euclaise/mathqa_programs huggingface dataset:
Problem: gold is 11 times as heavy as water and copper is 5 times as heavy as water . in what ratio should these be mixed to get an alloy 8 times as heavy as water ?
Options: a ) 3 : 2 , b ) 1 : 1 , c ) 3 : 1 , d ) 5 : 2 , e ) 4 : 3
Rationale: "g = 11 w c = 5 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 11 w + 5 wx = x + 1 * 8 w 11 + 5 x = 8 ( x + 1 ) x = 1 / 1 ratio of gold with copper = 1 : 1 = 1 : 1 answer is b"
Answer: b
Python program:
a = 8 - 5
b = 11 - 8
c = a / b
Problem: if a car went the first third of the distance at 80 kmh , the second third at 24 kmh , and the last third at 30 kmh , what was the average speed of the car for the entire trip ?
Options: a ) 36 kmh , b ) 40 kmh , c ) 42 kmh , d ) 44 kmh , e ) 34 kmh
Rationale: "assume d / 3 = 240 ( this number is convenient because it is divisible by 80 , 24 and 30 ) so : 240 = 80 * t 1 = 3 hrs 240 = 24 * t 2 = 10 hrs 240 = 30 * t 3 = 8 hrs t = t 1 + t 2 + t 3 = 21 hrs d = rt ( 240 * 3 ) = r * 21 r = 34 answer : e"
Answer: e
Python program:
a = 1 / 80
b = 1 / 24
c = a + b 
d = 1 / 30
e = c + d 
f = 3 / e
Problem: how many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 63 kmph ?
Options: a ) 22 sec , b ) 77 sec , c ) 25 sec , d ) 14.3 sec , e ) 17 sec
Rationale: "d = 100 + 150 = 250 s = 63 * 5 / 18 = 17.5 mps t = 250 / 17.5 = 14.3 sec answer : d"
Answer: d
Python program:
a = 150 + 100 
b = 63 * const_0_2778
c = a / b
Problem: a store reported total sales of $ 385 million for february of this year . if the total sales for the same month last year was $ 320 million , approximately what was the percent increase i in sales ?
Options: a ) 2 % , b ) 17 % , c ) 20 % , d ) 65 % , e ) 83 %
Rationale: "last year ' s sales = $ 320 million ; this year ' s sales = $ 385 million ; increase i = $ 65 million . now , 20 % of $ 320 million is $ 64 million , which is very close to actual increase of $ 65 million . answer : c ."
Answer: c
Python program:
a = 385 - 320
b = a / 320
c = b * 100
Problem: income and expenditure of a person are in the ratio 5 : 4 . if the income of the person is rs . 15000 , then find his savings ?
Options: a ) 3600 , b ) 3607 , c ) 3608 , d ) 3602 , e ) 3000
Rationale: "let the income and the expenditure of the person be rs . 5 x and rs . 4 x respectively . income , 5 x = 15000 = > x = 3000 savings = income - expenditure = 5 x - 4 x = x so , savings = rs . 3000 . answer : e"
Answer: e
Python program:
a = 4 / 5
b = a * 15000
c = 15000 - b
Problem: salesperson a ' s compensation for any week is $ 280 plus 6 percent of the portion of a ' s total sales above $ 1,000 for that week . salesperson b ' s compensation for any week is 8 percent of b ' s total sales for that week . for what amount of total weekly sales would both salespeople earn the same compensation ?
Options: a ) $ 5000 , b ) $ 7000 , c ) $ 9000 , d ) $ 11,000 , e ) $ 13,000
Rationale: "280 + 0.06 ( x - 1000 ) = 0.08 x 0.02 x = 220 x = $ 11,000 the answer is d ."
Answer: d
Python program:
a = 6 / 100
b = a * 1
c = 280 - b
d = 8 / 100
e = 6 / 100
f = d - e
g = c / f
h = 6 / 100
i = h * 1
j = 280 - i
k = 8 / 100
l = 6 / 100
m = k - l
n = j / m
o = g + n 
p = o / 1
Problem: rashmi walks to her bus stop at 5 kmph and reaches there late by 10 minutes . on the next day , she increases her speed to 6 kmph and reaches the bus stop 10 minutes early . how far is the bus stop ?
