The average age of the committee of 10 members is 40 years. A member of age 52 retires and a new member of age 38 takes his place. What is the average age of the present committee?

Options

A. 37.5 years
B. 35.5 years
C. 33.5 years
D. 38.6 years

Answer

To solve the problem, we will follow these steps:

1. **Calculate the total age of the original committee**:
The average age of the committee is given as 40 years, and there are 10 members.
\[ \text{Total age} = \text{Average age} \times \text{Number of members} = 40 \times 10 = 400 \text{ years} \]

2. **Determine the age change due to the retirement and new member**:
A member aged 52 retires and is replaced by a member aged 38.
We need to find the difference in age:
\[ \text{Age difference} = \text{Age of retiring member} - \text{Age of new member} = 52 - 38 = 14 \text{ years} \]

3. **Calculate the new total age of the committee**:
Since a member aged 52 is leaving and a member aged 38 is joining, the total age of the committee will decrease by 14 years:
\[ \text{New total age} = \text{Old total age} - \text{Age difference} = 400 - 14 = 386 \text{ years} \]

4. **Calculate the new average age of the committee**:
The number of members remains the same at 10. Therefore, the new average age can be calculated as:
\[ \text{New average age} = \frac{\text{New total age}}{\text{Number of members}} = \frac{386}{10} = 38.6 \text{ years} \]

Thus, the average age of the present committee is **38.6 years**.

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