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

Difficulty: Medium

8 : 5
7 : 3
5 : 2
9 : 5
None of these

Correct Answer: 7 : 3

Explanation:

Introduction / Context:
Two age relations are given at times symmetrically placed around the present: 10 years in the past and 10 years in the future. Modeling with variables and solving yields present ages and their ratio.

Given Data / Assumptions:

Ten years ago: F − 10 = 3(S − 10).
Ten years later: F + 10 = 2(S + 10).
Find present ratio F : S.

Concept / Approach:
Translate each condition into a linear equation in F and S, solve for S, then compute F and simplify the ratio.

Step-by-Step Solution:

Past: F − 10 = 3S − 30 ⇒ F = 3S − 20.Future: F + 10 = 2S + 20 ⇒ F = 2S + 10.Equate: 3S − 20 = 2S + 10 ⇒ S = 30.Then F = 2S + 10 = 70.Ratio: F : S = 70 : 30 = 7 : 3.

Verification / Alternative check:

Ten years ago: 60 vs 20 ⇒ father = 3 × son ✔. Ten years hence: 80 vs 40 ⇒ father = 2 × son ✔.

Why Other Options Are Wrong:

8 : 5, 5 : 2, 9 : 5 do not satisfy both temporal constraints.

Common Pitfalls:

Solving only one condition; both must hold simultaneously.Errors when moving from “years ago / hence” to equations.

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

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