euclaise/mathqa_programs huggingface dataset:
Problem: the grade point average of the entire class is 84 . if the average of one fourth of the class is 96 , what is the average of the rest of the class ?
Options: a ) 76 , b ) 77 , c ) 78 , d ) 79 , e ) 80
Rationale: "let x be the number of students in the class . let p be the average of the rest of the class . 84 x = ( 1 / 4 ) 96 x + ( 3 / 4 ) ( p ) x 336 = 96 + 3 p 3 p = 240 p = 80 . the answer is e ."
Answer: e
Python program:
a = 84 * 4
b = a - 96
c = 4 - 1
d = b / c
Problem: the average weight of 19 students is 15 kg . by the admission of a new student the average weight is reduced to 14.2 kg . the weight of the new student is ?
Options: a ) 1 kg , b ) 10.8 kg , c ) 11 kg , d ) 14.9 kg , e ) none
Rationale: "answer weight of new student = total weight of all 20 students - total weight of initial 19 students = ( 20 x 14.2 - 19 x 15 ) kg = 1 kg . correct option : a"
Answer: a
Python program:
a = 19 + 1 
b = a * 14
c = 19 * 15
d = b - c
Problem: if a student loses 6 kilograms , he will weigh twice as much as his sister . together they now weigh 132 kilograms . what is the student ' s present weight in kilograms ?
Options: a ) 82 , b ) 84 , c ) 86 , d ) 88 , e ) 90
Rationale: "let x be the weight of the sister . then the student ' s weight is 2 x + 6 . x + ( 2 x + 6 ) = 132 3 x = 126 x = 42 kg then the student ' s weight is 90 kg . the answer is e ."
Answer: e
Python program:
a = 132 - 6
b = a / 3
c = 132 - b
Problem: an ant walks an average of 600 meters in 10 minutes . a beetle walks 25 % less distance at the same time on the average . assuming the beetle walks at her regular rate , what is its speed in km / h ?
Options: a ) 2.215 . , b ) 2.5 . , c ) 2.6 , d ) 2.7 , e ) 3.5 .
Rationale: "the ant walks an average of 600 meters in 10 minutes 600 meters in 5 / 30 hours the beetle walks 25 % less distance = 600 - 150 = 450 meters in 10 minutes 0.450 km in 5 / 30 = 5 / 30 hours speed = 0.450 * 30 / 5 = 2.7 km / h i guess option d should be 2.7"
Answer: d
Python program:
a = 600 / 1000
b = 10 / const_60
c = a / b
d = 25 / 100
e = 1 - d
f = c * e
Problem: the width of a rectangular hall is ½ of its length . if the area of the hall is 578 sq . m , what is the difference between its length and breadth ?
Options: a ) 8 m , b ) 10 m , c ) 12 m , d ) 15 m , e ) 17 m
Rationale: "let the length of the hall be x m breadth of the hall = 1 x / 2 m area of the hall = length * breadth 578 = x * 1 x / 2 x ² = 1156 x = 34 difference between the length and breadth of the hall = x - 1 x / 2 = x / 2 = 34 / 2 = 17 m answer : e"
Answer: e
Python program:
a = 1 / 2
b = 578 / a
c = math.sqrt(b)
d = c / 2
Problem: how long does a train 165 meters long running at the rate of 90 kmph take to cross a bridge 660 meters in length ?
Options: a ) 28 , b ) 27 , c ) 33 , d ) 18 , e ) 12
Rationale: "t = ( 660 + 165 ) / 90 * 18 / 5 t = 33 answer : c"
Answer: c
Python program:
a = 165 + 660 
b = 90 * const_0_2778
c = a / b
Problem: a boat having a length 3 m and breadth 2 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of man is
Options: a ) 12 kg , b ) 60 kg , c ) 72 kg , d ) 96 kg , e ) none
Rationale: "solution volume of water displaced = ( 3 x 2 x 0.01 ) m 3 = 0.06 m 3 . mass of man = volume of water displaced × density of water = ( 0.06 × 1000 ) kg = 60 kg . answer b"
Answer: b
Python program:
a = 3 * 2
b = 1 / 100
c = a * b
d = c * 1000
Problem: how many different pairs of numbers ( s , t ) such that s = 3 t can be obtained if s and t are selected from the set of number { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 }
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: given s = 3 t t can take 0,1 , 2,3 , 4 and so s = 0,3 , 6,9 , 12 4 such pairs can be formed . answer e
Answer: e
Python program:
a = 12 / 3
b = a + 1
Problem: in one alloy there is 10 % chromium while in another alloy it is 8 % . 15 kg of the first alloy was melted together with 35 kg of the second one to form a third alloy . find the percentage of chromium in the new alloy .
