
Answer: e
Python program:
a = 14 + 20 
b = 2 * a
c = b / 4
d = c / 2
e = circumface / (
f = math.floor(e, 2)
Problem: working alone , printers x , y , and z can do a certain printing job , consisting of a large number of pages , in 16 , 12 , and 8 hours , respectively . what is the ratio of the time it takes printer x to do the job , working alone at its rate , to the time it takes printers y and z to do the job , working together at their individual rates ?
Options: a ) 5 / 2 , b ) 7 / 4 , c ) 8 / 5 , d ) 10 / 3 , e ) 12 / 5
Rationale: the time it takes printer x is 16 hours . the combined rate of y and z is 1 / 12 + 1 / 8 = 5 / 24 the time it takes y and z is 24 / 5 the ratio of times is 16 / ( 24 / 5 ) = 5 * 16 / 24 = 10 / 3 the answer is d .
Answer: d
Python program:
a = 1 / 12
b = 1 / 8
c = a + b 
d = 1 / c
e = 16 / d
Problem: a hollow iron pipe is 21 cm long and its external diameter is 8 cm . if the thickness of the pipe is 1 cm and iron weighs , then the weight of the pipe is
Options: a ) 3.496 kg , b ) 3.696 kg , c ) 3.690 kg , d ) 9.696 kg , e ) 3.296 kg
Rationale: explanation : external radius = 4 cm , internal radius = 3 cm . volume of iron = = weight of iron = ( 462 x 8 ) gm = 3696 gm = 3.696 kg answer : b ) 3.696 kg
Answer: b
Python program:
a = 21 + 1 
b = 4 + 3 
c = a / b
d = 4 ** 2
e = 3 ** 2
f = d - e
g = c * f
h = g * 21
i = 8 * h
j = i / 1000
Problem: j is 25 % less than p and 20 % less than t . t is r % less than p . what is the value of r ?
Options: a ) 93.5 , b ) 90 , c ) 6.75 , d ) 6.25 , e ) 2
Rationale: "usually we can solve every question of this type by choosing appropriate value of the variable and deriving the value of other related variables . let , p = 400 then j = ( 75 / 100 ) * 400 = 300 also j = ( 80 / 100 ) * t i . e . t = 300 * 100 / 80 = 375 and t = [ 1 - ( r / 100 ) ] * p i . e . 100 - r = 100 * t / p = 100 * 375 / 400 = 93.75 i . e . r = 6.25 answer : option d"
Answer: d
Python program:
a = 25 * 25
b = a / 100
Problem: if k is the greatest positive integer such that 3 ^ k is a divisor of 21 ! then k =
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 9
Rationale: "21 / 3 = 7 21 / 9 = 2.33 = 2 7 + 2 = 9 k = 9 answer : e"
Answer: e
Python program:
a = 21 / 3
b = 1 + a
Problem: a chemist mixes one liter of pure water with x liters of a 30 % salt solution , and the resulting mixture is a 20 % salt solution . what is the value of x ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 1 , e ) 2
Rationale: "concentration of salt in pure solution = 0 concentration of salt in salt solution = 30 % concentration of salt in the mixed solution = 20 % the pure solution and the salt solution is mixed in the ratio of - - > ( 30 - 20 ) / ( 20 - 0 ) = 1 / 2 1 / x = 1 / 2 x = 2 answer : e"
Answer: e
Python program:
a = 30 - 20
b = 20 / a
Problem: in an examination 35 % of the students passed and 546 failed . how many students appeared for the examination ?
Options: a ) a ) 540 , b ) b ) 400 , c ) c ) 700 , d ) d ) 650 , e ) e ) 840
Rationale: "let the number of students appeared be x then , 65 % of x = 546 65 x / 100 = 546 x = 546 * 100 / 65 = 840 answer is e"
Answer: e
Python program:
a = 546 * 100
b = 100 - 35
c = a / b
Problem: a person walks from one end to the other of a 90 - meter long moving walkway at a constant rate in 30 seconds , assisted by the walkway . when this person reaches the end , they reverse direction and continue walking with the same speed , but this time it takes 120 seconds because the person is traveling against the direction of the moving walkway . if the walkway were to stop moving , how many seconds would it take this person to walk from one end of the walkway to the other ?
