Family Averages — “Three years ago, the average age of husband, wife, and child was 27. Five years ago, the average of wife and child was 20. Find the husband’s present age.”

Introduction / Context:
We combine two time-shifted averages to reconstruct present totals and isolate one person’s current age. Careful bookkeeping of how many years to add to each group is essential.

Given Data / Assumptions:

• 3 years ago: average(H,W,C) = 27 ⇒ sum then = 27 * 3 = 81.
• Present sum(H,W,C) = 81 + 3*3 = 90.
• 5 years ago: average(W,C) = 20 ⇒ sum then = 20 * 2 = 40.
• Present sum(W,C) = 40 + 2*5 = 50.

Concept / Approach:
Convert each average to a total at its time, then advance totals to the present by adding 1 year per person per elapsed year. Subtract to isolate the remaining person’s present age.

Step-by-Step Solution:

Verification / Alternative check:
Rolling back 3 years from (40, W, C) decreases the total by 9 to reach 81; and rolling back 5 years from (W, C) decreases by 10 to reach 40. Both match the givens.

Why Other Options Are Wrong:
35/45/50/42 do not satisfy both time-shifted averages simultaneously when tested.

Common Pitfalls:
Adding 3 years only once for the trio instead of 3 persons × 3 years; forgetting 2 persons × 5 years for W and C.

Final Answer:
40 years