Options: a ) 13 , b ) 12 , c ) 11 , d ) 10 , e ) 9
Rationale: let the distance to the bus stop is ` ` d ' ' km time taken by her ( at 5 kmph ) = d / 5 hour , and time taken by her ( at 6 kmph ) = d / 6 hour as per given condition , d / 5 - d / 6 = 20 / 60 d = 10 kms answer : d
Answer: d
Python program:
a = 10 + 10 
b = 1 / 5
c = 1 / 6
d = b - c
e = const_60 * d
f = a / e
Problem: the amount of principal rs . 8000 at compound interest at the ratio of 5 % p . a . for 2 years is
Options: a ) s . 9621 , b ) s . 6921 , c ) s . 8820 , d ) s . 6261 , e ) s . 6361
Rationale: "c . i = p ( 1 + r / 100 ) ^ n = 8000 ( 1 + 5 / 100 ) ^ 2 = rs 8820 answer : c"
Answer: c
Python program:
a = 5 / 100
b = 1 + a 
c = b ** 2
d = 8000 * c
Problem: a cistern 6 m long and 4 m wide contains water up to a depth of 1 m 25 cm . the total area of the wet surface is :
Options: a ) 49 , b ) 50 , c ) 53.5 , d ) 55 , e ) 57
Rationale: "explanation : area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 4 x 1.25 + 6 x 1.25 ) + 6 x 4 ] m 2 = 49 m 2 answer : a"
Answer: a
Python program:
a = 25 / 100
b = a + 1 
c = b * 4
d = 25 / 100
e = d + 1 
f = e * 6
g = c + f 
h = 2 * g
i = 4 * 6
j = h + i
Problem: all the milk in container a which was filled to its brim was poured into two containers b and c . the quantity of milk in container b was 62.5 % less than the capacity of container a . if 152 liters was now transferred from c to b , then both the containers would have equal quantities of milk . what was the initial quantity of milk in container a ?
Options: a ) 1216 , b ) 1723 , c ) 1129 , d ) 2613 , e ) 1372
Rationale: a b has 62.5 % or ( 5 / 8 ) of the milk in a . therefore , let the quantity of milk in container a ( initially ) be 8 k . quantity of milk in b = 8 k - 5 k = 3 k . quantity of milk in container c = 8 k - 3 k = 5 k container : a b c quantity of milk : 8 k 3 k 5 k it is given that if 152 liters was transferred from container c to container b , then both the containers would have equal quantities of milk . 5 k - 152 = 3 k + 152 = > 2 k = 304 = > k = 152 the initial quantity of milk in a = 8 k = 8 * 152 = 1216 liters .
Answer: a
Python program:
a = 1/(2)
b = 62 / 5
c = 1 - b
d = a - c
e = 152 / d
Problem: the average expenditure of a labourer for 7 months was 85 and he fell into debt . in the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30 . his monthly income is
Options: a ) 70.11 , b ) 72.02 , c ) 86.5 , d ) 78.2 , e ) none of the above
Rationale: "income of 7 months = ( 7 × 85 ) – debt = 595 – debt income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ income of 10 months = 865 average monthly income = 865 ÷ 10 = 86.5 answer c"
Answer: c
Python program:
a = 85 * 7
b = 60 * 4
c = a + b 
d = c + 30 
e = 7 + 4 
f = d / e
Problem: a man leaves a point p at 6 a . m . and reaches the point q at 10 a . m . another man leaves the point give at 8 a . m . and reaches the point p at 12 noon . at what time do they meet ?
Options: a ) 2 a . m , b ) 6 a . m , c ) 9 a . m , d ) 5 a . m , e ) 1 a . m
Rationale: 9 a . m . answer : c
Answer: c
Python program:
a = 4 - 1
b = 6 + a
Problem: 35 % of major airline companies equip their planes with wireless internet access . 70 % of major airlines offer passengers free on - board snacks . what is the greatest possible percentage of major airline companies that offer both wireless internet and free on - board snacks ?