Options: a ) 36 , b ) 42 , c ) 48 , d ) 54 , e ) 60
Rationale: "let v be the speed of the person and let x be the speed of the walkway . 30 ( v + x ) = 90 then 120 ( v + x ) = 360 120 ( v - x ) = 90 when we add the two equations : 240 v = 450 v = 15 / 8 time = 90 / ( 15 / 8 ) = 48 seconds the answer is c ."
Answer: c
Python program:
a = 90 / 30
b = 90 / 120
c = a + b 
d = c / 2
e = 90 / d
Problem: right now , the ratio between the ages of sandy and molly is 4 : 3 . after 6 years , sandy ’ s age will be 34 years . what is molly ' s age right now ?
Options: a ) 12 , b ) 15 , c ) 18 , d ) 21 , e ) 24
Rationale: "now , sandy is 34 - 6 = 28 molly ' s age is ( 3 / 4 ) * 28 = 21 the answer is d ."
Answer: d
Python program:
a = 34 - 6
b = a / 4
c = b * 3
Problem: a 420 meter long train crosses a platform in 60 seconds while it crosses a signal pole in 30 seconds . what is the length of the platform ?
Options: a ) 120 , b ) 840 , c ) 350 , d ) 420 , e ) 210
Rationale: "speed = [ 420 / 30 ] m / sec = 14 m / sec . let the length of the platform be x meters . then , x + 420 / 60 = 14 x + 420 = 840 è x = 420 m . answer : d"
Answer: d
Python program:
a = 420 / 30
b = a * 60
c = b - 420
Problem: a , b and c rents a pasture for rs . 435 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should b pay ?
Options: a ) 180 , b ) 227 , c ) 268 , d ) 198 , e ) 176
Rationale: 12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 12 / 29 * 435 = 180 answer : a
Answer: a
Python program:
a = 12 * 8
b = 16 * 9
c = a + b 
d = 18 * 6
e = c + d 
f = 435 / e
g = 16 * 9
h = f * g
Problem: a , b and c enter into partnership . a invests some money at the beginning , b invests double the amount after 6 months , and c invests thrice the amount after 8 months . if the annual gain be rs . 15000 . a ' s share is ?
Options: a ) 2999 , b ) 2778 , c ) 6000 , d ) 5000 , e ) 6612
Rationale: "x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 15000 = 5000 answer : d"
Answer: d
Python program:
a = 1 * 12
b = 1 * 12
c = 12 - 6
d = c * 2
e = b + d 
f = 12 - 8
g = f * 3
h = e + g 
i = 15000 / h
j = a * i
Problem: a car traveled 80 % of the way from town x to town y at an average speed of 80 mph . the car traveled at an average speed of v mph for the remaining part of the trip . the average speed for the entire trip was 50 mph . what is v in mph ?
Options: a ) 25 , b ) 35 , c ) 45 , d ) 55 , e ) 20
Rationale: assume total distance = 100 miles time taken for 80 miles = 80 / 80 = 1 hour time taken for the rest of the 20 miles = 20 / v hours . average speed = 50 therefore the total time needed = 2 hours . 2 = 1 + 20 / v hence v = 20 mph answer : e
Answer: e
Python program:
a = 100 - 80
b = 80 / 80
c = a / b
Problem: a guy was asked to specify his age in years . he said , “ take my age 8 years hence , multiply it by 8 and subtract 8 times of my age 8 years ago and get the half of the result and you will know my age . ” what was the age of that guy ?
Options: a ) 18 , b ) 55 , c ) 63 , d ) 64 , e ) 70
Rationale: current age of the guy = a years . then , 8 ( a + 8 ) – 8 ( a – 8 ) = a ( 8 a + 64 ) – ( 8 a – 64 ) = a a = 128 / 2 = 64 d
Answer: d
Python program:
a = 8 * 8
Problem: there are 12 students in a class . on the day the test was given , ella was absent . the other 11 students took the test and their average was 74 . the next day , ella took the test , and with this grade included , the new average was 75 . what was ella ' s grade on the test ?
Options: a ) 82 , b ) 83 , c ) 84 , d ) 85 , e ) 86
Rationale: 11 * 74 + ella ' s grade = 12 * 75 ella ' s grade is 12 * 75 - 11 * 74 = 86 . the answer is e .
