Free Quantitative Aptitude questions with answers for MBA CET

Arithmetic, algebra, geometry, number systems, permutation and combination, probability and data interpretation - the quant questions that decide your MBA CET percentile. These 117 questions are also useful for CAT, MAT and ATMA. Tap “Show answer” under any question for the correct option and the explanation.

Question 81
A train travels 60% faster than a car. Both start from point A at the same time and reaches point B at the same time, which is 160 km away from each-other. If on the way the train stop for 20 minutes at station, then find the speed (in km/hr) of the train?
- (A)144
- (B)168
- (C)198
- (D)288
- (E)248
Show answer and explanation
Correct answer: (D) 288
Let the car's speed be v km/h, so the train's speed is 1.6v. Time taken by the car = 160/v. The train runs for 160/(1.6v) = 100/v and stops for 20 minutes (1/3 hour). 100/v + 1/3 = 160/v gives 60/v = 1/3, so v = 180 and the train's speed = 1.6 x 180 = 288 km/h.
Question 82
Find the ratio of area of a circle to area of square if perimeter of circle and square is equal?
- (A)11 : 14
- (B)11 : 4
- (C)8 : 11
- (D)14 : 11
- (E)2 : 4
Show answer and explanation
Correct answer: (D) 14 : 11
Let the common perimeter be P. Circle: radius P / 2 pi, area P^2 / 4 pi. Square: side P / 4, area P^2 / 16. Ratio = (1 / 4 pi) : (1 / 16) = 4 / pi = 4 x 7 / 22 = 14 : 11.
Question 83
Length of two chords AB and AC of a circle are 12 cm and 5 cm and ∠BAC = 90°. Find the radius of the circle.
- (A)14
- (B)13
- (C)16
- (D)6.5
Show answer and explanation
Correct answer: (D) 6.5
Angle BAC = 90 degrees, so BC is a diameter of the circle (the angle in a semicircle). BC = root(12^2 + 5^2) = root(169) = 13 cm, so the radius = 13 / 2 = 6.5 cm.
Question 84
The price of a commodity is increased by 25%. By what percentage should Rohan reduce his consumption so that his total expenditure increases by only 5%?
- (A)12%
- (B)14%
- (C)16%
- (D)18%
- (E)20%
Show answer and explanation
Correct answer: (C) 16%
New expenditure = (Price x 1.25) x (Consumption x (1 - x)) must equal 1.05 times the original expenditure. So 1.25 x (1 - x) = 1.05, giving (1 - x) = 0.84, so x = 16%.
Question 85
The average of 12 numbers is 48. The average of the first 7 numbers is 44, while the average of the last 6 numbers is 53. What is the seventh number?
- (A)46
- (B)48
- (C)50
- (D)52
- (E)54
Show answer and explanation
Correct answer: (C) 50
Sum of all 12 numbers = 12 x 48 = 576. Sum of the first 7 = 7 x 44 = 308. Sum of the last 6 (numbers 7-12) = 6 x 53 = 318. Adding these double-counts the 7th number: 308 + 318 = 626 = 576 + (7th number), so the 7th number = 50.
Question 86
The incomes of Shyam and Kunal are in the ratio 7:9 and their expenditures are in the ratio 4:5. If they save ₹6,000 and ₹9,000 respectively, what is Shyam's income?
- (A)₹36,000
- (B)₹40,000
- (C)₹42,000
- (D)₹45,000
- (E)₹48,000
Show answer and explanation
Correct answer: (C) ₹42,000
Let incomes be 7x and 9x, expenditures 4y and 5y. Savings: 7x - 4y = 6000 and 9x - 5y = 9000. Solving simultaneously gives x = 6000, so Shyam's income = 7x = ₹42,000.
Question 87
Amit invests ₹80,000 for 12 months, Bhavesh invests ₹1,20,000 for 8 months and Chirag invests ₹1,50,000 for 6 months. If the total profit is ₹94,000, what is Chirag's share?
- (A)₹28,000
- (B)₹30,000
- (C)₹32,000
- (D)₹34,000
