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Father & Son — “Currently, father + son = 70 years. After 10 years, the son’s age will be exactly half the father’s. Find their present ages.”

Difficulty: Medium

45 years, 25 years
50 years, 20 years
47 years, 23 years
50 years, 25 years
48 years, 22 years

Correct Answer: 50 years, 20 years

Explanation:

Introduction / Context:
We are given a present sum and a future proportional relation. Setting up two equations and solving simultaneously yields both present ages uniquely.

Given Data / Assumptions:

Let present father = F, present son = S.
F + S = 70.
After 10 years: S + 10 = (F + 10)/2.

Concept / Approach:
Use the future proportionality to form a linear equation, then combine with the sum equation to solve for S and F. Verify by plugging back into the future relation.

Step-by-Step Solution:

2(S + 10) = F + 10 ⇒ 2S + 20 = F + 10 ⇒ 2S − F = −10.With F + S = 70 ⇒ F = 70 − S.Substitute: 2S − (70 − S) = −10 ⇒ 3S − 70 = −10 ⇒ 3S = 60 ⇒ S = 20.Then F = 50.

Verification / Alternative check:
After 10 years: son 30, father 60 ⇒ son is exactly half of father. Conditions satisfied.

Why Other Options Are Wrong:
Any pair not equal to (50, 20) either breaks the sum 70 or fails the “half in 10 years” condition.

Common Pitfalls:
Forgetting to advance both ages by 10 in the future relation or mixing up which one becomes half of which.

Father & Son — “Currently, father + son = 70 years. After 10 years, the son’s age will be exactly half the father’s. Find their present ages.”

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