Options: a ) 25 % , b ) 35 % , c ) 45 % , d ) 55 % , e ) 65 %
Rationale: "to maximize the percentage of companies offering both , let ' s assume that all 35 % of companies which offer wireless internet also offer snacks . the answer is b ."
Answer: b
Python program:
a = 35 * 1
Problem: the batting average of a particular batsman is 59 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 ) 156 , b ) 208 , c ) 210 , d ) 223 , e ) 229
Rationale: "explanation : total runs scored by the batsman = 59 * 46 = 2714 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2714 – 2552 = 162 runs . let the highest score be x , hence the lowest score = x – 150 x + ( x - 150 ) = 162 2 x = 312 x = 156 runs answer a"
Answer: a
Python program:
a = 59 * 46
b = 46 - 2
c = 58 * b
d = a - c
e = 150 + d 
f = e / 2
Problem: find the simple interest on $ 3000 for 3 years at 10 % per annum ?
Options: a ) $ 900 , b ) $ 300 , c ) $ 500 , d ) $ 600 , e ) $ 1000
Rationale: "si = ptr / 100 = 3000 * 3 * 10 / 100 = $ 900 answer is a"
Answer: a
Python program:
a = 3 / 100
b = 3000 * a
Problem: if 9 ^ y = 3 ^ 12 , what is y ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "3 ^ 2 y = 3 ^ 12 2 y = 12 , therefore y = 6 e"
Answer: e
Python program:
a = 12 / 2
Problem: during a car trip , maria stopped to rest after she traveled 1 / 2 of the total distance to her destination . she stopped again after she traveled 1 / 4 of the distance remaining between her first stop and her destination , and then she drove the remaining 150 miles to her detination . what was the total distance , in miles from maria ' s starting point to her destination ?
Options: a ) 280 , b ) 320 , c ) 360 , d ) 400 , e ) 480
Rationale: "easy 400 is the answer . 3 / 4 ( x / 2 ) = 150 x = 150 * 8 / 3 = 400 . answer d"
Answer: d
Python program:
a = 1 / 2
b = 1 / 2
c = 1 / 4
d = b * c
e = a + d 
f = 1 - e
g = 150 / f
Problem: with a uniform speed a car covers the distance in 8 hours . had the speed been increased by 1 km / hr , the same distance could have been covered in 7 1 / 2 hours . what is the distance covered ?
Options: a ) 187 km , b ) 480 km , c ) 278 km , d ) 120 km , e ) 671 km
Rationale: "let the distance be x km . then , x / ( 7 1 / 2 ) - x / 8 = 1 2 x / 15 - x / 8 = 1 = > x = 120 km . answer : d"
Answer: d
Python program:
a = 1 / 2
Problem: the ratio of the present age of sandy to that of molly is 7 : 2 . eight years from now , the ratio of the ages of sandy to molly will be 5 : 2 . what was sandy ' s age 6 years ago ?
Options: a ) 18 , b ) 24 , c ) 30 , d ) 36 , e ) 42
Rationale: "let the present age of sandy be 7 x years and that of molly be 2 x years . ( 7 x + 8 ) / ( 2 x + 8 ) = 5 / 2 4 x = 24 x = 6 six years ago , sandy ' s age was 7 ( 6 ) - 6 = 36 the answer is d ."
