Ten years ago, a father's age was three times his son's age. Ten years hence, the father's age will be twice the son's. What is the ratio of their present ages (father : son)?

Problem restatementTwo linear relations connect present ages to past and future multiples. Solve for present ages and report the ratio.

Given data

• Present ages: Father = F, Son = S.
• F − 10 = 3(S − 10).
• F + 10 = 2(S + 10).

Concept/ApproachSolve the simultaneous equations to get S first, then F, then form the ratio F:S.

Step-by-Step calculationF − 10 = 3S − 30 ⇒ F = 3S − 20 …(1)F + 10 = 2S + 20 ⇒ F = 2S + 10 …(2)Equate (1) and (2): 3S − 20 = 2S + 10 ⇒ S = 30Then F = 2S + 10 = 70Ratio F:S = 70:30 = 7:3

Verification/AlternativeCheck past: 60 vs 20 (×3). Check future: 80 vs 40 (×2). Both hold.

Common pitfallsUsing 3(S − 10) = F + 10 (mixing past and future conditions).

Final Answer7:3