Four children at 4-year intervals – The sum of their present ages is 60. What is the age of the youngest child?

Introduction / Context:
When children are born at equal intervals, their ages form an arithmetic progression. Summation formulas for APs make such problems quick to solve.

Given Data / Assumptions:

• Let youngest = x.
• Then ages are x, x + 4, x + 8, x + 12.
• Sum = 60.

Concept / Approach:
Add the four-term AP and solve for x. Equally spaced terms keep the algebra simple.

Step-by-Step Solution:
x + (x + 4) + (x + 8) + (x + 12) = 60.4x + 24 = 60 ⇒ 4x = 36 ⇒ x = 9.

Verification / Alternative check:
Actual ages: 9, 13, 17, 21; sum = 60.

Why Other Options Are Wrong:
They do not satisfy the sum with 4-year spacing.

Common Pitfalls:
Using 3 terms or spacing by 3 years accidentally. Always match the stated interval.

Final Answer:
9