Options: a ) 9.0 % , b ) 9.4 % , c ) 9.2 % , d ) 8.8 % , e ) 8.6 %
Rationale: "the amount of chromium in the new 15 + 35 = 50 kg alloy is 0.10 * 15 + 0.08 * 35 = 4.3 kg , so the percentage is 4.3 / 50 * 100 = 8.6 % . answer : e ."
Answer: e
Python program:
a = 10 * 15
b = a / 100
c = 8 * 35
d = c / 100
e = b + d 
f = 15 + 35 
g = e / f
h = g * 100
Problem: on a certain date , pat invested $ 10,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 12 years will be $ 40,000 , in how many years , the total value of the investment plus interest will increase to $ 80,000 ?
Options: a ) 15 , b ) 16 , c ) 18 , d ) 20 , e ) 24
Rationale: "x - interest rate 80.000 = 10.000 ( 1 + x ) ^ year = > 8 = ( 1 + x ) ^ year 40.000 = 10.000 . ( 1 + x ) ^ 12 = > 4 = ( 1 + x ) ^ 12 = > 2 = ( 1 + x ) ^ 6 = > 8 = ( 1 + x ) ^ 18 so , after 18 years , the total value of the investment plus interest will increase to $ 80,000 . answer : c"
Answer: c
Python program:
a = 3 * 10
b = 4 + 1 
c = a / b
d = math.log(c)
e = 2 * 10
f = 4 + 1 
g = e / f
h = 1 / 12
i = g ** h
j = math.log(i)
k = d / j
Problem: in a river flowing at 2 km / hr , a boat travels 32 km upstream and then returns downstream to the starting point . if its speed in still water be 6 km / hr , find the total journey time .
Options: a ) 10 hours , b ) 12 hours , c ) 14 hours , d ) 16 hours , e ) none of these
Rationale: "explanation : speed of the boat = 6 km / hr speed downstream = ( 6 + 2 ) = 8 km / hr speed upstream = ( 6 - 2 ) = 4 km / hr distance travelled downstream = distance travelled upstream = 32 km total time taken = time taken downstream + time taken upstream = ( 32 / 8 ) + ( 32 / 4 ) = ( 32 / 8 ) + ( 64 / 8 ) = ( 96 / 8 ) = 12 hr . answer : option b"
Answer: b
Python program:
a = 6 - 2
b = 32 / a
c = 6 + 2 
d = 32 / c
e = b + d
Problem: a bowl of nuts is prepared for a party . brand p mixed nuts are 20 % almonds and brand q ' s deluxe nuts are 25 % almonds . if a bowl contains a total of 66 ounces of nuts , representing a mixture of both brands , and 15 ounces of the mixture are almonds , how many ounces of brand q ' s deluxe mixed nuts are used ?
Options: a ) 16 , b ) 20 , c ) 36 , d ) 44 , e ) 48
Rationale: "lets say x ounces of p is mixed with q . = > 66 - x ounces of q is present in the mixture ( as the total = 66 ounces ) given total almond weight = 15 ounces ( 20 x / 100 ) + ( 25 / 100 ) ( 66 - x ) = 15 = > x = 30 = > 66 - 30 = 36 ounces of q is present in the mixture . answer is c ."
Answer: c
Python program:
a = 20 / 100
b = a * 66
c = 15 - b
d = 25 / 100
e = 20 / 100
f = d - e
g = c / f
Problem: what is the units digit of ( 6 ! * 4 ! + 6 ! * 5 ! ) / 6 ?