Answer: e
Python program:
a = 74 + 75 
b = 11 + 12 
c = a - b
d = c - 75
e = 11 + 12 
f = d + e 
g = f + 11
Problem: at what price must an book costing $ 47.50 be marked in order that after deducting 20 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 72.5 , b ) 55.5 , c ) 64.2 , d ) 82.5 , e ) 60.5
Rationale: "c $ 62.50 cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 80 / 100 ) = 59.375 mp = 74.2"
Answer: c
Python program:
a = 100 + 25 
b = 47 * 50
c = b / 100
d = 100 - 20
e = c / d
f = e * 100
Problem: three fifth of the square of a certain number is 126.15 . what is the number ?
Options: a ) 210.25
b ) 75.69
c ) 14.5
d ) 145
e ) 150
Rationale: let the number be x given , 3 / 5 x ^ 2 = 126.5 x ^ 2 = 126.15 * 5 / 3 x ^ 2 = 42.05 * 5 = 210.25 x = 14.5 answer c .
Answer: c
Python program:
a = 1 + 4 
b = 3 / a
c = 126 / 15
d = math.sqrt(c)
Problem: one woman and one man can build a wall together in one hour , but the woman would need the help of two girls in order to complete the same job in the same amount of time . if one man and one girl worked together , it would take them two hours to build the wall . assuming that rates for men , women and girls remain constant , how many hours would it take one woman , one man , and one girl , working together , to build the wall ?
Options: a ) 5 / 7 , b ) 6 / 7 , c ) 10 / 7 , d ) 12 / 7 , e ) 22 / 7
Rationale: solution : let work done by man , women and girl per hour be m , w , g respectively . then , m + w = 1 / 1 - - > ( 1 ) , w + 2 g = 1 / 1 - - > ( 2 ) and m + g = 1 / 2 - - > ( 3 ) . no . of hours it would take forone woman , one man , and one girl , working together , to build the wall , n = 1 / m + w + g from ( 1 ) and ( 2 ) , m = 2 g and from ( 3 ) g = 1 / 6 , m = 1 / 3 and w = 2 / 3 . so , n = 1 / ( 7 / 6 ) = 6 / 7 option , b
Answer: b
Python program:
a = 2 + 2 
b = a + 3
Problem: in a certain circle there are 10 points . what is the number of the triangles connecting 4 points of the 10 points ?
Options: a ) 80 , b ) 96 , c ) 108 , d ) 120 , e ) 210
Rationale: "imo : e here we have to select 4 points out of 10 points . order is not important so the answer will be 10 c 4 = 210"
Answer: e
Python program:
a = math.factorial(10)
b = 10 / 2
c = math.factorial(b)
d = math.factorial(4)
e = c * d
f = a / e
Problem: two trains of length 400 m and 200 m are 200 m apart . they start moving towards each other on parallel tracks , at speeds 54 kmph and 36 kmph . after how much time will the trains meet ?
Options: a ) 8 sec , b ) 20 / 7 sec , c ) 33 / 7 sec , d ) 21 / 7 sec , e ) 32 / 7 sec
Rationale: "they are moving in opposite directions , relative speed is equal to the sum of their speeds . relative speed = ( 54 + 36 ) * 5 / 18 = 25 mps . the time required = d / s = 200 / 25 = 8 sec . answer : a"
Answer: a
Python program:
a = 54 + 36 
b = a * const_0_2778
c = 200 / b
Problem: the diagonals of two squares are in the ratio of 3 : 7 then find the ratio of its areas ?
Options: a ) 7 : 37 , b ) 6 : 46 , c ) 9 : 49 , d ) 8 : 68 , e ) 6 : 61
Rationale: "let the diagonals of the squares be 3 x and 7 x ratio of their areas = 1 / 2 ( 3 x ) ^ 2 : 1 / 2 ( 7 x ) ^ 2 = 9 x ^ 2 : 49 x ^ 2 = 9 : 49 answer is c"
Answer: c
Python program:
a = 7 ** 3
b = 4 / a
Problem: the average marks of a class of 30 students is 40 and that of another class of 50 students is 90 . find the average marks of all the students ?
Options: a ) 71.25 , b ) 52.9 , c ) 52.1 , d ) 52.3 , e ) 42.5
Rationale: "sum of the marks for the class of 30 students = 30 * 40 = 1200 sum of the marks for the class of 50 students = 50 * 90 = 4500 sum of the marks for the class of 80 students = 1200 + 4500 = 5700 average marks of all the students = 5700 / 80 = 71.25 answer : a"
Answer: a
Python program:
a = 30 * 40
b = 50 * 90
c = a + b 
d = 30 + 50 
e = c / d
Problem: in the storage room of a certain bakery , the ratio of sugar to flour is 3 to 8 , and the ratio of flour to baking soda is 10 to 1 . if there were 60 more pounds of baking soda in the room , the ratio of flour to baking soda would be 8 to 1 . how many pounds of sugar are stored in the room ?
