The sum of the ages of A and B is 12 years more than the sum of the ages of B and C. By how many years is C younger than A (in years)?

Introduction:
This is a simple algebraic ages comparison question. It checks whether you can translate a sentence about sums into an equation and simplify it. The important insight is that B appears in both sums, so it cancels out when we compare them. After cancellation, the relationship between A and C becomes direct and the difference can be read immediately.

Given Data / Assumptions:

• (A + B) is 12 more than (B + C)
• All values represent present ages in years
• We need how many years C is younger than A

Concept / Approach:
Convert the statement into an equation, cancel common terms, and interpret the remaining difference as an age gap.

Step-by-Step Solution:
Translate: A + B = (B + C) + 12A + B = B + C + 12Subtract B from both sides: A = C + 12So A is 12 years older than CTherefore, C is 12 years younger than A

Verification / Alternative check:
If A = C + 12, then A + B = (C + 12) + B = (B + C) + 12, which matches the given statement exactly. So the reasoning is consistent.

Why Other Options Are Wrong:
13, 14, 15: would require the difference between A and C to be different from 12, contradicting the simplified equation A = C + 12.11: similarly contradicts the exact “12 more” condition in the question.

Common Pitfalls:
Trying to assign random numbers to A, B, and C instead of simplifying algebraically.Forgetting that B cancels because it appears on both sides.Answering “A is older than C” but not giving the numeric difference.

Final Answer:
12 years