euclaise/mathqa_programs huggingface dataset:
Problem: the mean of 50 observations was 36 . it was found later that an observation 29 was wrongly taken as 23 . the corrected new mean is :
Options: a ) 36.1 , b ) 36.5 , c ) 36.22 , d ) 36.12 , e ) 36.18
Rationale: "explanation : correct sum = ( 36 * 50 + 29 - 23 ) = 1806 . correct mean = = 1806 / 50 = 36.12 answer : d ) 36.12"
Answer: d
Python program:
a = 36 * 50
b = 50 - 2
c = b - 23
d = a + c 
e = d / 50
Problem: shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $ 550 as interest . he invested the remaining in a bond that paid compound interest , interest being compounded annually , for the same 2 years at the same rate of interest and received $ 605 as interest . what was the value of his total savings before investing in these two bonds ?
Options: a ) $ 2,750 , b ) $ 5,500 , c ) $ 11,000 , d ) $ 22,000 , e ) $ 44,000
Rationale: "si for 1 st year = 550 / 2 = 275 275 + 275 + si on ( 275 ) = 605 = = > si on 275 = 55 = = > si on 275 = 275 * r * 1 / 100 = 55 r = 20 % now using si for 2 years on t / 2 of the money ( t / 2 ) * 20 * 2 / 100 = 550 t = 550 * 5 = 2750 answer : a"
Answer: a
Python program:
a = 550 / 2
b = 550 / 2
c = a * b
d = 605 - 550
e = c / d
f = e * 2
Problem: what percent is 350 gm of 1 kg ?
Options: a ) 25 % , b ) 40 % , c ) 35 % , d ) 8 % , e ) 12 %
Rationale: "1 kg = 1000 gm 350 / 1000 ã — 100 = 35000 / 1000 = 35 % answer is c"
Answer: c
Python program:
a = 350 / 1
b = a * 100
Problem: 7 people average age is 30 . youngest person age is 3 . find average of the people when youngest was born .
Options: a ) 23 , b ) 24 , c ) 25 , d ) 26 , e ) 27
Rationale: "average age of people = 30 so have total age = 210 before 7 years we have to deduct each person age by seven years 210 - 21 = 189 so average age would be 189 / 7 = 27 answer : e"
Answer: e
Python program:
a = 30 * 7
b = 3 * 7
c = a - b
d = c / 7
Problem: the average of first five multiples of 8 is :
Options: a ) 3 , b ) 9 , c ) 12 , d ) 15 , e ) 24
Rationale: "solution average = 8 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 120 / 5 = 24 answer e"
Answer: e
Python program:
a = 8 + 1
Problem: what is value of ( ( 2 ^ 5 ) * ( 9 ^ 2 ) ) / ( ( 8 ^ 2 ) * ( 3 ^ 5 ) ) = ?
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 2 / 3 , d ) 1 / 4 , e ) 4
Rationale: = > ( ( 2 ^ 5 ) * ( ( 3 ^ 2 ) ^ 2 ) / ( ( 2 ^ 3 ) ^ 2 ) * ( 3 ^ 5 ) ) = > ( ( 2 ^ 5 ) * ( 3 ^ 4 ) ) / ( ( 2 ^ 6 ) * ( 3 ^ 5 ) ) = > 1 / ( 2 * 3 ) = > 1 / 6 option a is answer
Answer: a
Python program:
a = 2 ** 5
b = 9 ** 2
c = a * b
d = 8 ** 2
e = 3 ** 5
f = d * e
g = c / f
Problem: two circular frames are kept one above the other . frame x has a diameter of 16 cm and frame y has a diameter of 12 cm . what fraction of the surface of frame x is not covered by frame y ?