Options: a ) 600 , b ) 900 , c ) 1500 , d ) 1600 , e ) 1750
Rationale: "sugar : flour = 3 : 8 = 15 : 40 ; flour : soda = 10 : 1 = 40 : 4 ; thus we have that sugar : flour : soda = 15 x : 40 x : 4 x . also given that 40 x / ( 4 x + 60 ) = 8 / 1 - - > x = 60 - - > sugar = 15 x = 900 . answer : b ."
Answer: b
Python program:
a = 3 / 8
b = 8 * 60
c = 10 - 8
d = b / c
e = 10 * d
f = a * e
Problem: jacob is 18 years old . he is 2 times as old as his brother . how old will jacob be when he is twice as old ?
Options: a ) 36 , b ) 38 , c ) 33 , d ) 32 , e ) 38
Rationale: j = 18 ; j = 2 b ; b = 18 / 2 = 9 ; twice as old so b = 9 ( now ) + ( 9 ) = 18 ; jacob is 18 + 18 = 36 answer : a
Answer: a
Python program:
a = 18 * 2
Problem: 3897 x 999 = ?
Options: a ) 3883203 , b ) 3893103 , c ) 3639403 , d ) 3791203 , e ) none of them
Rationale: "= 3897 x 999 = 3897 x ( 1000 - 1 ) = 3897 x 1000 - 3897 x 1 = 3897000 - 3897 = 3893103 answer is b"
Answer: b
Python program:
a = 3897 / 999
b = a * 100
Problem: the average monthly salary of 20 employees in an organisation is rs . 1500 . if the manager ' s salary is added , then the average salary increases by rs . 600 . what is the manager ' s monthly salary ?
Options: a ) rs . 16003 , b ) rs . 16029 , c ) rs . 11288 , d ) rs . 14100 , e ) rs . 16011
Rationale: "explanation : manager ' s monthly salary rs . ( 2100 * 21 - 1500 * 20 ) = rs . 14100 . answer : d"
Answer: d
Python program:
a = 1500 + 600 
b = 20 + 1 
c = a * b
d = 1500 * 20
e = c - d
Problem: noelle walks from point a to point b at an average speed of 5 kilometers per hour . at what speed , in kilometers per hour , must noelle walk from point b to point a so that her average speed for the entire trip is 8 kilometers per hour ?
Options: a ) 6.75 , b ) 7 , c ) 7.25 , d ) 7.5 , e ) 20
Rationale: "let ' s suppose that speed while returning was xkm / h since the distance is same , we can apply the formula of avg speed avg speed = 2 s 1 s 2 / s 1 + s 2 8 = 2 * 5 * x / 5 + x x = 20 e is the answer"
Answer: e
Python program:
a = 8 * 5
b = 2 * 5
c = b - 8
d = a / c
Problem: a man buy a book in rs 50 & sale it rs 90 . what is the rate of profit ? ? ?
Options: a ) 10 % , b ) 80 % , c ) 30 % , d ) 25 % , e ) 28 %
Rationale: cp = 50 sp = 90 profit = 90 - 50 = 40 % = 40 / 50 * 100 = 80 % answer : b
Answer: b
Python program:
a = 90 - 50
b = a / 50
c = b * 100
Problem: in what time will a train 250 metres long cross an electric pole , if its speed be 162 km / hr ?
Options: a ) 4 sec , b ) 5 sec , c ) 5.55 sec , d ) 6.55 sec , e ) 4.55 sec
Rationale: "solution speed = ( 162 x 5 / 18 ) m / sec = 45 m / sec time taken = ( 250 / 45 ) sec = 5.55 sec . answer c"
Answer: c
Python program:
a = 162 * const_0_2778
b = 250 / a
Problem: an ant is climbing 30 meters tall pole . it climbs 3 meter during the day and slips down 2 meters down during night in sleep , how many days it takes to reach the top of the pole ?
