Sum now and ratio in the past – The sum of the present ages of a father and son is 60. Six years ago the father was five times the son. After 6 years, what will be the son’s age?

Introduction / Context:
We have a present-time sum and a past-time ratio. Converting both into equations in present variables and solving yields the son’s current age, from which we can project six years into the future.

Given Data / Assumptions:

• Let F = father, S = son (present ages).
• F + S = 60.
• Six years ago: F − 6 = 5(S − 6).
• Asked: S + 6.

Concept / Approach:
From the past ratio: F = 5S − 24. Substitute into the sum to solve for S, then add 6.

Step-by-Step Solution:
F = 5S − 24.(5S − 24) + S = 60 ⇒ 6S = 84 ⇒ S = 14.After 6 years: S + 6 = 20.

Verification / Alternative check:
Check the past relation: F = 46; six years ago 40 and 8 → 40 = 5 × 8, true. Present sum: 46 + 14 = 60, true.

Why Other Options Are Wrong:
They do not follow from the unique solution S = 14.

Common Pitfalls:
Dropping the −6 term on only one side of the past equation or forgetting to compute “after 6 years.”

Final Answer:
20