Problems on Ages — “Three years ago, a family of five had average age 17 years. A baby is born; now the average is still 17. Find the baby’s present age.”

Introduction / Context:
Average over time with changing group size is a classic twist. Carefully track the sum of ages across the time gap, accounting for everyone aging equally and the addition of a new member (the baby).

Given Data / Assumptions:

• 3 years ago: members = 5; average = 17 ⇒ sum then = 85.
• Now: members = 6 (baby added); average now = 17 ⇒ sum now = 102.
• All original five aged 3 years each over the period.

Concept / Approach:
Compute the current combined age of the original five, then subtract from the current total to isolate the baby’s present age.

Step-by-Step Solution:

Verification / Alternative check:
If the baby were 1 year old, the total would be 101 (not 102). If 3 years, total 103 (too high). Thus 2 years is consistent.

Why Other Options Are Wrong:
6 or 9 months, 1 year, or 3 years do not reconcile with both the earlier 85 and the present 102 sums.

Common Pitfalls:
Forgetting to age the original members; or mistakenly averaging with 5 rather than 6 at present.

Final Answer:
2 years