Average age unchanged after a birth: Three years ago, the average age of a family of 5 was 17 years. A new child was born since then, and today the average remains 17. What is the child’s present age?

Introduction / Context:
Average age questions hinge on total ages. When the average is unchanged after several years and an extra family member is added, comparing totals before and after gives the newcomer’s current age directly. This problem tests careful accounting of the total age “carry-forward”.

Given Data / Assumptions:

• 3 years ago: 5 members, average 17 ⇒ total then = 5 * 17 = 85.
• Today: 6 members (one newborn added sometime in the last 3 years), average still 17 ⇒ total now = 6 * 17 = 102.
• The initial 5 members each aged 3 years over the period.

Concept / Approach:
Total of the original 5 today = 85 + (5 * 3) = 100. Since the current family total is 102, the difference 102 − 100 is precisely the present age of the child.

Step-by-Step Solution:

Verification / Alternative check:
If the child were born exactly t years ago (0 ≤ t ≤ 3), the child’s age now is t. The calculation shows t = 2, which is feasible within 0–3 years.

Why Other Options Are Wrong:
1, 3, or 2.5 fail to reconcile both totals and the fixed average condition.

Common Pitfalls:
Multiplying the average by the wrong headcount or forgetting that the five elders gain 3 years each.

Final Answer:
2 yr