Ages in arithmetic progression: Five children are born at intervals of 3 years each. The sum of their ages is 50. Find the age of the youngest child.

Introduction / Context:Ages at equal intervals form an arithmetic progression (AP). The sum of an AP can be written in terms of the first term and common difference, enabling a direct solution without enumerating all ages explicitly.

Given Data / Assumptions:Let the youngest be x. Then ages are x, x+3, x+6, x+9, x+12, and their sum is 50.

Concept / Approach:Use the AP sum formula specialized to these five terms with common difference 3. Solve for x and interpret as the youngest child's current age.

Step-by-Step Solution:

Verification / Alternative check:Ages are 4, 7, 10, 13, 16; sum = 50 (✓).

Why Other Options Are Wrong:Other numbers do not satisfy the fixed sum when the AP structure is honored.

Common Pitfalls:Using 3 as the average interval incorrectly or miscounting the total increment (it is 30 across five terms).

Final Answer:4 years