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XAT Problems on Ages Questions with Answers & Explanations

17 Problems on Ages questions from the Quantitative Ability & Data Interpretation section of XAT, each with the correct answer and a worked explanation. Try each question first, then tap Show answer to check. When you're ready, take the timed chapter-wise test to see your all-India rank.

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Question 1

The present ages of A and B are in the ratio 2 : 3. After 10 years, the ratio of their ages will be 4 : 5. What is the present age of B?

  1. A25 years
  2. B18 years
  3. C15 years
  4. D12 years
  5. E10 years
Show answer
Answer: (C) 15 years Let ages be 2x and 3x. (2x + 10)/(3x + 10) gives x = 5, so B = 15 years.
Question 2

The present ages of A and B are in the ratio 3 : 4. After 8 years, the ratio of their ages will be 4 : 5. What is the present age of B?

  1. A28 years
  2. B24 years
  3. C32 years
  4. D40 years
  5. E36 years
Show answer
Answer: (C) 32 years Let ages be 3x and 4x. (3x + 8)/(4x + 8) gives x = 8, so B = 32 years.
Question 3

The present ages of A and B are in the ratio 3 : 4. After 6 years, the ratio of their ages will be 9 : 11. What is the present age of B?

  1. A20 years
  2. B22 years
  3. C16 years
  4. D12 years
  5. ENone of these
Show answer
Answer: (C) 16 years Let ages be 3x and 4x. (3x + 6)/(4x + 6) gives x = 4, so B = 16 years.
Question 4

The present ages of A and B are in the ratio 4 : 5. After 5 years, the ratio of their ages will be 29 : 35. What is the present age of B?

  1. A30 years
  2. B35 years
  3. C25 years
  4. D24 years
  5. ENone of these
Show answer
Answer: (A) 30 years Let ages be 4x and 5x. (4x + 5)/(5x + 5) gives x = 6, so B = 30 years.
Question 5

The present ages of A and B are in the ratio 5 : 7. After 5 years, the ratio of their ages will be 25 : 33. What is the present age of B?

  1. A33 years
  2. B28 years
  3. C21 years
  4. D35 years
  5. E20 years
Show answer
Answer: (B) 28 years Let ages be 5x and 7x. (5x + 5)/(7x + 5) gives x = 4, so B = 28 years.
Question 6

The present ages of A and B are in the ratio 4 : 5. After 8 years, the ratio of their ages will be 44 : 53. What is the present age of B?

  1. A40 years
  2. B36 years
  3. C50 years
  4. D45 years
  5. E53 years
Show answer
Answer: (D) 45 years Let ages be 4x and 5x. (4x + 8)/(5x + 8) gives x = 9, so B = 45 years.
Question 7

The present ages of A and B are in the ratio 3 : 5. After 6 years, the ratio of their ages will be 9 : 13. What is the present age of B?

  1. A25 years
  2. B15 years
  3. C20 years
  4. D12 years
  5. E26 years
Show answer
Answer: (C) 20 years Let ages be 3x and 5x. (3x + 6)/(5x + 6) gives x = 4, so B = 20 years.
Question 8

The present ages of A and B are in the ratio 5 : 7. After 10 years, the ratio of their ages will be 7 : 9. What is the present age of B?

  1. A28 years
  2. B25 years
  3. C42 years
  4. D35 years
  5. E45 years
Show answer
Answer: (D) 35 years Let ages be 5x and 7x. (5x + 10)/(7x + 10) gives x = 5, so B = 35 years.
Question 9

The present ages of A and B are in the ratio 5 : 6. After 4 years, the ratio of their ages will be 49 : 58. What is the present age of B?

  1. A60 years
  2. B45 years
  3. C58 years
  4. D48 years
  5. E54 years
Show answer
Answer: (E) 54 years Let ages be 5x and 6x. (5x + 4)/(6x + 4) gives x = 9, so B = 54 years.
Question 10

The present ages of A and B are in the ratio 4 : 5. After 10 years, the ratio of their ages will be 17 : 20. What is the present age of B?

  1. A30 years
  2. B35 years
  3. C24 years
  4. D40 years
  5. E25 years
Show answer
Answer: (A) 30 years Let ages be 4x and 5x. (4x + 10)/(5x + 10) gives x = 6, so B = 30 years.

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Question 11

The present ages of A and B are in the ratio 5 : 6. After 5 years, the ratio of their ages will be 25 : 29. What is the present age of B?

  1. A20 years
  2. B18 years
  3. C30 years
  4. D29 years
  5. E24 years
Show answer
Answer: (E) 24 years Let ages be 5x and 6x. (5x + 5)/(6x + 5) gives x = 4, so B = 24 years.
Question 12

The present ages of A and B are in the ratio 5 : 6. After 10 years, the ratio of their ages will be 7 : 8. What is the present age of B?

  1. A30 years
  2. B24 years
  3. C25 years
  4. D36 years
  5. E40 years
Show answer
Answer: (A) 30 years Let ages be 5x and 6x. (5x + 10)/(6x + 10) gives x = 5, so B = 30 years.
Question 13

The present ages of A and B are in the ratio 3 : 5. After 5 years, the ratio of their ages will be 13 : 20. What is the present age of B?

  1. A21 years
  2. B35 years
  3. C40 years
  4. D30 years
  5. ENone of these
Show answer
Answer: (B) 35 years Let ages be 3x and 5x. (3x + 5)/(5x + 5) gives x = 7, so B = 35 years.
Question 14

The present ages of A and B are in the ratio 5 : 6. After 10 years, the ratio of their ages will be 25 : 29. What is the present age of B?

  1. A58 years
  2. B48 years
  3. C54 years
  4. D40 years
  5. E42 years
Show answer
Answer: (B) 48 years Let ages be 5x and 6x. (5x + 10)/(6x + 10) gives x = 8, so B = 48 years.
Question 15

The present ages of A and B are in the ratio 4 : 5. After 8 years, the ratio of their ages will be 6 : 7. What is the present age of B?

  1. A25 years
  2. B20 years
  3. C16 years
  4. D15 years
  5. E28 years
Show answer
Answer: (B) 20 years Let ages be 4x and 5x. (4x + 8)/(5x + 8) gives x = 4, so B = 20 years.
Question 16

The present ages of A and B are in the ratio 3 : 4. After 6 years, the ratio of their ages will be 15 : 19. What is the present age of B?

  1. A24 years
  2. B38 years
  3. C36 years
  4. D28 years
  5. E32 years
Show answer
Answer: (E) 32 years Let ages be 3x and 4x. (3x + 6)/(4x + 6) gives x = 8, so B = 32 years.
Question 17

The present ages of A and B are in the ratio 4 : 5. After 8 years, the ratio of their ages will be 36 : 43. What is the present age of B?

  1. A35 years
  2. B30 years
  3. C28 years
  4. D40 years
  5. E43 years
Show answer
Answer: (A) 35 years Let ages be 4x and 5x. (4x + 8)/(5x + 8) gives x = 7, so B = 35 years.

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