Problems on ages

1. 1

   The sum of the present ages of a father and his son is 74 years. 7 years ago, the father was 3 times as old as the son. How old is the son now?

   Question 1

   A15 years B29 years C19 years D22 years

   Answer and working

   Answer DD

   Let the son be s. Then (74 − s − 7) = 3(s − 7), so 88 = 4s and s = 22 years.

2. 2

   The sum of the present ages of a father and his son is 66 years. 3 years ago, the father was 3 times as old as the son. How old is the son now?

   Question 2

   A15 years B18 years C21 years D17 years

   Answer and working

   Answer BB

   Let the son be s. Then (66 − s − 3) = 3(s − 3), so 72 = 4s and s = 18 years.

3. 3

   The present ages of Asha and her elder brother are in the ratio 3 : 5. After 9 years, the ratio will be 3 : 4. What is Asha’s present age?

   Question 3

   A18 years B9 years C15 years D11 years

   Answer and working

   Answer BB

   Ages 3x and 5x. (3x + 9) : (5x + 9) = 3 : 4 gives x = 3. Asha is 3 × 3 = 9 years.

4. 4

   The sum of the present ages of a father and his son is 86 years. 4 years ago, the father was 5 times as old as the son. How old is the son now?

   Question 4

   A17 years B14 years C21 years D13 years

   Answer and working

   Answer AA

   Let the son be s. Then (86 − s − 4) = 5(s − 4), so 102 = 6s and s = 17 years.

5. 5

   The sum of the present ages of a father and his son is 80 years. 5 years ago, the father was 4 times as old as the son. How old is the son now?

   Question 5

   A19 years B14 years C24 years D16 years

   Answer and working

   Answer AA

   Let the son be s. Then (80 − s − 5) = 4(s − 5), so 95 = 5s and s = 19 years.

6. 6

   The present ages of Asha and her father are in the ratio 1 : 8. After 12 years, the ratio will be 4 : 11. What is Asha’s present age?

   Question 6

   A4 years B16 years C6 years D32 years

   Answer and working

   Answer AA

   Ages 1x and 8x. (1x + 12) : (8x + 12) = 4 : 11 gives x = 4. Asha is 1 × 4 = 4 years.

7. 7

   The present ages of Asha and her elder brother are in the ratio 3 : 4. After 3 years, the ratio will be 9 : 11. What is Asha’s present age?

   Question 7

   A8 years B6 years C9 years D3 years

   Answer and working

   Answer BB

   Ages 3x and 4x. (3x + 3) : (4x + 3) = 9 : 11 gives x = 2. Asha is 3 × 2 = 6 years.

8. 8

   The present ages of Asha and her elder brother are in the ratio 1 : 3. After 12 years, the ratio will be 2 : 3. What is Asha’s present age?

   Question 8

   A4 years B12 years C8 years D16 years

   Answer and working

   Answer AA

   Ages 1x and 3x. (1x + 12) : (3x + 12) = 2 : 3 gives x = 4. Asha is 1 × 4 = 4 years.

9. 9

   The present ages of Asha and her father are in the ratio 1 : 5. After 9 years, the ratio will be 1 : 3. What is Asha’s present age?

   Question 9

   A11 years B45 years C18 years D9 years

   Answer and working

   Answer DD

   Ages 1x and 5x. (1x + 9) : (5x + 9) = 1 : 3 gives x = 9. Asha is 1 × 9 = 9 years.

10. 10

    The sum of the present ages of a father and his son is 83 years. 3 years ago, the father was 6 times as old as the son. How old is the son now?

    Question 10

    A14 years B11 years C12 years D17 years

    Answer and working

    Answer AA

    Let the son be s. Then (83 − s − 3) = 6(s − 3), so 98 = 7s and s = 14 years.

More quantitative aptitude: Percentages, Profit, loss and discount, Simple interest, Compound interest, Ratio and proportion, Averages.