Options: a ) a - 30 , b ) b - 29 , c ) c - 28 , d ) d - 27 , e ) e - 26
Rationale: ants overall distance covered is 3 - 2 = 1 meter per day . in 27 days it will climb 27 meters . on 28 th day it will reach the top of the pole . answer : c
Answer: c
Python program:
a = 3 - 2
b = a * 30
Problem: if 50 apprentices can finish a job in 4 hours , and 30 journeymen can finish the same job in 5 hours , how much of the job should be completed by 10 apprentices and 15 journeymen in one hour ?
Options: a ) 1 / 9 , b ) 29 / 180 , c ) 26 / 143 , d ) 3 / 20 , e ) 39 / 121
Rationale: "50 apprentices can finish the job in 4 hours , thus : 10 apprentices can finish the job in 4 * 5 = 20 hours ; in 1 hour 10 apprentices can finish 1 / 20 of the job . 30 journeymen can finish the same job in 4,5 hours , thus : 15 journeymen can finish the job in 5 * 2 = 10 hours ; in 1 hour 15 journeymen can finish 1 / 10 of the job . therefore , in 1 hour 10 apprentices and 15 journeymen can finish 1 / 20 + 1 / 10 = 3 / 20 of the job . answer : d ."
Answer: d
Python program:
a = 50 * 4
b = a / 10
c = 1 / b
d = 30 * 5
e = d / 15
f = 1 / e
g = c + f
Problem: a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 3 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 of liquid a was contained by the can initially ?
Options: a ) 7 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "ci * vi = cf * vf ( 7 / 12 ) * ( v 1 - 3 ) = ( 7 / 16 ) * v 1 ( v 1 - 3 ) / v 1 = 3 / 4 3 accounts for the difference of 1 on ratio scale so initial volume = v 1 = 4 * 3 = 12 litres . 7 / 12 of the initial mixture was liquid a so liquid a was ( 7 / 12 ) * 12 = 7 litres . answer : a"
Answer: a
Python program:
a = 7 + 3 
b = 7 + 5 
c = 5 / b
d = c * 3
e = 3 - d
f = a * e
g = 3 * 7
h = 7 * 5
i = g - h
j = f / i
k = 7 * j
Problem: rohan spends 40 % of his salary on food , 20 % on house rent , 10 % on entertainment and 10 % on conveyance . if his savings at the end of a month are rs . 1500 . then his monthly salary is
Options: a ) rs . 6000 , b ) rs . 7500 , c ) rs . 8000 , d ) rs . 10,000 , e ) none
Rationale: "sol . saving = [ 100 - ( 40 + 20 + 10 + 10 ] % = 20 % . let the monthly salary be rs . x . then , 20 % of x = 1500 ⇔ 20 / 100 x = 1500 ⇔ x = 1500 × 5 = 7500 . answer b"
Answer: b
Python program:
a = 4 + 1 
b = 1500 * a
Problem: what percentage of numbers from 1 to 95 have squares that end in the digit 0 ?
Options: a ) 1 , b ) 14 , c ) 9.47 , d ) 21 , e ) 22
Rationale: clearly , the numbers which have 1 or 9 in the unit ' s digit , have squares that end in the digit 1 . such numbers from 1 to 95 are 10 , 20,30 , 40,50 , 60,70 , 80,90 . number of such numbers = 14 . required percentage = ( 9 / 95 * 100 ) = 9.47 % answer : c
Answer: c
Python program:
a = 95 / 10
b = math.floor(a)
c = b / 95
d = c * 100
Problem: what is the square root of 400 , divided by 2 ?
Options: a ) 9 , b ) 36 , c ) 122 , d ) 6 , e ) 10
Rationale: "square root is a number times itself square root of 400 = 20 , 20 / 2 = 10 ( e ) 1"
Answer: e
Python program:
a = math.sqrt(400)
b = a / 2
Problem: for a recipe for triple berry pie calls for cups of strawberries , raspberries , and blueberries in a ratio of 1 : 2 : 3 . how many total cups of fruit will you need to make the pie ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: the ratio 1 : 2 : 3 represents 1 cup strawberries : 2 cups raspberries : 3 cups blueberries . 1 + 2 + 3 = 6 6 cups will be used for the pie . the answer is e
Answer: e
Python program:
a = 1 + 2 
b = 3 + a
Problem: two trains 121 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 7.19 , b ) 7.18 , c ) 7.16 , d ) 7.15 , e ) 7.12
Rationale: "t = ( 121 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 7.15 answer : d"
Answer: d
Python program:
a = 121 + 165 
b = 80 + 65 
c = b * const_0_2778
d = a / c
Problem: the number which exceeds 16 % of it by 63 is :
Options: a ) 75 , b ) 52 , c ) 58 , d ) 60 , e ) 62
Rationale: "solution solution let the number be x . x - 16 % of x = 63 x - 16 / 100 x = 63 x - 4 / 25 x = 63 21 / 25 x = 63 x = ( 63 x 25 / 21 ) = 75 answer a"
Answer: a
Python program:
a = 63 * 100
b = 100 - 16
c = a / b
Problem: the batting average of a particular batsman is 58 runs in 46 innings . if the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs , find his highest score .
