Average of three ages given a ratio: The average age of three boys is 15 years. If their ages are in the ratio 3 : 5 : 7, what is the age of the youngest boy?

Introduction / Context:We translate the ratio to actual ages using the total derived from the average.

Given Data / Assumptions:

• Average of 3 boys = 15 → sum = 45
• Ratio of ages = 3 : 5 : 7 → total parts = 15

Concept / Approach:If total parts = 15 correspond to total age 45, then each part = 45 / 15 = 3 years. Multiply the youngest’s parts by 3 to get his age.

Step-by-Step Solution:One part = 45 / 15 = 3 yearsYoungest (3 parts) = 3 * 3 = 9 years

Verification / Alternative check:The ages are 9, 15, 21; average is (9 + 15 + 21) / 3 = 45 / 3 = 15, consistent.

Why Other Options Are Wrong:12, 15, 18, 21 do not match the youngest boy determined from the ratio and total sum.

Common Pitfalls:Using 3 as the answer (the ratio number) instead of converting to years using the total sum.

Final Answer:9 year