Options: a ) 1 , b ) 0 , c ) 2 , d ) 3 , e ) 4
Rationale: ( 6 ! * 4 ! + 6 ! * 5 ! ) / 6 = 6 ! ( 4 ! + 5 ! ) / 6 = 720 ( 24 + 120 ) / 6 = ( 720 * 144 ) / 6 = 720 * 24 units digit of the above product will be equal to 0 answer b
Answer: b
Python program:
a = math.factorial(6)
b = math.factorial(4)
c = a * b
d = math.factorial(6)
e = math.factorial(5)
f = d * e
g = c + f 
h = g / 6
Problem: if x and y are sets of integers , x # y denotes the set of integers that belong to set x or set y , but not both . if x consists of 8 integers , y consists of 10 integers , and 6 of the integers are in both x and y , then x # y consists of how many integers ?
Options: a ) 6 , b ) 16 , c ) 22 , d ) 30 , e ) 174
Rationale: "the number of integers that belong to set x only is 8 - 6 = 2 ; the number of integers that belong to set y only is 10 - 6 = 4 ; the number of integers that belong to set x or set y , but not both is 2 + 4 = 6 . answer : a ."
Answer: a
Python program:
a = 10 - 6
b = 8 - 6
c = a + b
Problem: the mean of 50 observations was 36 . it was found later that an observation 48 was wrongly taken as 21 . the corrected new mean is :
Options: a ) 36.54 , b ) 36.58 , c ) 36.23 , d ) 36.14 , e ) 36.81
Rationale: "explanation : correct sum = ( 36 * 50 + 48 - 21 ) = 1827 . correct mean = = 1827 / 50 = 36.54 answer : a ) 36.54"
Answer: a
Python program:
a = 36 * 50
b = 50 - 2
c = b - 21
d = a + c 
e = d / 50
Problem: if an object travels at ten feet per second , how many feet does it travel in two hours ?
Options: a ) 60000 , b ) 30000 , c ) 18000 , d ) 72000 , e ) 22200
Rationale: "if an object travels at 10 feet per second it covers 10 x 60 feet in one minute , and 10 x 60 x 2 x 60 feet in two hour . answer = 72000 answer : d"
Answer: d
Python program:
a = 3 * const_60
b = a * const_60
Problem: 3 medical experts , working together at the same constant rate , can write an anatomy textbook in 24 days . how many additional experts , working together at this same constant rate , are needed to write the textbook in 18 days ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: each expert can write 1 / 72 of the book per day . to complete the book in 18 days , we need 72 / 18 = 4 experts , thus 1 more expert is needed . the answer is a .
Answer: a
Python program:
a = 3 * 24
b = a / 18
c = b - 3
Problem: the value of ( 34.31 * 0.473 * 1.567 ) / ( 0.0673 * 23.25 * 7.57 ) is close to
Options: a ) 2 , b ) 1.15 , c ) 2.05 , d ) 2.15 , e ) 2.35
Rationale: "( 34.31 * 0.473 * 1.567 ) / ( 0.0673 * 23.25 * 7.57 ) = 25.4303 / 11.845 = 2.15 answer : d"
Answer: d
Python program:
a = 34 * 31
b = a * 1
c = 7 * 57
d = c * 0
e = b / d
f = e / 10
Problem: the cost of carpeting a room 15 meters long with a carpet 75 cm wide at 30 paise per meter is rs . 36 . the breadth of the room is ?
Options: a ) 6 meters , b ) 7 meters , c ) 8 meters , d ) 9 meters , e ) 10 meters
Rationale: "length of carpet = total cost / rate = 3600 / 30 = 120 m area of carpet = ( 120 x 75 ) / 100 m 2 = 90 m 2 ∴ area of the room = 90 m 2 breadth of the room = area / length = 90 / 15 m = 6 m answer : a"
Answer: a
Python program:
a = 36 * 100
b = a / 30
c = 75 / 100
d = b * c
e = d / 15
Problem: an aeroplane covers a certain distance of 590 kmph in 8 hours . to cover the same distance in 2 3 / 4 hours , it must travel at a speed of
Options: a ) 1780 , b ) 1716 , c ) 1890 , d ) 1980 , e ) 1450
Rationale: speed of aeroplane = 590 kmph distance travelled in 8 hours = 590 * 8 = 4720 km speed of aeroplane to acver 4720 km in 11 / 4 = 4720 * 4 / 11 = 1716 km answer b .
