Three-member family with linked differences: A man is 3 years older than his wife and four times as old as his son. If the son will be 15 after 3 years, what is the wife's present age?

Introduction / Context:Combine a known future age of the son with proportional and difference relations to deduce the wife's present age.

Given Data / Assumptions:

• Son in 3 years = 15 ⇒ Son now = 12.
• Man = 4 × Son ⇒ Man now = 48.
• Man is 3 years older than wife ⇒ Wife now = 48 − 3.

Concept / Approach:Anchor absolute ages using the son's future age, then step through the chained relations.

Step-by-Step Solution:1) Son now = 15 − 3 = 12.2) Man now = 4 × 12 = 48.3) Wife now = 48 − 3 = 45.

Verification / Alternative check:Relations hold: (48, 45, 12) satisfy “man 3 older than wife” and “man 4× son.”

Why Other Options Are Wrong:They break one of the given constraints when checked.

Common Pitfalls:Adding 3 instead of subtracting when moving from the husband's age to the wife's age.

Final Answer:45 years