Options: a ) 179 , b ) 208 , c ) 210 , d ) 133 , e ) 229
Rationale: "explanation : total runs scored by the batsman = 58 * 46 = 2668 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2668 – 2552 = 116 runs . let the highest score be x , hence the lowest score = x – 150 x + ( x - 150 ) = 116 2 x = 266 x = 133 runs answer d"
Answer: d
Python program:
a = 58 * 46
b = 46 - 2
c = 58 * b
d = a - c
e = 150 + d 
f = e / 2
Problem: the average monthly income of p and q is rs . 5050 . the average monthly income of q and r is 6250 and the average monthly income of p and r is rs . 5200 . the monthly income of p is ?
Options: a ) rs . 4007 , b ) rs . 4000 , c ) rs . 4028 , d ) rs . 4050 , e ) rs . 4032
Rationale: "let p , q and r represent their respective monthly incomes . then , we have : p + q = ( 5050 * 2 ) = 10100 - - - ( i ) q + r = ( 6250 * 2 ) = 12500 - - - ( ii ) p + r = ( 5200 * 2 ) = 10400 - - - ( iii ) adding ( i ) , ( ii ) and ( iii ) , we get : 2 ( p + q + r ) = 33000 = p + q + r = 16500 - - - ( iv ) subtracting ( ii ) from ( iv ) , we get , p = 4000 . p ' s monthly income = rs . 4000 . answer : b"
Answer: b
Python program:
a = 5050 + 5200 
b = a - 6250
Problem: how many integers between 324,700 and 387,600 have tens digit 1 and units digit 3 ?
Options: a ) 438 , b ) 629 , c ) 780 , d ) 879 , e ) 924
Rationale: "the integers are : 324,713 324,813 etc . . . 387,513 the number of integers is 3876 - 3247 = 629 the answer is b ."
Answer: b
Python program:
a = 2 * 100
b = 3 + 4 
c = b * 10
d = a + c 
e = d + 2 
f = 387 - 600
Problem: the salary of a , b , c , d , e is rs . 10000 , rs . 5000 , rs . 11000 , rs . 7000 , rs . 9000 per month respectively , then the average salary of a , b , c , d , and e per month is
Options: a ) rs . 7000 , b ) rs . 8400 , c ) rs . 8500 , d ) rs . 9000 , e ) none
Rationale: "answer average salary = 10000 + 5000 + 11000 + 7000 + 9000 / 5 = rs . 8400 correct option : b"
Answer: b
Python program:
a = 10000 + 5000 
b = a + 11000 
c = b + 7000 
d = c + 9000 
e = 4 + 1 
f = d / e
Problem: running at the same constant rate , 6 identical machines can produce a total of 300 bottles per minute . at this rate , how many bottles could 10 such machines produce in 4 minutes ?
Options: a ) 648 , b ) 1800 , c ) 2000 , d ) 10800 , e ) 10900
Rationale: "let the required number of bottles be x . more machines , more bottles ( direct proportion ) more minutes , more bottles ( direct proportion ) machines 6 : 10 : : 300 : x time ( in minutes ) 1 : 4 6 x 1 x x = 10 x 4 x 300 x = ( 10 x 4 x 300 ) / ( 6 ) x = 2000 . answer : c"
Answer: c
Python program:
a = 300 / 6
b = a * 4
c = b * 10
Problem: reema took a loan of rs 1500 with simple interest for as many years as the rate of interest . if she paid rs . 735 as interest at the end of the loan period , what was the rate of interest .
Options: a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 9 %
Rationale: explanation : let rate = r % then time = r years . = > 1500 ∗ r ∗ r / 100 = 735 = > r 2 = 49 = > r = 7 % option c
Answer: c
Python program:
a = 1500 / 100
b = 735 / a
c = math.sqrt(b)