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MAT Problems on Ages Questions with Answers & Explanations

18 Problems on Ages questions from the Mathematical Skills section of MAT, 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 5 : 6. After 10 years, the ratio of their ages will be 20 : 23. What is the present age of B?

  1. A36 years
  2. B46 years
  3. C30 years
  4. D42 years
Show answer
Answer: (A) 36 years Let ages be 5x and 6x. (5x + 10)/(6x + 10) gives x = 6, so B = 36 years.
Question 2

The present ages of A and B are in the ratio 5 : 6. After 5 years, the ratio of their ages will be 45 : 53. What is the present age of B?

  1. A53 years
  2. B48 years
  3. C42 years
  4. D54 years
Show answer
Answer: (B) 48 years Let ages be 5x and 6x. (5x + 5)/(6x + 5) gives x = 8, so B = 48 years.
Question 3

The present ages of A and B are in the ratio 5 : 6. After 8 years, the ratio of their ages will be 53 : 62. What is the present age of B?

  1. A60 years
  2. B62 years
  3. C45 years
  4. D54 years
Show answer
Answer: (D) 54 years Let ages be 5x and 6x. (5x + 8)/(6x + 8) gives x = 9, so B = 54 years.
Question 4

The present ages of A and B are in the ratio 5 : 7. After 5 years, the ratio of their ages will be 35 : 47. What is the present age of B?

  1. A47 years
  2. B30 years
  3. C42 years
  4. D35 years
Show answer
Answer: (C) 42 years Let ages be 5x and 7x. (5x + 5)/(7x + 5) gives x = 6, so B = 42 years.
Question 5

The present ages of A and B are in the ratio 3 : 5. After 5 years, the ratio of their ages will be 17 : 25. What is the present age of B?

  1. A15 years
  2. B20 years
  3. C25 years
  4. D12 years
Show answer
Answer: (B) 20 years Let ages be 3x and 5x. (3x + 5)/(5x + 5) gives x = 4, so B = 20 years.
Question 6

The present ages of A and B are in the ratio 3 : 4. After 6 years, the ratio of their ages will be 27 : 34. What is the present age of B?

  1. A32 years
  2. B21 years
  3. C34 years
  4. D28 years
Show answer
Answer: (D) 28 years Let ages be 3x and 4x. (3x + 6)/(4x + 6) gives x = 7, so B = 28 years.
Question 7

The present ages of A and B are in the ratio 2 : 3. After 4 years, the ratio of their ages will be 8 : 11. What is the present age of B?

  1. A12 years
  2. B15 years
  3. C22 years
  4. D18 years
Show answer
Answer: (D) 18 years Let ages be 2x and 3x. (2x + 4)/(3x + 4) gives x = 6, so B = 18 years.
Question 8

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

  1. A20 years
  2. B25 years
  3. C15 years
  4. D16 years
Show answer
Answer: (A) 20 years Let ages be 3x and 4x. (3x + 5)/(4x + 5) gives x = 5, so B = 20 years.
Question 9

The present ages of A and B are in the ratio 5 : 7. After 6 years, the ratio of their ages will be 13 : 17. What is the present age of B?

  1. A35 years
  2. B34 years
  3. C28 years
  4. D21 years
Show answer
Answer: (C) 28 years Let ages be 5x and 7x. (5x + 6)/(7x + 6) gives x = 4, so B = 28 years.
Question 10

The present ages of A and B are in the ratio 3 : 5. After 5 years, the ratio of their ages will be 29 : 45. What is the present age of B?

  1. A45 years
  2. B35 years
  3. C24 years
  4. D40 years
Show answer
Answer: (D) 40 years Let ages be 3x and 5x. (3x + 5)/(5x + 5) gives x = 8, so B = 40 years.

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Question 11

The present ages of A and B are in the ratio 5 : 6. After 6 years, the ratio of their ages will be 41 : 48. What is the present age of B?

  1. A36 years
  2. B48 years
  3. C35 years
  4. D42 years
Show answer
Answer: (D) 42 years Let ages be 5x and 6x. (5x + 6)/(6x + 6) gives x = 7, so B = 42 years.
Question 12

The present ages of A and B are in the ratio 3 : 4. After 10 years, the ratio of their ages will be 5 : 6. What is the present age of B?

  1. A30 years
  2. B15 years
  3. C16 years
  4. D20 years
Show answer
Answer: (D) 20 years Let ages be 3x and 4x. (3x + 10)/(4x + 10) gives x = 5, so B = 20 years.
Question 13

The present ages of A and B are in the ratio 3 : 5. After 10 years, the ratio of their ages will be 37 : 55. What is the present age of B?

  1. A50 years
  2. B27 years
  3. C55 years
  4. D45 years
Show answer
Answer: (D) 45 years Let ages be 3x and 5x. (3x + 10)/(5x + 10) gives x = 9, so B = 45 years.
Question 14

The present ages of A and B are in the ratio 3 : 5. After 4 years, the ratio of their ages will be 11 : 17. What is the present age of B?

  1. A34 years
  2. B35 years
  3. C30 years
  4. D18 years
Show answer
Answer: (C) 30 years Let ages be 3x and 5x. (3x + 4)/(5x + 4) gives x = 6, so B = 30 years.
Question 15

The present ages of A and B are in the ratio 5 : 7. After 8 years, the ratio of their ages will be 19 : 25. What is the present age of B?

  1. A30 years
  2. B35 years
  3. C42 years
  4. D49 years
Show answer
Answer: (C) 42 years Let ages be 5x and 7x. (5x + 8)/(7x + 8) gives x = 6, so B = 42 years.
Question 16

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

  1. A20 years
  2. B25 years
  3. C12 years
  4. D15 years
Show answer
Answer: (A) 20 years Let ages be 3x and 5x. (3x + 4)/(5x + 4) gives x = 4, so B = 20 years.
Question 17

The present ages of A and B are in the ratio 3 : 4. After 6 years, the ratio of their ages will be 27 : 34. What is the present age of B?

  1. A28 years
  2. B32 years
  3. C24 years
  4. D21 years
Show answer
Answer: (A) 28 years Let ages be 3x and 4x. (3x + 6)/(4x + 6) gives x = 7, so B = 28 years.
Question 18

The present ages of A and B are in the ratio 3 : 5. After 8 years, the ratio of their ages will be 29 : 43. What is the present age of B?

  1. A43 years
  2. B21 years
  3. C35 years
  4. D40 years
Show answer
Answer: (C) 35 years Let ages be 3x and 5x. (3x + 8)/(5x + 8) gives x = 7, so B = 35 years.

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