Question

The ratio of ages of Aruna and Nidhi is 11 : 13. 3 years ago, the ratio of their ages is 3 : 5. What is the difference between their ages?
1. 1 year
2. 9 months
3. 8 months
4. 1.5 years
5. 2 years

Answer 1

Correct Answer - Option 2 : 9 months

Concept Used:

If present age is x years, then a years ago the age is (x - a).

Calculations:

Let the multiplying factor of ages be x.

Ratio of ages of Aruna and Nidhi = 11 : 13

3 years ago, ratio of their ages = 3 : 5

⇒ At present, ratio of their ages = (3x + 3) : (5x + 3)

Now, (3x + 3)/(5x + 3) = 11/13

⇒ 13 × (3x + 3) = 11 × (5x + 3)

⇒ 39x + 39 = 55x + 33

⇒ 16x = 6

⇒ x = (3/8) × 12 = 9/2 months      [1 year = 12 months]

Difference between ages of Aruna and Nidhi = (5x + 3) - (3x + 3) = 2x

⇒ Difference between ages of Aruna and Nidhi = 2x = 2(9/2) months

∴ The difference between ages of Aruna and Nidhi is 9 months.