- (E)₹36,000
Show answer and explanation
Correct answer: (B) ₹30,000
Capital x time: Amit = 80,000x12 = 9,60,000; Bhavesh = 1,20,000x8 = 9,60,000; Chirag = 1,50,000x6 = 9,00,000. Total = 28,20,000. Chirag's share = (9,00,000/28,20,000) x 94,000 = ₹30,000.
Question 88
A retailer marks an article 60% above its cost price and allows successive discounts of 20% and 10%. What is his profit percentage?
- (A)12%
- (B)14.4%
- (C)15.2%
- (D)16%
- (E)18%
Show answer and explanation
Correct answer: (C) 15.2%
Let CP = 100. Marked price = 160. After successive discounts of 20% and 10%: 160 x 0.8 x 0.9 = 115.2. Profit % = 15.2%.
Question 89
What is the difference between compound interest and simple interest on ₹20,000 for 3 years at 10% per annum?
- (A)₹600
- (B)₹610
- (C)₹620
- (D)₹640
- (E)₹660
Show answer and explanation
Correct answer: (C) ₹620
SI = (20,000 x 10 x 3)/100 = ₹6,000. CI = 20,000 x (1.1)³ - 20,000 = 26,620 - 20,000 = ₹6,620. Difference = 6,620 - 6,000 = ₹620.
Question 90
Arjun can complete a job in 18 days and Varun in 24 days. They work together for 4 days, after which Deepak, who can complete the job alone in 36 days, joins them. How many more days will all three together require to complete the remaining work?
- (A)4⅓ days
- (B)4⅔ days
- (C)4⅘ days
- (D)4 8/9 days
- (E)4⅞ days
Show answer and explanation
Correct answer: (D) 4 8/9 days
Arjun and Varun together complete 1/18 + 1/24 = 7/72 of the work per day; in 4 days they finish 28/72 = 7/18, leaving 11/18. With Deepak joining, the combined rate becomes 1/18 + 1/24 + 1/36 = 9/72 = 1/8 per day. Time for the remaining work = (11/18) / (1/8) = 44/9 = 4 8/9 days.
Question 91
Pipe A can fill a tank in 20 minutes and Pipe B in 30 minutes. A leak can empty the full tank in 60 minutes. If all three are opened simultaneously, in how many minutes will the empty tank be filled?
- (A)12
- (B)15
- (C)18
- (D)20
- (E)24
Show answer and explanation
Correct answer: (B) 15
Combined rate = 1/20 + 1/30 - 1/60 (leak) = 3/60 + 2/60 - 1/60 = 4/60 = 1/15. So the tank fills in 15 minutes.
Question 92
Two trains, 180 metres and 220 metres long, are moving in opposite directions at 54 km/h and 72 km/h respectively. How long will they take to completely cross each other?
- (A)10 seconds
- (B)10 6/7 seconds
- (C)11 3/7 seconds
- (D)12 seconds
- (E)12 4/7 seconds
Show answer and explanation
Correct answer: (C) 11 3/7 seconds
Relative speed (opposite directions) = 54 + 72 = 126 km/h = 126 x 5/18 = 35 m/s. Total length = 180 + 220 = 400 m. Time = 400/35 = 11 3/7 seconds.
Question 93
A boat travels at 24 km/h downstream and 16 km/h upstream. How much total time will it take to travel 96 km downstream and 64 km upstream?
- (A)7 hours
- (B)7.5 hours
- (C)8 hours
- (D)8.5 hours
- (E)9 hours
Show answer and explanation
Correct answer: (C) 8 hours
Time downstream = 96/24 = 4 hours. Time upstream = 64/16 = 4 hours. Total time = 8 hours.
Question 94
A vessel contains 60 litres of milk and water in the ratio 7:3. Some quantity of the mixture is removed and replaced with the same quantity of water. The resulting ratio of milk to water becomes 7:5. How much mixture was removed?
- (A)8 litres
- (B)10 litres
- (C)12 litres
- (D)15 litres
- (E)18 litres
Show answer and explanation
Correct answer: (B) 10 litres
