Problems on Ages — “Average age of A, B, C is 25 years; their ratio is 3 : 5 : 7. Find A’s present age.”

Introduction / Context:Average plus ratio is the standard “total and split” pattern. Recover the total from the average, then apportion by ratio parts to get each individual age.

Given Data / Assumptions:

• Average of three = 25 ⇒ total = 75.
• Ratio A : B : C = 3 : 5 : 7 (sum of parts = 15).

Concept / Approach:One part = total / number of parts. Then A = 3 parts, B = 5 parts, C = 7 parts.

Step-by-Step Solution:

Verification / Alternative check:Ages become (15, 25, 35). Average = (15 + 25 + 35)/3 = 75/3 = 25 ✓.

Why Other Options Are Wrong:12/18/21/24 are not equal to 3 parts with part size 5.

Common Pitfalls:Taking 25 directly as a part value or dividing by 3 incorrectly; always form the total first.

Final Answer:15 years