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Bala’s grandmother was 8 times older to him 16 years ago. She would be 3 times his age after 8 years from now. Eight years ago, what was the ratio of Bala’s age to that of his grandmother?


1. 10 : 57
2. 11 : 52
3. 16 : 53
4. 11 : 53
5. 12 : 59

1 Answer

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Correct Answer - Option 4 : 11 : 53

Calculations:

16 years ago,

Let Bala’s age be x, and grandmother’s age is 8x.

After 8 years from now,

Bala’s age = x + 16 + 8

⇒ x + 24

Grandmother’s age = 8x + 16 + 8

⇒ 8x + 24

∴ Required equation:

⇒ 8x + 24 = 3 (x + 24)

⇒ 8x + 24 = 3x + 72

⇒ 5x = 48

⇒ x = 48/5

∴ 8 years ago required ratio :

⇒ (x + 8) : (8x + 8)

⇒ 48/5 + 8 : 8 × 48/5 + 8

⇒ 88/5 : 424/5

⇒ 88 : 424

⇒ 11 : 53

 The ratio of Bala’s age to that of his grandmother 8 years ago was 11 : 53.

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