A’s present age is one fourth of his mother’s age two years ago.  After 10 years, A’s mother’s age will be twice of B’s age. If B’s 12th birthday was celebrated 4 years ago, then what is A’s present age?

A’s present age is one fourth of his mother’s age two years ago.  After 10 years, A’s mother’s age will be twice of B’s age. If B’s 12th birthday was celebrated 4 years ago, then what is A’s present age? Correct Answer 10 years

Given:

A’s age = 1/4 (Mother’s age two years ago)

Mother’s age = 2 × (B’s age after 10 years)

B’s 12^th birthday was 4 years ago

Concept:

4 years ago B’s age was 12. So present age of B is 16

Explanation:

Let’s denote A’s mother’s age by M

⇒ A = 1/4 × (M – 2)

And, M + 10 = 2 × (B + 10)

B = 16 (∵ 4 years ago B’s age was 12)

Calculation:

According to the Question,

 M + 10 = 2 × (16 + 10)

⇒ M = 42

We have, A = 1/4 (M – 2)

⇒ A = 1/4 × (42 – 2) = 10

∴ Present age of A is 10 years