Options: a ) 3 / 5
b ) 7 / 16
c ) 12 / 16
d ) 24 / 12
e ) 2 / 3
Rationale: the questions asks us to find the surface which is not covered by the frame y i . e . , area of the surface not covered . where as circumference is the length along the edge of the circle , 2 * pi * r implies the length of the curve pi * r ^ 2 implies area enclosed by that curve . . hence area of the circle is considered for this problem area of the frame y = pi * r ^ 2 , where r = 6 = > pi * 36 area of the frame x = pi * 64 surface not covered by the frame y = pi * 64 - pi * 36 = pi * 28 fraction of frame x ' s surface is not covered by a frame y = pi * 28 / total area of the frame x = 28 / 64 = 7 / 16 answer is b
Answer: b
Python program:
a = 16 / 2
b = circle_area - (
c = 12 / 2
d = b / circle_area
Problem: a car gets 40 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 140 kilometers ?
Options: a ) 4.5 , b ) 5.5 , c ) 6.5 , d ) 7.5 , e ) 3.5
Rationale: "each 40 kilometers , 1 gallon is needed . we need to know how many 40 kilometers are there in 140 kilometers ? 140 ÷ 40 = 3.5 × 1 gallon = 3.5 gallons correct answer e"
Answer: e
Python program:
a = 140 / 40
Problem: in some quantity of ghee , 60 % of pure ghee and 40 % of is vanaspati . if 10 kg of pure ghee is added , then the strength of vanaspati ghee becomes 20 % . the original quantity was ?
Options: a ) 5 kg , b ) 10 kg , c ) 15 kg , d ) 20 kg , e ) 25 kg
Rationale: let the original quantity be x kg vanaspati ghee in x kg = 40 / 100 * x = 2 x / 5 kg ( 2 x / 5 ) / ( x + 10 ) = 20 / 100 2 x / ( 5 x + 50 ) = 1 / 5 5 x = 50 x = 10 kg answer is b
Answer: b
Python program:
a = 20 / 100
b = a * 10
c = 40 / 100
d = 20 / 100
e = c - d
f = b / e
Problem: jack and jill are marathon runners . jack can finish a marathon ( 42 km ) in 6 hours and jill can run a marathon in 4.2 hours . what is the ratio of their average running speed ? ( jack : jill )
Options: a ) 7 / 10 , b ) 15 / 14 , c ) 4 / 5 , d ) 5 / 4 , e ) can not be determined
Rationale: "average speed of jack = distance / time = 42 / 6 = 7 average speed of jill = 42 / ( 4.2 ) = 10 ratio of average speed of jack to jill = 7 / 10 answer a"
Answer: a
Python program:
a = 42 / 6
b = 42 / 4
c = a / b
Problem: ( 128.5 x 4 ) + ( 13.8 x 5 ) = ? x 10
Options: a ) 524.48 , b ) 556.02 , c ) 58.3 , d ) 585.64 , e ) 595.46
Rationale: "explanation : ? = ( 128.5 x 4 ) + ( 13.8 x 5 ) / 10 = 514 + 69 / 10 = 58.3 answer : option c"
Answer: c
Python program:
a = 4 + 1 
b = a ** 4
c = 128 * 5
Problem: when a natural number n is successively divided by 12 , 34 the remainders are 56 , 78 . what will be the sum of the remainders if the order of the division is reversed ?
Options: a ) 11 , b ) 12 , c ) 10 , d ) 2 , e ) 7
Rationale: 1 2 3 4 5 6 7 8 leave the top right - most number 8 start with bottom right - most number 5 8 * 3 + 7 = 31 31 * 2 + 6 = 68 68 * 1 + 5 = 73 this is the number required now , do the successive division in the reverse order the sum of the remainders is 10 hence , the correct option is c
Answer: c
Python program:
a = 12 + 34 
b = 56 - a
Problem: speed of a boat in still water is 5 km / hr and speed of the stream is 2 kmph . a man rows to a place at a distance of 252 km and comes back to the starting point the total time taken by him is .
