Parent–children sum relationships: A father’s present age is four times the sum of his three children’s present ages. Six years hence, his age will be only double the sum of their ages. What is the father’s present age?

Introduction / Context:This is a two-equation problem involving a parent and the combined ages of three children, now and 6 years later. Because three children each gain 6 years, their total increases by 18.

Given Data / Assumptions:

• Let S be the sum of the three children’s present ages
• Father now F = 4S
• After 6 years: F + 6 = 2 * (S + 18)

Concept / Approach:Use the two linear relations to eliminate S. First relation gives F in terms of S; second relates F and S after 6 years. Solve for S, then get F immediately.

Step-by-Step Solution:

Verification / Alternative check:Check future condition: F + 6 = 66 and S + 18 = 33; 2 * 33 = 66 ✓.

Why Other Options Are Wrong:30, 40, 45 do not satisfy both the “now” and “after 6 years” constraints simultaneously.

Common Pitfalls:Forgetting that three children together gain 3 * 6 = 18 in six years; using 6 instead of 18 leads to incorrect results.

Final Answer:60 years