Answer: d
Python program:
a = 10 + 6 
b = 5 * a
c = 10 + 6 
d = 2 * c
e = b - d
f = e * 7
g = 2 + 2 
h = f / g
i = h - 6
Problem: the average monthly salary of 8 workers and one supervisor in a factory was 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . whenthesupervisor , whosesalarywas 430 . when the supervisor , whose salary was 870 per month , retired , a new person was appointed and then the average salary of 9 people was $ $ 420 per month . the salary of the new supervisor is :
Options: a ) 233 , b ) 600 , c ) 287 , d ) 780 , e ) 191
Rationale: "explanation : total salary of 8 workers and supervisor together = 9 ã — 430 = 3870 now total salary of 8 workers = 3870 â ˆ ’ 870 = 3000 total salary of 9 workers including the new supervisor = 9 ã — 420 = 3780 salary of the new supervisor = 3780 â ˆ ’ 3000 = 780 answer : d"
Answer: d
Python program:
a = 420 * 9
b = 430 * 9
c = b - 870
d = a - c
Problem: the average of 6 no . ' s is 3.95 . the average of 2 of them is 3.6 , while the average of the other 2 is 3.85 . what is the average of the remaining 2 no ' s ?
Options: a ) 4.2 , b ) 4.4 , c ) 4.6 , d ) 5.6 , e ) 5.7
Rationale: "sum of the remaining two numbers = ( 3.95 * 6 ) - [ ( 3.6 * 2 ) + ( 3.85 * 2 ) ] = 8.8 . required average = ( 8.8 / 2 ) = 4.4 . b"
Answer: b
Python program:
a = 6 * 3
b = 2 * 3
c = 2 * 3
d = b + c 
e = a - d
f = e / 2
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 55 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 7.19 , b ) 7.17 , c ) 7.62 , d ) 7.15 , e ) 7.11
Rationale: "t = ( 121 + 165 ) / ( 80 + 55 ) * 18 / 5 t = 7.62 answer : c"
Answer: c
Python program:
a = 121 + 165 
b = 80 + 55 
c = b * const_0_2778
d = a / c
Problem: 24 oz of juice p and 25 oz of juice q are mixed to make smothies x and y . the ratio of p to q in smothie x is 4 is to 1 and that in y is 1 is to 5 . how many ounces of juice p are contained in the smothie x ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: easy way to solve this question is start from the answer and then conform the information provided in the question . we can start from option d i . e 20 . . . as a quantity of juice p in x because it is the only one option that gets divided by 4 is 20 . . . since in the x the juice p to q ratio is 4 : 1 this gives us that quantity of juice p in x = 20 therefore quantity of juice v will be 5 . . . hence ratio = 4 : 1 this will lead to quantity of juice p in x = 4 and quantity of juice v = 20 . . . hence ratio 1 : 5 if we calculate total juice p = 24 and total of juice q = 25 it fits because totals are same as what mentioned in the question . . . thus ans is d
Answer: d
Python program:
a = 24 + 25 
b = a / 2
c = 4 + 1 
d = 4 / c
e = b * d
Problem: a shirt goes on sale for 90 % of its original price . one week later , the sale price is marked down 10 % . the final price is what percent of the original price ?
Options: a ) 72 % , b ) 81 % , c ) 52 % , d ) 50 % , e ) 28 %
Rationale: "just assume original price is 100 . sale price = 90 then it is marked down by 10 % = 90 - 9 = 81 . hence it is 81 % od the original price . hence answer is b ."
Answer: b
Python program:
a = 90 / 100
b = a * 10
c = 90 - b
Problem: in a certain parking lot , 2 % of the cars are towed for parking illegally . however 80 % of the cars which are parked illegally are not towed . what percentage of cars in the parking lot are parked illegally ?
Options: a ) 4 % , b ) 6 % , c ) 8 % , d ) 10 % , e ) 12 %
Rationale: let x be the number of cars and let y be the number of cars parked illegally . 2 % * x = 20 % * y y / x = 1 / 10 = 10 % the answer is d .
Answer: d
Python program:
a = 80 / 100
b = 1 - a
c = 2 / 100
d = b / c
Problem: the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 145 , what is the difference between the ages of patrick and monica ?
