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

Options

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

Answer

To solve the problem step by step, we will use algebraic expressions to represent the ages of A, B, and C.

### Step 1: Define the variables
Let:
- A = age of A
- B = age of B
- C = age of C

### Step 2: Write the equation based on the problem statement
According to the problem, the total age of A and B is 12 years more than the total age of B and C. We can express this as:
\[ A + B = (B + C) + 12 \]

### Step 3: Simplify the equation
Now, we can 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 the equation to find the relationship between A and C
From the equation \( A = C + 12 \), we can rearrange it to find how much younger C is than A:
\[ C = A - 12 \]

### Step 5: Conclusion
This means that C is 12 years younger than A.

### Final Answer
C is 12 years younger than A.