The average age of 8 persons in a committee is increased by 2 years when two men aged 35 years and 45 years are substituted by two women. What is the average age of these two women ?

Answer

To find the average age of the two women who replaced the two men aged 35 and 45 years, we can follow these steps:

### Step 1: Calculate the total age of the original committee
Let the average age of the 8 persons in the committee be \( x \). Therefore, the total age of the 8 persons can be calculated as:
\[ \text{Total age of 8 persons} = 8x \]

### Step 2: Calculate the total age of the two men being replaced
The ages of the two men are 35 years and 45 years. Therefore, their total age is:
\[ \text{Total age of the two men} = 35 + 45 = 80 \text{ years} \]

### Step 3: Calculate the total age of the new committee after the replacement
When the two men are replaced by two women, the average age of the committee increases by 2 years. The new average age becomes \( x + 2 \). Thus, the total age of the new committee is:
\[ \text{Total age of new committee} = 8(x + 2) = 8x + 16 \]

### Step 4: Set up the equation for the total age of the new committee
The total age of the new committee can also be expressed as the total age of the original committee minus the age of the two men plus the age of the two women. Let the total age of the two women be \( W \). Therefore, we have:
\[ 8x + 16 = 8x - 80 + W \]

### Step 5: Simplify the equation
Now, we can simplify the equation:
\[ 8x + 16 = 8x - 80 + W \]
Subtract \( 8x \) from both sides:
\[ 16 = -80 + W \]
Now, add 80 to both sides:
\[ W = 16 + 80 = 96 \text{ years} \]

### Step 6: Calculate the average age of the two women
The average age of the two women can be calculated by dividing their total age by 2:
\[ \text{Average age of the two women} = \frac{W}{2} = \frac{96}{2} = 48 \text{ years} \]

### Final Answer
The average age of the two women is **48 years**.

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