Options: a ) 27 , b ) 48 , c ) 45 , d ) 72 , e ) 18
Rationale: "ages of p and mi = 3 x + 5 x ages of mi and mo = 3 x : 5 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 25 x sum = 47 x = 145 x = 3 difference if ages of pa and mo = 25 x - 9 x = 16 x = 16 * 3 = 48 answer b"
Answer: b
Python program:
a = 5 * 5
b = 3 * 3
c = 3 * 5
d = b + c 
e = 5 * 5
f = d + e 
g = 145 / f
h = a * g
i = 3 * 3
j = 3 * 3
k = 3 * 5
l = j + k 
m = 5 * 5
n = l + m 
o = 145 / n
p = i * o
q = h - p
Problem: a is an integer greater than 29 but less than 41 , b is an integer greater than 39 but less than 51 , what is the range of a / b ?
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 2 / 5 , d ) 1 , e ) 5 / 4
Rationale: "min value of a / b will be when b is highest and a is lowest - - - > a = 30 and b = 50 so , a / b = 3 / 5 max value of a / b will be when b is lowest and a is highest - - - > a = 40 and b = 40 so , a / b = 1 range is 1 - ( 3 / 5 ) = 2 / 5 answer should be c ."
Answer: c
Python program:
a = 41 - 1
b = 39 + 1 
c = a / b
d = 29 + 1 
e = 51 - 1
f = d / e
g = c - f
Problem: in one year , the population , of a village increased by 5 % and in the next year , it decreased by 5 % . if at the end of 2 nd year , the population was 9975 , what was it in the beginning ?
Options: a ) 7787 , b ) 10000 , c ) 1988 , d ) 1277 , e ) 2081
Rationale: "x * 105 / 100 * 95 / 100 = 9975 x * 0.9975 = 9975 x = 9975 / 0.9975 = > 10000 answer : b"
Answer: b
Python program:
a = 5 / 100
b = 1 - a
c = 9975 / b
d = 5 / 100
e = 1 + d 
f = c / e
Problem: if 2 ^ ( 2 w ) = 8 ^ ( w − 1 ) , what is the value of w ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "2 ^ ( 2 w ) = 8 ^ ( w − 1 ) 2 ^ ( 2 w ) = 2 ^ ( 3 * ( w − 1 ) ) 2 ^ ( 2 w ) = 2 ^ ( 3 w - 3 ) let ' s equate the exponents as the bases are equal . 2 w = 3 w - 3 w = 3 the answer is a ."
Answer: a
Python program:
a = math.log(2)
b = 12 * a
c = math.log(2)
d = b / c
Problem: a person travels equal distances with speeds of 7 km / hr , 8 km / hr and 9 km / hr and takes a total time of 47 minutes . the total distance is ?
Options: a ) 6 km , b ) 3 km , c ) 7 km , d ) 9 km , e ) 2 km
Rationale: "let the total distance be 3 x km . then , x / 7 + x / 8 + x / 9 = 47 / 60 36 x / 95 = 47 / 60 = > x = 2.07 . total distance = 3 * 2.07 = 6.2 km . answer : a"
Answer: a
Python program:
a = 47 / const_60
b = 1 / 7
c = 1 / 8
d = b + c 
e = 1 / 9
f = d + e 
g = a / f
h = g * 3
i = h * 1000
Problem: a leak in the bottom of a tank can empty the full tank in 9 hours . an inlet pipe fills water at the rate of 6 litres a minute . when the tank is full , the inlet is opened and due to the leak , the tank is empty in 12 hours . how many litres does the cistern hold ?
Options: a ) 7580 , b ) 12960 , c ) 8290 , d ) 8640 , e ) none
Rationale: "solution work done by the inlet in 1 hour = ( 1 / 9 - 1 / 12 ) = 1 / 36 work done by the inlet in 1 min . = ( 1 / 36 × 1 / 60 ) = 0.000463 volume of 0.000463 part = 6 litres . therefore , volume of whole = 1 / 0.000463 x 6 ‹ = › 12960 litres . answer b"
Answer: b
Python program:
a = 12 * const_60
b = 6 * a
c = 12 * const_60
d = 9 * const_60
e = c / d
f = e - 1
g = b / f
Problem: if k ^ 2 is divisible by 240 what is the least possible value of integer k ?