Answer: b
Python program:
a = 590 * 8
b = 4 * 2
c = b + 3 
d = c / 4
e = a / d
Problem: a work can be completed by 12 boys in 24 days and 12 girls in 12 days . in how many days would the 6 boys and 6 girls working together complete the work ?
Options: a ) 12 , b ) 18 , c ) 16 , d ) 20 , e ) 24
Rationale: in 1 day , 12 boys does 1 / 24 of the total work . = > in 1 day , 1 boy does 1 / ( 24 * 12 ) of the total work = > in 1 days , 6 boys do 6 / ( 24 * 12 ) = 1 / 48 of the total work in 1 day , 12 girls do 1 / 12 of the total work . = > in 1 day , 1 girl does 1 / ( 12 * 12 ) of the total work = > in 1 day , 6 girls do 6 / ( 12 * 12 ) = 1 / 24 of the total work in 1 day , 6 boys and 6 girls do 1 / 48 + 1 / 24 of the total work = > in 1 days , 6 boys and 6 girls do 3 / 48 = 1 / 16 of the total work so , 6 boys and 6 girls complete all work in 16 days . hence , the answer is c
Answer: c
Python program:
a = 12 * 24
b = 6 / a
c = 12 * 12
d = 6 / c
e = b + d 
f = 1/(e)
Problem: walking at 75 % of his usual speed a man takes 24 minutes more to cover a distance . what is his usual time to cover this distance ?
Options: a ) 30 , b ) 36 , c ) 42 , d ) 48 , e ) 72
Rationale: "speed is inversly proprtional to time walking at 75 % of speed meand 3 / 4 s takes 4 / 3 t . it takes 24 minutes extra to cover the distance . then 4 / 3 t = t + 24 4 t = 3 t + 72 t = 72 option e is correct"
Answer: e
Python program:
a = 75 / 100
b = 1 / a
c = b - 1
d = 24 / c
Problem: anusha , banu and esha run a running race of 100 meters . anusha is the fastest followed by banu and then esha . anusha , banu and esha maintain constant speeds during the entire race . when anusha reached the goal post , banu was 10 m behind . when banu reached the goal post esha was 10 m behind . how far was behind anusha when the latter reached the goal post .
Options: a ) 22 , b ) 88 , c ) 81 , d ) 66 , e ) 22
Rationale: by that time anusha covered 100 m , bhanu covered 90 m . so ratio of their speeds = 10 : 9 by that time bhanu reached 100 m , esha covered 90 m . so ratio of their speeds = 10 : 9 ratio of the speed of all the three = 100 : 90 : 81 by that time anusha covered 100 m , esha covers only 81 . answer : c
Answer: c
Python program:
a = 100 - 10
b = 100 - 10
c = 100 / b
d = 1/(c)
e = a * 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 30 % . 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 ) 79 %
Rationale: "the original output increases by 10 % and then 30 % . total % change = a + b + ab / 100 total % change = 10 + 30 + 10 * 30 / 100 = 43 % now , you want to change it to 0 , so , 0 = 43 + x + 43 x / 100 x = - 43 ( 100 ) / 143 = 30 % approximately answer is c"
Answer: c
Python program:
a = 100 + 10 
b = 100 + 10 
c = 30 / 100
d = b * c
e = a + d 
f = e - 100
g = f * 100
h = 100 + 10 
i = 100 + 10 
j = 30 / 100
k = i * j
l = h + k 
m = g / l
Problem: if the cost price is 89 % of selling price then what is the profit percentage .
Options: a ) 8.35 , b ) 9.35 , c ) 10.35 , d ) 11.35 , e ) 12.35
Rationale: "selling price = rs 100 : then cost price = rs 89 : profit = rs 11 . profit = { ( 11 / 89 ) * 100 } % = 12.35 % answer is e ."
