Ten years ago, the average age of a family of 4 members was 24 years. Since then two children were born, and the average age of the family is the same (24 years) today. If the two children differ in age by 2 years, what is the present age of the youngest child?

Introduction:
Family average age questions are solved by converting averages to totals and tracking how totals change as years pass and members are added. The constancy of the average despite added members reveals the combined current age of the new children, which can be split using their given age gap.

Given Data / Assumptions:

• 10 years ago: 4 members, average 24 → total then = 24 * 4 = 96
• Now: 6 members, average still 24 → total now = 24 * 6 = 144
• Two new children; their ages differ by 2 years

Concept / Approach:
If the original 4 members aged 10 years each, their combined total increased by 40. Therefore current total from the original 4 is 96 + 40 = 136. Since the family total is 144, the two children together sum to 8 years now. Let the younger be x and the older be x + 2. Then 2x + 2 = 8 → x = 3.

Step-by-Step Solution:

Verification / Alternative check:
With children aged 3 and 5, the current average returns to 24 for 6 members exactly.

Why Other Options Are Wrong:
1, 2, 4, or 5 years for the youngest break the 8-year total constraint or the 2-year gap.

Common Pitfalls:
Forgetting that each of the initial 4 members adds 10 years to the total; mixing up “difference” and “sum”.

Final Answer:
3 years