Mean-of-extremes age relation: A is as much younger than B as he is older than C (i.e., B − A = A − C). If B + C = 40, find A’s present age.

Introduction / Context:The statement “A is as much younger than B as he is older than C” means A is the arithmetic mean of B and C. Therefore A equals (B + C)/2, and the problem collapses to a single quick computation with the given sum.

Given Data / Assumptions:

• B − A = A − C ⇒ 2A = B + C.
• B + C = 40.

Concept / Approach:Use the mean relation directly: A = (B + C)/2. This recognizes the symmetry implied by the verbal statement and eliminates unnecessary algebra.

Step-by-Step Solution:

Verification / Alternative check:If B and C were, say, 28 and 12, A = 20 satisfies B − A = 8 and A − C = 8.

Why Other Options Are Wrong:25/30/27 do not equal half of 40.

Common Pitfalls:Misinterpreting the verbal relation as multiplicative; it is additive and symmetric.

Final Answer:20 years