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

Introduction / Context:
This is an algebraic age relation question. It checks whether you can manipulate simple equations involving sums of ages and interpret the difference between two individuals ages from those sums.

Given Data / Assumptions:

• Let present ages be A, B and C years.
• Given that A + B is 12 years more than B + C.
• We must find how many years younger C is than A.

Concept / Approach:
The key is to write the relation between the sums of ages as an equation. Once we remove B from both sides, we get a direct relationship between A and C. That relationship will immediately reveal the difference in their ages, which is exactly what the question is asking.

Step-by-Step Solution:
Given: A + B is 12 years more than B + C. So we write: A + B = (B + C) + 12. Simplify by subtracting B from both sides. A = C + 12. This means that the age of A is 12 years more than the age of C.

Verification / Alternative check:
We can cross-check with a simple example. Suppose C is 10 years old. Then A should be 22 years old since A = C + 12. The sum A + B would be 22 + B, while B + C would be B + 10. The difference (A + B) - (B + C) = 12, which fits the original statement. This confirms our interpretation is consistent.

Why Other Options Are Wrong:
Options 13, 14 and 15 would mean that A is 13, 14 or 15 years older than C. But the equation derived from the statement clearly produces a difference of exactly 12 years, not any other value.

Common Pitfalls:
A common mistake is to overcomplicate the situation, creating multiple equations when one simple linear equation is enough. Another pitfall is misreading the word more as less and reversing the direction of the inequality or equation. Always translate such phrases carefully before doing algebraic manipulations.

Final Answer:
C is 12 years younger than A.