Aptitude questions

Aptitude Updated 11 Oct 2026

These aptitude questions cover the topics that appear most often in placement tests and in SSC, bank and railway exams. There are 40 quantitative aptitude questions and answers on number system, percentage, profit and loss, ratio and average, time and work, speed and distance, interest, and a set of logical aptitude questions on number series, coding, blood relation, calendar and clock.

Every answer has been worked out and comes with a short explanation that shows the method, so you can check your steps and learn the shortcut at the same time.

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Number system aptitude questions

Q1. What is the smallest number that is exactly divisible by 12, 15 and 20?
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Answer: D. 60
The LCM of 12, 15 and 20 is the smallest common multiple. 12 = 2² × 3, 15 = 3 × 5, 20 = 2² × 5, so LCM = 2² × 3 × 5 = 60.
Q2. What is the HCF of 84 and 126?
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Answer: A. 42
84 = 2² × 3 × 7 and 126 = 2 × 3² × 7. Common factors give HCF = 2 × 3 × 7 = 42.
Q3. What is the sum of the first 50 natural numbers?
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Answer: C. 1275
Sum = n(n + 1)/2 = 50 × 51/2 = 1275.
Q4. How many prime numbers are there between 1 and 50?
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Answer: B. 15
The primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47, which makes 15. Note that 1 is neither prime nor composite.
Q5. What is the unit digit of 7^95?
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Answer: D. 3
Unit digits of powers of 7 repeat in the cycle 7, 9, 3, 1. 95 ÷ 4 leaves remainder 3, so the unit digit is the third in the cycle, 3.

Percentage questions

Q6. What is 35% of 240?
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Answer: B. 84
35% of 240 = 35/100 × 240 = 84.
Q7. A number is first increased by 20% and then decreased by 20%. What is the net change?
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Answer: C. 4% decrease
Net change = 20 − 20 − (20 × 20)/100 = −4, so the number falls by 4%. For example, 100 becomes 120 and then 96.
Q8. A's salary is 25% more than B's salary. By what percent is B's salary less than A's?
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Answer: A. 20%
Take B = 100, so A = 125. B is less by 25 on 125, which is 25/125 × 100 = 20%.
Q9. The population of a town is 10,000 and it grows by 10% every year. What will it be after 2 years?
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Answer: C. 12,100
Population = 10000 × 1.1 × 1.1 = 12,100. Growth is compounded, so the second year adds 10% of 11,000.
Q10. A student scores 360 marks out of 450. What is the percentage score?
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Answer: A. 80%
Percentage = 360/450 × 100 = 80%.

Profit and loss questions

Q11. An article bought for ₹400 is sold for ₹500. What is the profit percent?
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Answer: B. 25%
Profit = 500 − 400 = ₹100. Profit % = 100/400 × 100 = 25%. Profit percent is always calculated on cost price.
Q12. By selling an article for ₹640, a man loses 20%. What is its cost price?
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Answer: D. ₹800
Selling price = 80% of CP, so CP = 640 ÷ 0.8 = ₹800.
Q13. The marked price of a shirt is ₹1,200 and a discount of 15% is given. What is the selling price?
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Answer: D. ₹1,020
Discount = 15% of 1200 = ₹180. Selling price = 1200 − 180 = ₹1,020.
Q14. Two successive discounts of 20% and 10% are equal to a single discount of:
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Answer: B. 28%
Equivalent discount = 20 + 10 − (20 × 10)/100 = 28%.
Q15. A shopkeeper buys pens at 5 for ₹20 and sells them at 4 for ₹20. What is his profit percent?
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Answer: C. 25%
CP of one pen = 20/5 = ₹4 and SP = 20/4 = ₹5. Profit % = 1/4 × 100 = 25%.

Ratio, average and ages

Q16. ₹720 is divided between A and B in the ratio 4 : 5. What is B's share?
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Answer: A. ₹400
B's share = 5/9 × 720 = ₹400, and A gets 4/9 × 720 = ₹320.
Q17. The average of 5 numbers is 24. If one number is removed, the average of the rest becomes 22. What number was removed?
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Answer: B. 32
Total of 5 numbers = 5 × 24 = 120. Total of 4 = 4 × 22 = 88. Removed number = 120 − 88 = 32.
Q18. What is the average of the first 10 even natural numbers?
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Answer: A. 11
The first 10 even numbers are 2 to 20. Average = (2 + 20)/2 = 11, since the average of the first n even numbers is n + 1.
Q19. The ages of A and B are in the ratio 3 : 5 and their sum is 48 years. What is B's age?
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Answer: D. 30 years
Total parts = 3 + 5 = 8, so one part = 48/8 = 6 years. B = 5 × 6 = 30 years.
Q20. What is the mean proportional between 9 and 16?
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Answer: C. 12
Mean proportional of a and b = √(ab) = √(9 × 16) = √144 = 12.

Time and work, speed and distance

Q21. A can finish a job in 12 days and B in 24 days. In how many days can they finish it together?
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Answer: B. 8 days
One day's work = 1/12 + 1/24 = 3/24 = 1/8. So together they take 8 days.
Q22. 6 men can build a wall in 10 days. How many days will 15 men take to build the same wall?
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Answer: A. 4 days
Total work = 6 × 10 = 60 man-days. 15 men need 60/15 = 4 days.
Q23. A speed of 72 km/h is equal to how many metres per second?
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Answer: D. 20 m/s
To convert km/h to m/s multiply by 5/18. 72 × 5/18 = 20 m/s.
Q24. A train 150 m long crosses a pole in 10 seconds. What is its speed?
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Answer: C. 54 km/h
Speed = 150/10 = 15 m/s. In km/h, 15 × 18/5 = 54 km/h.
Q25. A car goes from A to B at 40 km/h and returns at 60 km/h. What is its average speed for the whole journey?
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Answer: A. 48 km/h
For equal distances, average speed = 2xy/(x + y) = 2 × 40 × 60/100 = 48 km/h.
Q26. Pipe A fills a tank in 6 hours and pipe B empties it in 9 hours. If both are opened together, in how many hours is the empty tank filled?
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Answer: B. 18 hours
Net filling per hour = 1/6 − 1/9 = 1/18. So the tank fills in 18 hours.