Initially milk = 42 L and water = 18 L. If x litres of mixture are removed and replaced with water, milk left = 42x(1 - x/60) and water left = 18x(1 - x/60) + x. Setting the new ratio to 7:5 and solving gives x = 10 litres.
Question 95
Five years ago, the ages of Neeraj and Mohit were in the ratio 4:3. Five years from now, their ages will be in the ratio 6:5. What is the sum of their present ages?
- (A)40 years
- (B)42 years
- (C)45 years
- (D)48 years
- (E)50 years
Show answer and explanation
Correct answer: (C) 45 years
Let ages 5 years ago be 4k and 3k. Five years from now: (4k+10) : (3k+10) = 6:5. Solving gives k = 5, so present ages are 4k+5 = 25 and 3k+5 = 20. Sum = 45 years.
Question 96
A quantity is first increased by 20% and then increased by 25%. By what percentage must the resulting quantity be reduced so that the final value is 9% more than the original value?
- (A)25⅓%
- (B)26⅔%
- (C)27⅓%
- (D)28%
- (E)29⅓%
Show answer and explanation
Correct answer: (C) 27⅓%
Increasing by 20% then 25% multiplies the quantity by 1.2 x 1.25 = 1.5. To end 9% above the original (i.e., at 1.09), reduce by y%: 1.5 x (1 - y) = 1.09, so (1 - y) = 0.7267, giving y = 27⅓%.
Question 97
What is the value of x? I. x + y = 18 II. xy = 77 and x > y
- (A)Statement I alone is sufficient
- (B)Statement II alone is sufficient
- (C)Both statements together are sufficient
- (D)Either statement alone is sufficient
- (E)Even both statements together are insufficient
Show answer and explanation
Correct answer: (C) Both statements together are sufficient
Statement I alone (x + y = 18) has infinitely many solutions for x, so it's insufficient. Statement II alone (xy = 77, x > y) also has no unique solution without more constraints. Combining both: x and y are roots of t² - 18t + 77 = 0, giving t = 11 or 7; since x > y, x = 11 (unique). So both statements together are required and sufficient.
Question 98
What is the positive integer n? I. n is divisible by 12 and n < 50. II. n is divisible by 18 and n > 30.
- (A)Statement I alone is sufficient
- (B)Statement II alone is sufficient
- (C)Both statements together are sufficient
- (D)Either statement alone is sufficient
- (E)Even both statements together are insufficient
Show answer and explanation
Correct answer: (C) Both statements together are sufficient
Statement I alone allows n = 12, 24, 36, or 48 - not unique. Statement II alone allows n = 36, 54, 72, ... - not unique. Combining both: n must be a multiple of LCM(12, 18) = 36, with 30 < n < 50, so n = 36 (unique). Both statements together are required and sufficient.
Question 99
What is the remainder when 7¹⁰³ is divided by 100?
- (A)1
- (B)7
- (C)21
- (D)43
- (E)49
Show answer and explanation
Correct answer: (D) 43
Since 7⁴ = 2401 = 1 (mod 100), powers of 7 repeat every 4 steps mod 100. 103 = 4x25 + 3, so 7¹⁰³ = 7³ = 343 = 43 (mod 100).
Question 100
Find the least positive number which leaves a remainder of 5 when divided by 12, 15 and 18, and is also exactly divisible by 7.
- (A)725
- (B)905
- (C)1,085
- (D)1,265
- (E)1,445
Show answer and explanation
Correct answer: (C) 1,085
The LCM of 12, 15, and 18 is 180, so the number is of the form 180k + 5. For this to be divisible by 7: 180k + 5 = 0 (mod 7), which gives 5k + 5 = 0 (mod 7), so k = 6 (mod 7). The smallest such k is 6, giving 180x6 + 5 = 1,085.

Practise under exam conditions

Take a timed sectional test or a full-length mock and see your percentile and section-wise analysis.

Take a mock test