Question

The sum of ages of 5 children born at intervals of 3 years each is 50 years. What is the age of the youngest child?

• A. 4 years
• B. 5 years
• C. 6 years
• D. 8 years
• E. 10 years

Hint:

In an arithmetic progression with an odd number of terms, the middle term is the average. Here, $50 / 5 = 10$ is the age of the 3rd child. Subtract $3 \times 2$ to find the youngest: $10 - 6 = 4$.

Answer 1

The Correct Option is A

Step 1: Analyse options.
- Let the age of the youngest child be $x$. - The ages are $x, (x+3), (x+6), (x+9), (x+12)$. - Sum: $x + (x+3) + (x+6) + (x+9) + (x+12) = 50$. - $5x + 30 = 50 \Rightarrow 5x = 20 \Rightarrow x = 4$.
Step 2: Conclusion.
The age of the youngest child is 4 years. Final Answer: (a) 4 years