Options: a ) 60 , b ) 30 , c ) 12 , d ) 90 , e ) 120
Rationale: "240 can be written as ( 2 ^ 4 ) * 3 * 5 . for k ^ 2 to be divisible by 240 it should contain at least 2 ^ 4 and 3 and 5 in its factors . we can leave out option c because 12 doesnt have 5 as one of its factor . now if we check for option b , 30 can be written as 2 * 3 * 5 , hence 30 ^ 2 will have 2 as the maximum power of 2 , so we can leave out this option too . option c is the right answer if we follow the same method as we followed for other two previous options . 60 = ( 2 ^ 2 ) * 3 * 5 ; 60 ^ 2 = ( 2 ^ 4 ) * ( 3 ^ 2 ) * ( 5 ^ 2 ) . so it shows that 60 ^ 2 is divisible by 240 and hence the answer . answer : a"
Answer: a
Python program:
a = 240 / 2
b = a / 2
Problem: you enter a weight loss challenge game and manage to lose 11 % of your body weight . for the final weigh in you are forced to wear clothes that add 2 % to your weight . what percentage of weight loss is measured at the final weigh in ?
Options: a ) 13 % , b ) 9.22 % , c ) 9 % , d ) 14 % , e ) 12 %
Rationale: "( 100 % - 11 % ) * ( 100 % + 2 % ) = 0.89 * 1.02 = 9.22 % the weigh in records your weight loss at 9.22 % ! the answer is b"
Answer: b
Python program:
a = 11 / 100
b = 1 - a
c = 2 / 100
d = 1 + c 
e = b * d
f = 1 - e
g = f * 100
Problem: in a certain game , a large bag is filled with blue , green , purple and red chips worth 1 , 5 , x and 11 points each , respectively . the purple chips are worth more than the green chips , but less than the red chips . a certain number of chips are then selected from the bag . if the product of the point values of the selected chips is 2200 , how many purple chips were selected ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "2200 = 1 * 5 ^ 2 * 8 * 11 the factor of 8 must come from the purple point value , so there is 1 purple chip . the answer is a ."
Answer: a
Python program:
a = 5 - 2
Problem: solution a is 40 % salt and solution b is 80 % salt . if you have 30 ounces of solution a and 60 ounces of solution b , in what ratio could you mix solution a with solution b to produce 50 ounces of a 50 % salt solution ?
Options: a ) 6 : 4 , b ) 6 : 14 , c ) 4 : 4 , d ) 4 : 6 , e ) 3 : 1
Rationale: forget the volumes for the time being . you have to mix 20 % and 80 % solutions to get 50 % . this is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities . if this does n ' t strike , use w 1 / w 2 = ( a 2 - aavg ) / ( aavg - a 1 ) w 1 / w 2 = ( 80 - 50 ) / ( 50 - 40 ) = 3 / 1 so the volume of the two solutions will be equal . answer has to be 3 : 1 . e
Answer: e
Python program:
a = 80 / 100
b = 50 * a
c = 50 / 100
d = 50 * c
e = b - d
f = 80 / 100
g = 40 / 100
h = f - g
i = e / h
j = 80 / 100
k = 50 * j
l = 50 / 100
m = 50 * l
n = k - m
o = 80 / 100
p = 40 / 100
q = o - p
r = n / q
s = 50 - r
t = i / s
Problem: a no . when divided by the sum of 555 and 445 gives 2 times their difference as quotient & 40 as remainder . find the no . is ?
Options: a ) 220044 , b ) 145778 , c ) 220400 , d ) 220014 , e ) 220040
Rationale: "( 555 + 445 ) * 2 * 110 + 30 = 220000 + 30 = 220040 e"
Answer: e
Python program:
a = 555 + 445 
b = a * 2
c = 555 - 445
d = b * c
e = d + 40
Problem: a , b and c started a business with capitals of rs . 8000 , rs . 10000 and rs . 12000 respectively . at the end of the year , the profit share of b is rs . 1500 . the difference between the profit shares of a and c is ?