Options: a ) 160 hr , b ) 200 hr , c ) 120 hr , d ) 140 hr , e ) 180 hr
Rationale: explanation : speed up stream = 5 - 2 = 3 km / hr speed down stream = 5 + 2 = 7 km / hr total time taken = 252 / 3 + 252 / 7 = 84 + 36 = 120 hr answer : option b
Answer: b
Python program:
a = 5 + 2 
b = 252 / a
c = 5 - 2
d = 252 / c
e = b + d 
f = e / const_60
g = f * 100
Problem: each week , harry is paid x dollars per hour for the first 30 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 42 hours if harry and james were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 39
Rationale: "james worked for 41 hours hence he earned 40 * x + 2 * 2 x = 44 x dollars ; we know that harry also earned the same 44 x dollars , out of which he earned 30 x dollars for thefirst 30 hoursplus 14 x additional dollars . since for each additional hour he gets 1.5 x dollars then he worked for 14 x / 1.5 x = 9 additional hours , so harry worked for total of 30 + 9 = 39 hours . answer : e ."
Answer: e
Python program:
a = 40 + 2 
b = a - 30
c = b / 1
d = c + 30
Problem: some of 50 % - intensity red paint is replaced with 25 % solution of red paint such that the new paint intensity is 35 % . what fraction of the original paint was replaced ?
Options: a ) 1 / 35 , b ) 1 / 5 , c ) 2 / 3 , d ) 3 / 5 , e ) 4 / 5
Rationale: "35 % is 10 % - points above 25 % and 15 % - points below 50 % . thus the ratio of 25 % - solution to 50 % - solution is 3 : 2 . 3 / 5 of the original paint was replaced . the answer is d ."
Answer: d
Python program:
a = 35 / 100
b = 50 / 100
c = a - b
d = 25 / 100
e = 50 / 100
f = d - e
g = c / f
Problem: the shopkeeper increased the price of a product by 25 % so that customer finds it difficult to purchase the required amount . but somehow the customer managed to purchase only 64 % of the required amount . what is the net difference in the expenditure on that product ?
Options: a ) 12.5 % , b ) 13 % , c ) 15 % , d ) 17 % , e ) 20 %
Rationale: "quantity x rate = price 1 x 1 = 1 0.64 x 1.25 = 0.8 decrease in price = ( 0.2 / 1 ) × 100 = 20 % e )"
Answer: e
Python program:
a = 100 * 100
b = 100 + 25 
c = b * 64
d = a - c
e = d * 100
f = 100 * 100
g = e / f
Problem: an engineer undertakes a project to build a road 10 km long in 30 days and employs 30 men for the purpose . after 10 days , he finds only 2 km of the road has been completed . find the ( approximate ) number of extra men he must employ to finish the work in time .
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: "30 workers working already let x be the total men required to finish the task in next 20 days 2 km done hence remaining is 8 km also , work has to be completed in next 20 days ( 30 - 10 = 20 ) we know that , proportion of men to distance is direct proportion and , proportion of men to days is inverse proportion hence , x = ( 30 * 8 * 10 ) / ( 2 * 20 ) thus , x = 60 thus , more men needed to finish the task = 60 - 30 = 30 answer : a"
Answer: a
Python program:
a = 10 - 2
b = 30 * a
c = b * 10
d = 30 - 10
e = 2 * d
f = c / e
g = f - 30
Problem: the number 155 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ?
Options: a ) 17 , b ) 16 , c ) 15 , d ) 14 , e ) 21
Rationale: "7 ^ 2 + 5 ^ 2 + 9 ^ 2 = 49 + 25 + 81 = 155 7 + 5 + 9 = 21 hence answer is e"
Answer: e
Python program:
a = 4 + 3 
b = 3 + 2 
c = a + b 
d = c + 3
Problem: two digits in john ' s age are the same as the digit in the wilson ' s age , but in reverse order . in 21 years john will be twice as old as wilson will be then . what is the difference in their current age ?
Options: a ) 25 , b ) 43 , c ) 14 , d ) 36 , e ) 12
Rationale: john ' s age = 10 x + y so wilson ' s age = 10 y + x . . after 21 years , 10 x + y + 21 = 2 * ( 10 y + x + 21 ) . . . . so 21 + 19 y = 8 x . . . check for odd values of y , y = 1 satisfies the eqn with x = 5 . . . so ages are 51 and 15 and ans as found correctly by u is d . . 36
Answer: d
Python program:
a = 21 + 3 
b = a * 2
c = 3 * 4
d = b - c
Problem: a cab driver 5 days income was $ 45 , $ 50 , $ 60 , $ 65 , $ 70 . then his average income is ?
