The average age of 5 members of a committee is the same as it was 3 years ago because an old member has been replaced by a new member the difference between the ages of old and new member is

Options

A. 2 years
B. 4 years
C. 8 ears
D. 15 years

Answer

To solve the problem step by step, we need to analyze the information given about the average age of the committee members and the replacement of an old member with a new member.

### Step-by-Step Solution:

1. **Understanding the Average Age**:
- Let the average age of the 5 members of the committee 3 years ago be \( A \).
- Therefore, the total age of the 5 members 3 years ago was \( 5A \).

2. **Calculating the Total Age Now**:
- Since 3 years have passed, each of the 5 members has aged 3 years.
- Thus, the total age of the 5 members now would be \( 5A + 15 \) (because \( 5 \times 3 = 15 \)).

3. **Replacement of the Old Member**:
- Let’s denote the age of the old member who was replaced as \( E \) and the age of the new member as \( F \).
- After replacing the old member, the total age of the committee members now is \( (5A + 15 - E + F) \).

4. **Setting Up the Equation**:
- According to the problem, the average age now is the same as it was 3 years ago. Therefore:
\[ \frac{5A + 15 - E + F}{5} = A \]

5. **Simplifying the Equation**:
- Multiply both sides by 5:
\[ 5A + 15 - E + F = 5A \]
- This simplifies to:
\[ 15 - E + F = 0 \]
- Rearranging gives us:
\[ F - E = -15 \]
- Hence, we can express the age difference as:
\[ E - F = 15 \]

6. **Conclusion**:
- The difference between the ages of the old member and the new member is 15 years.
- Therefore, the answer is **15 years** (Option D).