Answer: e
Python program:
a = 100 - 89
b = a / 89
c = b * 100
Problem: the rate of interest on a sum of money is 2 % p . a . for the first 3 years , 4 % p . a . for the next 4 years , and 5 % for the period beyond 7 years . if the s . i , occured on the sum for the total period of 8 years is rs . 540 / - , the sum is
Options: a ) 2,200 , b ) 2,000 , c ) 2,100 , d ) 2,250 , e ) 2,560
Rationale: "explanation : i 1 = ( p x 3 x 2 ) / 100 = 3 p / 50 i 2 = ( p x 4 x 4 ) / 100 = 4 p / 25 i 3 = ( p x 1 x 5 ) / 100 = p / 20 3 p / 50 + 4 p / 25 + p / 20 = 540 the l . c . m of 50 , 25 , 20 = 100 ( 6 p + 16 p + 5 p ) / 100 = 540 27 p / 100 = 540 27 p = 54000 p = 54000 / 27 p = 2000 answer : option b"
Answer: b
Python program:
a = 540 / 540
Problem: at what rate percent per annum will the simple interest on a sum of money be 7 / 5 of the amount in 10 years ?
Options: a ) 4 % , b ) 7 % , c ) 9 % , d ) 3 % , e ) 14 %
Rationale: "let sum = x . then , s . i . = 7 x / 5 , time = 10 years . rate = ( 100 * 7 x ) / ( x * 5 * 10 ) = 14 % answer : e"
Answer: e
Python program:
a = 7 / 5
b = a * 100
c = b / 10
Problem: two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 2.9 km and 1.6 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
Options: a ) 99 , b ) 277 , c ) 48 , d ) 96 , e ) 108
Rationale: "relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 2.9 + 1.6 = 4.5 km = 4500 m . required time = 4500 * 3 / 125 = 108 sec . answer : e"
Answer: e
Python program:
a = 2 * 9
b = 60 * 1000
c = b / 3600
d = a / c
e = 1 * 6
f = 90 * 1000
g = f / 3600
h = e / g
i = d - h
Problem: how many integers between 324,700 and 458,600 have a 2 in the tens digit and a 1 in the units digit ?
Options: a ) 1339 , b ) 2300 , c ) 4200 , d ) 1340 , e ) 2414
Rationale: "there is one number in hundred with 2 in th tens digit and 1 in the units digit : 21 , 121 , 221 , 321 , . . . the difference between 324,700 and 458,600 is 458,600 - 324,700 = 133,900 - one number per each hundred gives 133,900 / 100 = 1,339 numbers . answer : 1,339 a"
Answer: a
Python program:
a = 2 * 100
b = 3 + 4 
c = b * 10
d = a + c 
e = d + 2 
f = 458 - 600
Problem: in a graduating class of 242 students , 144 took geometry and 119 took biology . what is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology ?
Options: a ) 144 , b ) 119 , c ) 113 , d ) 88 , e ) 123
Rationale: "greatest possible number taken both should be 144 ( as it is maximum for one ) smallest possible number taken both should be given by total - neither = a + b - both both = a + b + neither - total ( neither must be 0 to minimize the both ) so 144 + 119 + 0 - 242 = 21 greatest - smallest is 144 - 21 = 123 so answer must be e . 123"
Answer: e
Python program:
a = 144 + 119 
b = a - 242
c = 119 - b
Problem: the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 20 are excluded , the average mark of the remaining will be 95 . find the number of students who wrote the exam .
Options: a ) 15 , b ) 45 , c ) 35 , d ) 25 , e ) 55
Rationale: let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 95 ( x - 5 ) 80 x - ( 5 * 20 ) = 95 ( x - 5 ) 375 = 15 x = > x = 25 answer : d
Answer: d
Python program:
a = 95 * 5
b = 5 * 20
c = a - b
d = 95 - 80
e = c / d
Problem: real - estate salesman z is selling a house at a 30 percent discount from its retail price . real - estate salesman x vows to match this price , and then offers an additional 30 percent discount . real - estate salesman y decides to average the prices of salesmen z and x , then offer an additional 30 percent discount . salesman y ' s final price is what fraction of salesman x ' s final price ?
