The average age of 6 persons in a committee is increased by 2 years, when two men aged 55 years and 60 years are substituted by two women. The average age of these two women is

Options

A. 127 years
B. 103 years
C. 63.5 years
D. 51.5 years

Answer

To solve the problem, we will follow these steps:

### Step 1: Calculate the total age of the committee before substitution.
Let the average age of the 6 persons initially be \( A \). Therefore, the total age of the 6 persons is:
\[ \text{Total age} = 6A \]

### Step 2: Determine the new average age after substitution.
According to the problem, the average age increases by 2 years when the two men are replaced. Thus, the new average age becomes:
\[ A + 2 \]
The total age of the committee after substitution is:
\[ \text{New total age} = 6(A + 2) = 6A + 12 \]

### Step 3: Calculate the total age of the two men being replaced.
The ages of the two men being replaced are 55 years and 60 years. Therefore, their total age is:
\[ \text{Total age of two men} = 55 + 60 = 115 \]

### Step 4: Set up the equation for the total age after substitution.
When the two men are replaced by two women, the total age of the committee changes as follows:
\[ \text{New total age} = \text{Old total age} - \text{Total age of two men} + \text{Total age of two women} \]
Substituting the values we have:
\[ 6A + 12 = 6A - 115 + \text{Total age of two women} \]

### Step 5: Solve for the total age of the two women.
Rearranging the equation gives:
\[ 6A + 12 + 115 = 6A + \text{Total age of two women} \]
\[ 127 = \text{Total age of two women} \]

### Step 6: Calculate the average age of the two women.
The average age of the two women is given by:
\[ \text{Average age of two women} = \frac{\text{Total age of two women}}{2} = \frac{127}{2} = 63.5 \]

### Final Answer:
The average age of the two women is **63.5 years**.

---