Family average unchanged after addition: Three years ago, the average age of a 5-member family was 27 years. Today, after adding a child, the average is still 27 years. Find the present age of the child.

Introduction / Context:
Average age problems over time can be handled using totals. Every existing member’s age increases by the elapsed years, and adding a new member increases count and total simultaneously.

Given Data / Assumptions:

• 3 years ago: 5 members, average = 27
• Today: 6 members (child added), average = 27

Concept / Approach:
Compute the old total from the past average, add the 3-year growth for the original five to get their total today, then compare with the current grand total to get the child’s age now.

Step-by-Step Solution:

Verification / Alternative check:
The unchanged average implies the child’s age offsets the total 3-year increase across the five members (15 years) plus keeps the mean at 27 for six members, which is satisfied by 12 years.

Why Other Options Are Wrong:

• 16, 24, 20, 10: do not yield the required overall total of 162.

Common Pitfalls:
Multiplying the average change by the new count or forgetting to add the 3-year increment for all original five members.

Final Answer:
12 yr