Ages (sum shift comparison): The sum of A and B is 12 more than the sum of B and C. How many years younger is C than A?

Introduction / Context:Comparing two sums that share one common term is a quick route to a direct difference between the other two terms. No time-shift is involved; it is a pure algebraic rearrangement task.

Given Data / Assumptions:A + B = (B + C) + 12.

Concept / Approach:Cancel the common B from both sides to isolate A and C. The resulting equation immediately reveals how much older A is than C.

Step-by-Step Solution:

Verification / Alternative check:Pick any C and add 12 to obtain A; then sums differ by 12 for all values of B, confirming generality.

Why Other Options Are Wrong:10 and 24 contradict the derived identity; “Data inadequate” is incorrect because the relation uniquely fixes the difference A − C.

Common Pitfalls:Forgetting to cancel B or overcomplicating with unnecessary assumptions about actual ages.

Final Answer:12