Question

Eight years ago, the ratio of the ages of A and B was 9 ∶ 10. The ratio of their ages 4 years from now will be 12 ∶ 13. If the age of C is 4 years less than the present age of A, then what is the present age (in years) of C?
1. 48
2. 44
3. 52
4. 40

Answer 1

Correct Answer - Option 4 : 40

Given:

Eight years ago ages of A and B is 9 : 10.

Four years now the ratio of Ages of A and B is 12 ∶ 13

The age of C is 4 years less than the present age of A.

Concept used:

By ratio method.

Calculation:

Let eight years ago age of A be 9x years

Eight years ago age of B be 10x years

Present age,

A's age = 9x + 8

B's age = 10x + 8

After four year,

A's age = 9x + 8 + 4 = 9x + 12

B's age = 10x + 8 + 4 = 10x + 12

According to the question,

(9x + 12)/(10x + 12) = 12/13
⇒ 13(9x + 12) = 12(10x + 12)

⇒ 117x + 156 = 120x + 144

⇒ 3x = 12

⇒ x = 4

So, Present age of A = 9x + 8 = 9 × 4 + 8 = 44

The present age of C = 4 years less than the present age of A

⇒ Present age of C = 44 – 4 = 40

∴  The Present age of C is 40 years.