Options: a ) $ 58 , b ) $ 42 , c ) $ 65 , d ) $ 48 , e ) $ 62
Rationale: avg = sum of observations / number of observations avg income = ( 45 + 50 + 60 + 65 + 70 ) / 5 = 58 answer is a
Answer: a
Python program:
a = 45 + 50 
b = a + 60 
c = b + 65 
d = c + 70 
e = d / 5
Problem: if a : b is 3 : 4 and b : c is 4 : 5 then a : c is equal to
Options: a ) 1 : 3 , b ) 3 : 5 , c ) 3 : 4 , d ) 3 : 7 , e ) 1 : 5
Rationale: the two ratios given are having the same number 4 for b in both the ratios . hence - a : b = 3 : 4 b : c = 4 : 5 = > a : c = 3 : 5 answer b
Answer: b
Python program:
a = 4 / 5
b = 3 / 4
c = a * b
Problem: in a box of 9 pencils , a total of 2 are defective . if a customer buys 3 pencils selected at random from the box , what is the probability that neither pencils will be defective ?
Options: a ) 5 / 12 , b ) 1 / 15 , c ) 2 / 13 , d ) 2 / 15 , e ) 1 / 17
Rationale: first , there are 7 c 3 ways you can select 3 good pencils from 4 good ones . second , there are 9 c 3 ways you select 3 pencils from 6 ones in the box . then , the probability that neither pen will be defective is : 7 c 3 / 9 c 3 = 35 / 84 = 5 / 12 answer is a
Answer: a
Python program:
a = 9 - 2
b = math.factorial(a)
c = 9 - 2
d = c - 3
e = math.factorial(d)
f = math.factorial(3)
g = e * f
h = b / g
i = math.factorial(9)
j = 9 - 3
k = math.factorial(j)
l = math.factorial(3)
m = k * l
n = i / m
o = h / n
Problem: what profit percent is made by selling an article at a certain price , if by selling at 2 / 3 rd of that price , there would be a loss of 18 % ?
Options: a ) 20 % , b ) 26 % , c ) 42 % , d ) 27 % , e ) 23 %
Rationale: sp 2 = 2 / 3 sp 1 cp = 100 sp 2 = 82 2 / 3 sp 1 = 82 sp 1 = 123 100 - - - 23 = > 23 % answer : e
Answer: e
Python program:
a = 100 - 18
b = 2 / 3
c = a / b
d = c - 100
Problem: 8 identical machines , working alone and at their constant rates , take 6 hours to complete a job lot . how long would it take for 6 such machines to perform the same job ?
Options: a ) 2.25 hours , b ) 8 hours , c ) 12 hours , d ) 14.25 hours , e ) 16 hours
Rationale: "let each machine do 1 unit of work for 1 hour 8 machines - - > 8 units of work in 1 hour for 6 hours = 8 * 6 = 48 units of total work is done . now this 48 units of total work must be done by 6 machines 6 units of work ( 6 machines ) - - - > 1 hour for 48 units of work 6 * 8 - - - > 1 * 8 hours b 8 hours"
Answer: b
Python program:
a = 6 * 8
b = a / 6
Problem: by selling an article at rs . 800 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 40 % ?
Options: a ) s . 429 , b ) s . 480 , c ) s . 429 , d ) s . 128 , e ) s . 384
Rationale: "sp = 800 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 800 * [ 100 / 125 ] = 640 loss = 40 % = 40 % of 640 = rs . 256 sp = cp - loss = 640 - 256 = rs . 384 answer : e"
Answer: e
Python program:
a = 800 * 100
b = 25 + 100 
c = a / b
d = 800 * 100
e = 25 + 100 
f = d / e
g = f * 40
h = g / 100
i = c - h
Problem: milk contains 10 % water . what content of pure milk should be added to 20 liters of milk to reduce this to 5 % ?
