13 years ago my father's age was triple my brother's age. Five years from now my father will be twice as old as my brother. Find…

Question

13 years ago my father's age was triple my brother's age. Five years from now my father will be twice as old as my brother. Find my present age if I am currently twice my brother's age.

1. A. 62 (Correct answer)
2. B. 63
3. C. 92
4. D. 15

Correct Answer

Option A — 62

Detailed Solution & Explanation

The correct answer is 62.

Key Points

• This is a problem on ages with three conditions.
• Let the brother's present age = b and the father's present age = f.
• Condition 1 (13 years ago): f − 13 = 3(b − 13) → f = 3b − 26.
• Condition 2 (5 years hence): f + 5 = 2(b + 5) → f = 2b + 5.
• Equating the two: 3b − 26 = 2b + 5 → b = 31, so the brother is 31 and the father f = 2(31) + 5 = 67.
• Condition 3 (present): 'I am currently twice my brother's age', so my age = 2 × 31 = 62.
• convert each time reference ('years ago' = subtract, 'years hence' = add) into an equation, solve the pair simultaneously, then apply the final relation asked.

Exam Tip

• always define variables for the present ages and adjust with ± the time gap — mixing up past and future ages is the usual error.