Options: a ) 8867 , b ) 299 , c ) 279 , d ) 600 , e ) 2612
Rationale: "ratio of investments of a , b and c is 8000 : 10000 : 12000 = 4 : 5 : 6 and also given that , profit share of b is rs . 1500 = > 5 parts out of 15 parts is rs . 1500 now , required difference is 6 - 4 = 2 parts required difference = 2 / 5 ( 1500 ) = rs . 600 . answer : d"
Answer: d
Python program:
a = 12000 / 10000
b = 8000 / 10000
c = a - b
d = c * 1500
Problem: a cement mixture is composed of 3 elements . by weight , 1 / 3 of the mixture is sand , 1 / 2 of the mixture is water , and the remaining 8 pounds of the mixture is gravel . what is the weight of the entire mixture in pounds ?
Options: a ) 30 , b ) 36 , c ) 42 , d ) 46 , e ) 48
Rationale: "let the total weight be x . sand content = ( 1 / 3 ) x water content = ( 1 / 2 ) x gravel = x - ( 1 / 3 ) x - ( 1 / 2 ) x = ( 1 / 6 ) x = 8 x = 48 then answer will be e = 48"
Answer: e
Python program:
a = 1 / 3
b = 1 / 2
c = a + b 
d = 1 - c
e = 8 / d
Problem: machine a and machine b are each used to manufacture 330 sprockets . it takes machine a 10 hours longer to produce 330 sprockets than machine b . machine b produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machineaproduce ?
Options: a ) 3.3 , b ) 6.6 , c ) 60 , d ) 100 , e ) 110
Rationale: "time taken by b = t time taken by a = t + 10 qty produced by a = q qty produced by b = 1.1 q for b : t ( 1.1 q ) = 330 qt = 300 for a : ( t + 10 ) ( q ) = 330 qt + 10 q = 330 300 + 10 q = 330 q = 3 so a can produce 3 / hour . then b can produce = 3 ( 1.1 ) = 3.3 / hour . a"
Answer: a
Python program:
a = 10 * 330
b = 100 + 10 
c = b / 100
d = a * c
e = 100 + 10 
f = e / 100
g = 330 * f
h = g - 330
i = d / h
j = 330 / i
Problem: albert is 2 times mary ’ s age and 4 times as old as betty . mary is 14 years younger than albert . how old is betty ?
Options: a ) 5 , b ) 7 , c ) 10 , d ) 15 , e ) 18
Rationale: "a = 2 m = m + 14 m = 14 a = 28 a = 4 b , and so b = 7 the answer is b ."
Answer: b
Python program:
a = 2 * 14
b = a / 4
Problem: how many kg of pure salt must be added to 100 kg of 10 % solution of salt and water to increase it to a 35 % solution ?
Options: a ) a ) 6.7 , b ) b ) 38.5 , c ) c ) 9.6 , d ) d ) 12.5 , e ) e ) 7.9
Rationale: "amount salt in 100 kg solution = 10 * 100 / 100 = 10 kg let x kg of pure salt be added then ( 10 + x ) / ( 100 + x ) = 35 / 100 200 + 20 x = 700 + 7 x 13 x = 500 x = 28.5 answer is b"
Answer: b
Python program:
a = 35 - 10
b = 35 / 100
c = 1 - b
d = a / c
Problem: when 200 is divided by positive integer x , the remainder is 2 . what is the remainder when 398 is divided by x ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: "f 200 / x leaves a reminder 2 then ( 200 - 2 ) i . e . 198 is divisible by x so ( 200 + 198 ) / x leaves a reminder rem ( 200 / x ) + rem ( 198 / x ) = > 2 + 0 = 2 answer : a"
Answer: a
Python program:
a = 398 - 200
b = 200 - a
Problem: what quantity of water should taken out to concentrate 12 liters of 40 % acidic liquid to 60 % acidic liquid ?
Options: a ) 4 liters , b ) 10 liters , c ) 15 liters , d ) 8 liters , e ) 6 liters
Rationale: "required answer is = 12 ( 60 - 40 ) / 60 = 4 liters answer is a"
Answer: a
Python program:
a = 12 * 40
b = a / 60
c = 12 - b