The Average age of 12 men is decreased by one year when two of them having ages 28 years and 32 years are replaced by two women of same age . The age of a women is?

Options

A. a. 26
B. b. 33
C. c. 24
D. d. 61

Answer

To solve the problem, we need to find the age of the women who replace two men aged 28 and 32 years, resulting in a decrease of the average age of 12 men by one year.

### Step-by-Step Solution:

1. **Calculate the total age of 12 men before replacement:**
Let the average age of the 12 men be \( A \). Therefore, the total age of the 12 men is:
\[ \text{Total age of 12 men} = 12A \]

2. **Calculate the total age of the two men being replaced:**
The ages of the two men are 28 and 32 years. Thus, their total age is:
\[ \text{Total age of two men} = 28 + 32 = 60 \text{ years} \]

3. **Determine the new average age after replacement:**
When the two men are replaced by two women of the same age \( x \), the new average age becomes \( A - 1 \). Therefore, the total age of the 12 men after replacement is:
\[ \text{Total age after replacement} = 12(A - 1) = 12A - 12 \]

4. **Set up the equation:**
The total age after replacement can also be expressed as the total age before replacement minus the age of the two men plus the age of the two women:
\[ 12A - 12 = 12A - 60 + 2x \]

5. **Simplify the equation:**
We can simplify the equation:
\[ 12A - 12 = 12A - 60 + 2x \]
By canceling \( 12A \) from both sides, we get:
\[ -12 = -60 + 2x \]

6. **Solve for \( x \):**
Rearranging the equation gives:
\[ 2x = -12 + 60 \]
\[ 2x = 48 \]
\[ x = \frac{48}{2} = 24 \]

7. **Conclusion:**
The age of each woman is \( 24 \) years.

### Final Answer:
The age of the women is **24 years**.