Options: a ) 20 liters , b ) 25 liters , c ) 30 liters , d ) 15 liters , e ) 18 liters
Rationale: quantity of water in 20 liters = 10 % of 20 liters = 2 liters let x liters of pure milk be added . then , 2 / ( 20 + x ) = 5 / 100 5 x = 100 x = 20 liters answer is a
Answer: a
Python program:
a = 10 / 100
b = a * 20
c = 5 / 100
d = b / c
e = d - 20
Problem: it takes avery 3 hours to build a brick wall while tom can do it in 2 hours . if the two start working together and after an hour avery leaves , how much time will it take tom to complete the wall on his own ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "avery takes 3 hours tom takes 2 hours efficiency of avery is 1 / 3 units / hr efficiency of tom is 1 / 2 units / hr combined efficiency of tom and avery is 1 / 3 + 1 / 2 = 5 / 6 units / hr since they worked for 1 hour they completed 5 / 6 units of work and 1 / 6 units of work is left which is to be completed by tom ( since avery left ) so time taken by tom to complete the remaining work will be 1 / 6 / 1 / 2 hours = > 1 / 3 * 60 = 20 minutes . . . answer will be ( a )"
Answer: a
Python program:
a = 1 / 3
b = 1 / 2
c = a + b 
d = 1 - c
e = 1 / 2
f = d / e
g = f * const_60
Problem: salesperson a ' s compensation for any week is $ 360 plus 6 percent of the portion of a ' s total sales above $ 2,000 for that week . salesperson b ' s compensation for any week is 8 percent of a ' s total sales for that week . for what amount of total weekly sales would both salepeople earn the same compensation ?
Options: a ) $ 12,000 , b ) $ 18,000 , c ) $ 15,000 , d ) $ 4,500 , e ) $ 4,000
Rationale: "sometime , setting up an equation is an easy way to go with : 360 + 0.06 ( x - 2000 ) = 0.08 x x = 12000 ans : a"
Answer: a
Python program:
a = 6 / 100
b = a * 2
c = 360 - b
d = 8 / 100
e = 6 / 100
f = d - e
g = c / f
h = 6 / 100
i = h * 2
j = 360 - i
k = 8 / 100
l = 6 / 100
m = k - l
n = j / m
o = g + n 
p = o / 2
Problem: a car gets 40 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 200 kilometers ?
Options: a ) 4.5 , b ) 5 , c ) 6.5 , d ) 7.5 , e ) 8.5
Rationale: "each 40 kilometers , 1 gallon is needed . we need to know how many 40 kilometers are there in 180 kilometers ? 200 ÷ 40 = 5 × 1 gallon = 5 gallons correct answer b"
Answer: b
Python program:
a = 200 / 40
Problem: at a monthly meeting , 3 / 5 of the attendees were males and 7 / 8 of the male attendees arrived on time . if 9 / 10 of the female attendees arrived on time , what fraction of the attendees at the monthly meeting did not arrive on time ?
Options: a ) 23 / 200 , b ) 11 / 100 , c ) 7 / 50 , d ) 3 / 20 , e ) 4 / 25
Rationale: males who did not arrive on time are 1 / 8 * 3 / 5 = 3 / 40 of the attendees . females who did not arrive on time are 1 / 10 * 2 / 5 = 2 / 50 of the attendees . the fraction of all attendees who did not arrive on time is 3 / 40 + 2 / 50 = 23 / 200 the answer is a .
Answer: a
Python program:
a = 9 / 10
b = 1 - a
c = 3 / 5
d = 1 - c
e = b * d
f = 7 / 8
g = 1 - f
h = 3 / 5
i = g * h
j = e + i
Problem: there are 15 boys and 10 girls in a class . if three students are selected at random , in how many ways that 1 girl and 2 boys are selected ?
Options: a ) 950 , b ) 1050 , c ) 2150 , d ) 2050 , e ) 1000
Rationale: "n ( s ) = sample space = 25 c 3 = 2300 e = event that 1 girl and 2 boys are selected n ( e ) = we have to select 2 boys from 15 and 1 girl from 10 = 15 c 2 * 10 c 1 = 1050 ans - b"
Answer: b
Python program:
a = math.comb(15, 2)
b = math.comb(10, 1)
c = a * b
Problem: 12 men can complete a piece of work in 25 days . in how many days can 20 men complete that piece of work ?