Options: a ) 12 / 13 , b ) 11 / 15 , c ) 11 / 17 , d ) 11 / 14 , e ) 11 / 7
Rationale: "let the retail price be = x selling price of z = 0.70 x selling price of x = 0.70 * 0.80 x = 0.56 x selling price of y = ( ( 0.70 x + 0.56 x ) / 2 ) * 0.70 = 0.63 x * 0.70 = 0.44 x 0.44 x = k * 0.56 x k = 0.44 / 0.56 = 44 / 56 = 11 / 14 answer : d"
Answer: d
Python program:
a = 100 - 30
b = 100 - 30
c = 100 - 30
d = c / 100
e = b * d
f = a + e 
g = f / 2
h = 100 - 30
i = g * h
j = i / 100
k = 100 - 30
l = 100 - 30
m = l / 100
n = k * m
o = j / n
p = o * 10
Problem: a student has to obtain 33 % of the total marks to pass . he got 92 marks and failed by 40 marks . the maximum marks are ?
Options: a ) 400 , b ) 300 , c ) 500 , d ) 610 , e ) 175
Rationale: "let the maximum marks be x then , 33 % of x = 92 + 40 33 x / 100 = 132 x = 400 answer is a"
Answer: a
Python program:
a = 92 + 40 
b = 33 / 100
c = a / b
Problem: p works 25 % more efficiently than q and q works 50 % more efficiently than r . to complete a certain project , p alone takes 50 days less than q alone . if , in this project p alone works for 60 days and then q alone works for 150 days , in how many days can r alone complete the remaining work ?
Options: a ) 50 days , b ) 75 days , c ) 120 days , d ) 150 days , e ) 80 days
Rationale: "p works 25 % more efficiently than q : something that takes q 5 days , takes p 4 days q works 50 % more efficiently than r : something that takes r 7.5 days , takes q 5 days p alone takes 50 days less than q : for every 4 days p works , q has to work an extra day . hence p alone can do it in 200 days and q alone in 250 days and hence r alone in 400 days p works for 60 days - - > 60 / 200 work done = > 30 % q works for 150 days - - > 150 / 250 work done = > 60 % 30 % work left . . . r alone will take 30 % * 400 = 120 days answer is ( c )"
Answer: c
Python program:
a = 4 * 50
b = 150 / 100
c = b * 60
d = a - c
Problem: what is the sum of the multiples of 6 from 48 to 72 , inclusive ?
Options: a ) 500 , b ) 600 , c ) 700 , d ) 300 , e ) 400
Rationale: "the formula we want to use in this type of problem is this : average * total numbers = sum first , find the average by taking the sum of the f + l number and divide it by 2 : a = ( f + l ) / 2 second , find the total numbers in our range by dividing our f and l numbers by 7 and add 1 . ( 72 / 6 ) - ( 48 / 6 ) + 1 multiply these together so what we show average * total numbers = sum ( 48 + 72 ) / 2 * ( 72 / 6 ) - ( 48 / 6 ) + 1 = sum 60 * 5 = 300 d"
Answer: d
Python program:
a = 72 - 3
b = 48 + 2 
c = a + b 
d = c / 2
e = 72 - 3
f = 48 + 2 
g = e - f
h = g / 6
i = h + 1 
j = d * i
Problem: if d = 1 / ( 2 ^ 3 * 5 ^ 10 ) is expressed as a terminating decimal , how many nonzero digits will d have ?
Options: a ) one , b ) two , c ) three , d ) seven , e ) ten
Rationale: another way to do it is : we know x ^ a * y ^ a = ( x * y ) ^ a given = 1 / ( 2 ^ 3 * 5 ^ 10 ) = multiply and divide by 2 ^ 7 = 2 ^ 7 / ( 2 ^ 3 * 2 ^ 7 * 5 ^ 10 ) = 2 ^ 7 / 10 ^ 10 = > non zero digits are 128 = > ans c
Answer: c
Python program:
a = 1 + 2
Problem: a , band c enter into partnership . a invests 3 times as much as b and b invests two - third of what c invests . at the end of the year , the profit earned is rs . 3300 . what is the share of b ?
