The average age of a committee of 11 persons increases by 2 yr when 3 men of 32 yr, 34 yr and 33 yr are replaced by 3 women. What will be the average age of those 3 women?

Options

A. 40yr
B. `41 (1)/(3) yr `
C. 41 yr
D. `40 (1)/(3) yr `

Answer

To solve the problem step by step, we need to find the average age of the three women who replace the three men in the committee.

### Step 1: Understand the Problem
We know that the average age of a committee of 11 persons increases by 2 years when 3 men (aged 32, 34, and 33 years) are replaced by 3 women.

### Step 2: Calculate the Total Increase in Age
Since the average age increases by 2 years for 11 persons, the total increase in age for the committee can be calculated as follows:
\[ \text{Total Increase in Age} = \text{Increase in Average Age} \times \text{Number of Persons} \]
\[ \text{Total Increase in Age} = 2 \, \text{years} \times 11 = 22 \, \text{years} \]

### Step 3: Calculate the Total Age of the 3 Men
Next, we calculate the total age of the three men being replaced:
\[ \text{Total Age of Men} = 32 + 34 + 33 = 99 \, \text{years} \]

### Step 4: Determine the Total Age of the Committee After Replacement
Let the total age of the committee before the replacement be \( T \). After replacing the three men with the three women, the total age of the committee becomes:
\[ T - \text{Total Age of Men} + \text{Total Age of Women} = T + 22 \]
This means:
\[ \text{Total Age of Women} = T + 22 - T + 99 = 121 \, \text{years} \]

### Step 5: Calculate the Average Age of the 3 Women
Now, we can find the average age of the three women:
\[ \text{Average Age of Women} = \frac{\text{Total Age of Women}}{3} = \frac{121}{3} \approx 40.33 \, \text{years} \]

### Final Answer
The average age of the three women is approximately 40.33 years.

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