Options: a ) 55 days , b ) 77 days , c ) 20 days , d ) 88 days , e ) 15 days
Rationale: "12 * 25 = 20 * x = > x = 15 days answer : e"
Answer: e
Python program:
a = 25 * 12
b = a / 20
Problem: consider a lady took a loan from a bank at the rate of 12 % p . a . simple interest . after 3 years she had to pay rs . 7200 interest only for the period . the principal amount borrowed by her was
Options: a ) rs . 2000 , b ) rs . 10000 , c ) rs . 15000 , d ) rs . 20000 , e ) none of these
Rationale: explanation : principal = rs . ( 100 × 7200 / 12 × 3 ) = > rs . 20,000 . answer : d
Answer: d
Python program:
a = 3 * 12
b = a / 100
c = 7200 / b
Problem: how many pages do you need if you have to write 150 lines of information into pages that each hold 30 lines ?
Options: a ) a ) 7 , b ) b ) 5 , c ) c ) 9 , d ) d ) 8 , e ) e ) none of the above
Rationale: sol . 30 lines per page total 150 lines = 150 / 30 = 5 answer : b
Answer: b
Python program:
a = 150 / 30
Problem: a dog takes 10 leaps for every 2 leaps of a hare . if one leap of the dog is equal to 2 leaps of the hare , the ratio of the speed of the dog to that of the hare is :
Options: a ) 5 : 1 , b ) 10 : 1 , c ) 15 : 1 , d ) 20 : 1 , e ) 25 : 1
Rationale: "explanation : dog : hare = ( 10 * 2 ) leaps of hare : 2 leaps of hare = 20 : 2 . answer : b ) 10 : 1"
Answer: b
Python program:
a = 10 * 2
b = a / 2
Problem: a train running at the speed of 60 km / hr crosses a pole in 9 seconds . what is the length of the train ?
Options: a ) 100 , b ) 120 , c ) 130 , d ) 150 , e ) 160
Rationale: "speed = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec length of the train = ( speed x time ) = ( 50 / 3 * 9 ) m = 150 m . answer : option d"
Answer: d
Python program:
a = 60 * 1000
b = a / 3600
c = b * 9
Problem: triangle xyz is an isosceles right triangle . if side xy is longer than side yz , and the area of the triangle is 64 , what is the measure of side xy ?
Options: a ) 4 , b ) 16 , c ) 8 , d ) 8 √ 2 , e ) can not be determined from the information provided
Rationale: "ans b . . 16 . xy being larger means it is the hyp . . area = ( 1 / 2 ) * ( yz ) ^ 2 = 64 or yz = 8 * \ sqrt { 2 } . . therefore hyp = xy = 16"
Answer: b
Python program:
a = math.sqrt(64)
b = math.sqrt(2)
c = a * b
d = c ** 2
e = math.sqrt(64)
f = math.sqrt(2)
g = e * f
h = g ** 2
i = d + h 
j = math.sqrt(i)
Problem: a sum of money lent out at s . i . amounts to rs . 780 after 2 years and to rs . 1020 after a further period of 5 years . the sum is ?