Options: a ) 1100 , b ) 800 , c ) 1400 , d ) 600 , e ) none of them
Rationale: "let c ' s capital = rs . x . then , b ' s capital = rs . ( 2 / 3 ) x a ’ s capital = rs . ( 3 x ( 2 / 3 ) . x ) = rs . 2 x . ratio of their capitals = 2 x : ( 2 / 3 ) x : x = 6 : 2 : 3 . hence , b ' s share = rs . ( 3300 x ( 2 / 11 ) ) = rs . 600 answer is d ."
Answer: d
Python program:
a = 2 * 3
b = 2 / 3
c = b * 3
d = a + c 
e = d + 3 
f = 2 / e
g = 3300 * f
Problem: tanks a and b are each in the shape of a right circular cylinder . the interior of tank a has a height of 10 meters and a circumference of 11 meters , and the interior of tank b has a height of 11 meters and a circumference of 10 meters . the capacity of tank a is what percent of the capacity of tank b ?
Options: a ) 75 % , b ) 80 % , c ) 100 % , d ) 110 % , e ) 125 %
Rationale: "the radius of tank a is 11 / ( 2 * pi ) . the capacity of tank a is 10 * pi * 121 / ( 4 * pi ^ 2 ) = 605 / ( 2 * pi ) the radius of tank b is 10 / ( 2 * pi ) . the capacity of tank b is 11 * pi * 100 / ( 4 * pi ^ 2 ) = 550 / ( 2 * pi ) tank a / tank b = 605 / 550 = 11 / 10 = 110 % the answer is d ."
Answer: d
Python program:
a = 11 / 10
b = a ** 2
c = 10 / 11
d = b * c
e = d * 100
Problem: the cost price of a radio is rs . 1500 and it was sold for rs . 1335 , find the loss % ?
Options: a ) 18 , b ) 16 , c ) 26 , d ) 17 , e ) 11
Rationale: "explanation : 1500 - - - - 165 100 - - - - ? = > 11 % answer : e"
Answer: e
Python program:
a = 1500 - 1335
b = a / 1500
c = b * 100
Problem: each of the products produced yesterday was checked by worker x or worker y . 0.5 % of the products checked by worker x are defective and 0.8 % of the products checked by worker y are defective . if the total defective rate of all the products checked by worker x and worker y is 0.6 % , what fraction of the products was checked by worker y ?
Options: a ) 1 / 5 , b ) 1 / 4 , c ) 1 / 3 , d ) 2 / 5 , e ) 3 / 7
Rationale: "x : 0.5 % is 0.1 % - points from 0.6 % . y : 0.8 % is 0.2 % - points from 0.6 % . therefore the ratio of products checked by y : x is 1 : 2 . thus , worker y checked 1 / 3 of the products . the answer is c ."
Answer: c
Python program:
a = 0 - 6
b = 0 - 8
c = a / b
Problem: in 1998 the profits of company n were 10 percent of revenues . in 1999 , the revenues of company n fell by 30 percent , but profits were 15 percent of revenues . the profits in 1999 were what percent of the profits in 1998 ?
Options: a ) 80 % , b ) 105 % , c ) 120 % , d ) 124.2 % , e ) 138 %
Rationale: "0,105 r = x / 100 * 0.1 r answer b"
Answer: b
Python program:
a = 30 / 100
b = 1 - a
c = 15 / 100
d = b * c
e = 10 / 100
f = d / e
g = f * 100
Problem: a shopkeeper sells 300 metres of cloth for rs . 18000 at a loss of rs . 5 per metre . find his cost price for one metre of cloth ?
Options: a ) 12 , b ) 27 , c ) 29 , d ) 50 , e ) 65
Rationale: sp per metre = 18000 / 300 = rs . 60 loss per metre = rs . 5 cp per metre = 60 + 5 = rs . 65 . answer : e
Answer: e
Python program:
a = 18000 / 300
b = a + 5
Problem: ? % of 360 = 144
Options: a ) 277 , b ) 36 , c ) 64 , d ) 40 , e ) none of these
Rationale: "? % of 360 = 144 or , ? = 144 × 100 / 360 = 40 answer d"
Answer: d
Python program:
a = 144 * 100
b = a / 360