Average-based relations among A, B, C: C is twice the average of A, B, C; A is half the average; B = 5 years. What is the average age of A, B, C?

Introduction / Context:
Average constraints can sometimes define each person directly in terms of the same average T, which then must satisfy its own definition T = (A + B + C)/3. Substituting these forms yields a single linear equation in T.

Given Data / Assumptions:

• Let average be T.
• C = 2T; A = T/2; B = 5.
• Average definition: (A + B + C)/3 = T.

Concept / Approach:
Plug forms into the definition and solve for T. This ensures internal consistency and avoids guessing individual ages first.

Step-by-Step Solution:

Verification / Alternative check:
Then A = 5, B = 5, C = 20; their average (5 + 5 + 20)/3 = 10, matching T.

Why Other Options Are Wrong:
15/12/9 do not satisfy both role definitions and the average identity simultaneously.

Common Pitfalls:
Using average of given numbers only (e.g., averaging 5 and 20) without enforcing all constraints together.

Final Answer:
10 years