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Problems on ages: practice questions for bank exams

By the PrepMatic team · Updated 9 Oct 2026 · 4 min read

Problems on ages give a few facts about people's ages now, in the past or in the future, and ask for one present age. They look like story puzzles but reduce to one or two linear equations. Bank exams use them as quick prelims questions and as part of mains-level arithmetic. The five questions below cover the standard types.

Rules that never change

Three facts about ages do most of the work, and they are easy to forget under time pressure.

• The difference between two people's ages stays constant over the years.
• Each person adds one year per year. The sum of ages of n people grows by n each year.
• Ratios do change. A ratio of 4 : 5 now does not stay 4 : 5 after five years, so write the ages as numbers before and after.

Five practice questions

Question 1

The present ages of A and B are in the ratio 4 : 5. Five years from now the ratio will be 5 : 6. What is A's present age?

• A. 16 years
• B. 20 years
• C. 24 years
• D. 25 years

Question 2

The sum of the present ages of a mother and her daughter is 56 years. Four years ago the mother was three times as old as the daughter. What is the mother's present age?

• A. 40 years
• B. 42 years
• C. 44 years
• D. 48 years

Question 3

The ages of A, B and C are in the ratio 3 : 4 : 5, and their average age is 28 years. What will B's age be after 6 years?

• A. 28 years
• B. 34 years
• C. 35 years
• D. 40 years

Question 4

The present ages of a father and his son are in the ratio 8 : 3. After 8 years the father will be twice as old as the son. What is the sum of their present ages?

• A. 36 years
• B. 40 years
• C. 44 years
• D. 48 years

Question 5

Four years ago the ages of A and B were in the ratio 3 : 4. Six years from now the ratio will be 4 : 5. What is A's present age?

• A. 34 years
• B. 40 years
• C. 44 years
• D. 50 years

Answers and explanations

1. B. Let the ages be 4k and 5k. Then (4k + 5) ÷ (5k + 5) = 5 ÷ 6, which gives 24k + 30 = 25k + 25, so k = 5. A is 4 × 5 = 20. Check: B is 25, and after 5 years the ages 25 and 30 are in the ratio 5 : 6.
2. A. Let the daughter be d, so the mother is 56 − d. Four years ago, 56 − d − 4 = 3(d − 4), which gives 52 − d = 3d − 12, so d = 16. The mother is 40. Check: four years ago they were 36 and 12.
3. B. The three ages sum to 3 × 28 = 84, and the ratio parts total 12, so one part is 7. B is 4 × 7 = 28 now, and 34 after 6 years. The option 28 is the trap of giving B's present age, and 35 is C's present age.
4. C. Let the ages be 8k and 3k. After 8 years, 8k + 8 = 2(3k + 8), so 2k = 8 and k = 4. The ages are 32 and 12, and their sum is 44.
5. A. Let the ages four years ago be 3k and 4k. Six years from now (10 years later) they are 3k + 10 and 4k + 10, so (3k + 10) ÷ (4k + 10) = 4 ÷ 5. Then 15k + 50 = 16k + 40, so k = 10. A was 30 four years ago, so he is 34 now. B is 44 now.

How to prepare ages

• Define the variable at the present time. Calling today's age x or 4k, and expressing the past and the future from it, avoids sign mistakes.
• Always ask "which time is this ratio for?" In Question 5 the first ratio is for four years ago and the second for six years ahead, a gap of 10 years.
• Use the sum rule. Sum of two ages grows by 2 each year, so one fact about the sum can replace an equation.
• Substitute to check. Plug your answer into every statement. It takes 15 seconds and catches the slip of answering B's age.
• Beware the trap options. Setters include another person's age or the age at the wrong time, so reread what is asked.
• Link to ratio. Ages with ratios build on ratio and proportion, so revise that first if k is still unfamiliar.

A target of 45 seconds per question is realistic. Treat a question with three people and two time frames as mains-level and attempt it later.

The full problems on ages topic test is on PrepMatic (about 15 questions, 30 minutes). See the Quantitative Aptitude guide for the full Quant topic list, and the bank exam hub for each exam's pattern.

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