Options: a ) s . 684 , b ) s . 500 , c ) s . 540 , d ) s . 740 , e ) s . 840
Rationale: "s . i for 5 years = ( 1020 - 780 ) = rs . 240 . s . i . for 2 years = 240 / 5 * 2 = rs . 96 . principal = ( 780 - 96 ) = rs . 684 answer : a"
Answer: a
Python program:
a = 1020 - 780
b = a / 5
c = b * 2
d = 780 - c
Problem: there are 40 balls which are red , blue or green . if 15 balls are green and the sum of red balls and green balls is less than 25 , at most how many red balls are there ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: "r + g + b = 40 g = 15 r + g < 25 = > r + 15 < 25 = > r < 10 = > at most 6 red balls answer : e"
Answer: e
Python program:
a = 15 - 1
Problem: the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 13 % , then the cost price of the article is :
Options: a ) 545 , b ) 334 , c ) 555 , d ) 664 , e ) 5598
Rationale: "110 % of s . p . = 616 s . p . = ( 616 * 100 ) / 110 = rs . 560 c . p = ( 110 * 560 ) / 113 = rs . 545 answer : option a"
Answer: a
Python program:
a = 616 * 100
b = 100 + 10 
c = a / b
d = 100 + 10 
e = c * d
f = 100 + 13 
g = e / f
Problem: in order to obtain an income of rs . 580 from 15 % stock at rs . 100 , one must make an investment of
Options: a ) 5363 , b ) 6240 , c ) 8700 , d ) 5600 , e ) 2732
Rationale: "to obtain rs . 10 , investment = rs . 100 . to obtain rs . 580 , investment = = rs . 8700 . answer : c"
Answer: c
Python program:
a = 100 / 15
b = a * 580
Problem: a shopkeeper sold an article offering a discount of 4 % and earned a profit of 20 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 25 , b ) 28 , c ) 30 , d ) 32 , e ) 34
Rationale: "let c . p . be rs . 100 . then , s . p . = rs . 120 let marked price be rs . x . then , 96 / 100 x = 120 x = 12000 / 96 = rs . 125 now , s . p . = rs . 125 , c . p . = rs . 100 profit % = 25 % . answer : a"
Answer: a
Python program:
a = 100 + 20 
b = a * 100
c = 100 - 4
d = b / c
e = d - 100
Problem: apple street begins at peach street and runs directly east for 3.2 kilometers until it ends when it meets cherry street . apple street is intersected every 200 meters by a perpendicular street , and each of those streets other than peach street and cherry street is given a number beginning at 1 st street ( one block east of peach street ) and continuing consecutively ( 2 nd street , 3 rd street , etc . . . ) until the highest - numbered street one block west of cherry street . what is the highest - numbered street that intersects apple street ?
Options: a ) 14 th , b ) 15 th , c ) 16 th , d ) 17 th , e ) 18 th
Rationale: 3.2 km / 200 m = 16 . however , the street at the 3.2 - km mark is not 16 th street ; it is cherry street . therefore , the highest numbered street is 15 th street . the answer is b .
Answer: b
Python program:
a = 3 * 2
b = a / 200
c = b - 1
Problem: a bag contains 8 red , 6 blue and 4 green balls . if 2 ballsare picked at random , what is the probability that both are red ?
Options: a ) 1 / 13 , b ) 2 / 23 , c ) 5 / 26 , d ) 7 / 30 , e ) 3 / 23
Rationale: "p ( both are red ) , = 8 c 216 c 2 = 8 c 216 c 2 = 28 / 120 = 7 / 30 d"
Answer: d
Python program:
a = math.comb(8, 2)
b = 8 + 6 
c = b + 4 
d = math.comb(c, 2)
e = a / d
Problem: a , b and c completed a piece of work , a worked for 6 days , b for 9 days and c for 4 days . their daily wages were in the ratio of 3 : 4 : 5 . find the daily wages of c , if their total earning was $ 1480 ?
Options: a ) $ 100 , b ) $ 150 , c ) $ 125 , d ) $ 134 , e ) $ 243
Rationale: a $ 100 3 x 4 x 5 x 6 9 4 18 x + 36 x + 20 x = 1480 74 x = 1480 = > x = 20 5 x = 100 rs .
Answer: a
Python program:
a = 6 * 3
b = 9 * 4
c = a + b 
d = 4 * 5
e = c + d 
f = 1480 / e
g = 5 * f
Problem: the average salary of the employees in a office is rs . 120 / month . the avg salary of officers is rs . 440 and of non officers is rs 110 . if the no . of officers is 15 , then find the no of nonofficers in the office .
Options: a ) 400 , b ) 420 , c ) 480 , d ) 450 , e ) 510
Rationale: "let no . of non - officers be x 15 * 440 + x * 110 = ( x + 15 ) 120 x = 480 c"
Answer: c
Python program:
a = 15 * 440
b = 15 * 120
c = a - b
d = 120 - 110
e = c / d