The total age of A and B is 12 years more than the total age of B and C. C is how many years younger than A?

Options

A. 12
B. 24
C. C is elder than A
D. Data inadequate

Answer

To solve the problem, we need to set up an equation based on the information given in the question.

**Step 1: Understand the relationship between the ages.**
We are told that the total age of A and B is 12 years more than the total age of B and C. This can be expressed mathematically.

**Step 2: Set up the equation.**
The total age of A and B can be represented as \( A + B \), and the total age of B and C can be represented as \( B + C \). According to the problem, we have:
\[ A + B = (B + C) + 12 \]

**Step 3: Simplify the equation.**
Now, let's simplify the equation:
1. Start with the equation:
\[ A + B = B + C + 12 \]
2. Subtract \( B \) from both sides:
\[ A = C + 12 \]

**Step 4: Rearrange to find the relationship between A and C.**
Now, we want to find out how many years younger C is than A. We can rearrange the equation:
\[ A - C = 12 \]

**Step 5: Conclusion.**
From the equation \( A - C = 12 \), we can conclude that C is 12 years younger than A.

Thus, the answer is:
C is 12 years younger than A.

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