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.