Simple and compound interest

Q27. What is the simple interest on ₹5,000 at 8% per annum for 3 years?
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Answer: C. ₹1,200
SI = P × R × T/100 = 5000 × 8 × 3/100 = ₹1,200.
Q28. What is the compound interest on ₹10,000 at 10% per annum for 2 years, compounded annually?
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Answer: D. ₹2,100
Amount = 10000 × 1.1² = ₹12,100. CI = 12,100 − 10,000 = ₹2,100.
Q29. At what rate of simple interest does a sum double itself in 8 years?
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Answer: C. 12.5%
Doubling means interest = principal, so 100 = 100 × R × 8/100, giving R = 100/8 = 12.5%.
Q30. What is the difference between compound interest and simple interest on ₹2,000 at 10% per annum for 2 years?
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Answer: D. ₹20
For 2 years, CI − SI = P(R/100)² = 2000 × (0.1)² = ₹20.

Number series, coding, blood relation and calendar

Q31. Find the next number in the series: 2, 6, 12, 20, 30, ?
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Answer: B. 42
The differences are 4, 6, 8, 10, so the next difference is 12. 30 + 12 = 42. Each term is n(n + 1).
Q32. Find the next number in the series: 3, 7, 15, 31, 63, ?
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Answer: A. 127
Each term is double the previous term plus 1: 63 × 2 + 1 = 127.
Q33. Find the next number in the series: 4, 10, 22, 46, ?
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Answer: B. 94
Each term is double the previous term plus 2: 4 × 2 + 2 = 10, 10 × 2 + 2 = 22, so 46 × 2 + 2 = 94.
Q34. If CAT is written as DBU in a code, how is DOG written in that code?
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Answer: C. EPH
Each letter moves one step forward: D→E, O→P, G→H. So DOG becomes EPH.
Q35. If CAB = 6 (the sum of the positions of its letters in the alphabet), what is FACE?
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Answer: D. 15
F = 6, A = 1, C = 3, E = 5. Sum = 6 + 1 + 3 + 5 = 15.
Q36. Pointing to a boy, Riya says, 'He is the son of my paternal grandfather's only son.' How is the boy related to Riya?
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Answer: A. Brother
Riya's paternal grandfather's only son must be Riya's father. The son of Riya's father is her brother.
Q37. A is the brother of B. B is the daughter of C. How is A related to C?
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Answer: D. Son
B is C's daughter and A is B's brother, so A is also a child of C. A is a male, so A is C's son.
Q38. If 1 January of a non-leap year is a Monday, what day of the week is 31 December of the same year?
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Answer: A. Monday
A non-leap year has 365 days = 52 weeks + 1 day. 31 December is 364 days after 1 January, which is exactly 52 weeks, so it is also Monday.
Q39. The Constitution of India came into force on 26 January 1950. What day of the week was it?
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Answer: C. Thursday
Odd days up to the end of 1949: 1600 years give 0, 300 years give 1 and 49 years (12 leap, 37 ordinary) give 61 = 5, total 6. Adding 26 days of January (5 odd days) gives 11 = 4 odd days, which means Thursday.
Q40. What is the angle between the hour hand and the minute hand of a clock at 3:40?
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Answer: B. 130°
Angle = |30H − 5.5M| = |30 × 3 − 5.5 × 40| = |90 − 220| = 130°.

How to prepare

Treat this page as a mixed aptitude test. Attempt all 40 questions with a timer, aiming for about one minute per question, then check each answer and read the working for every question you missed or guessed. Most placement and bank tests reward speed, so the explanations use formulas such as LCM by prime factors, 2xy/(x + y) for average speed and a + b + ab/100 for successive changes.

After the first attempt, list the topics where you lost marks and practise them on the topic pages for percentage, simplification, number series, blood relation and others. Come back to this mixed set a week later to see how much faster and more accurate you have become.

Study tips

Learn squares up to 30, cubes up to 20 and fraction to percentage conversions so that calculations take seconds.
For every topic write down the one or two formulas used here and revise them daily before a test.
In a timed test skip any question that takes more than two minutes and return to it at the end.

Questions people ask

What are aptitude questions?

Aptitude questions test your ability to solve numerical and logical problems quickly. They include quantitative topics such as percentage, profit and loss and time and work, and logical topics such as number series, coding and blood relation.

Which aptitude topics are most important for placement tests?

Percentage, profit and loss, ratio, average, time and work, speed and distance, simple and compound interest and number series appear in almost every placement test. Logical topics such as coding-decoding, blood relation and calendar are also common.

How can I solve aptitude questions faster?

Learn the standard formulas and shortcuts, practise mental calculation and use the options to eliminate wrong answers. Regular timed practice is the most reliable way to improve speed.

How do I solve calendar aptitude questions?

Use the odd days method. Count the extra days beyond complete weeks, add them up from a known reference and divide by 7; the remainder gives the day of the week, with 0 as Sunday.

Are these aptitude questions useful for bank and SSC exams?

Yes. The topics and difficulty match the quantitative aptitude and reasoning sections of bank, SSC and railway exams, as well as campus placement tests.

Every question on this page is written and fact-checked by the GK Quizzes team. Spotted a mistake? Tell us and we will fix it. How we make our questions.