The average age of 30 women decreases by 3 months if a new person Priyanka is included in place of a 25 yr old woman. Calculate the age of Priyanka.

Options

A. 17.5 yr
B. 20 yr
C. 30 yr
D. 22 yr

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript.

### Step-by-Step Solution:

1. **Understanding the Problem**:
We know that the average age of 30 women decreases by 3 months when a new person, Priyanka, replaces a 25-year-old woman. We need to find Priyanka's age.

2. **Convert Months to Years**:
Since the average age is given in years, we convert 3 months into years:
\[ 3 \text{ months} = \frac{3}{12} \text{ years} = \frac{1}{4} \text{ years} \]

3. **Let the Average Age be A**:
Let the average age of the 30 women be \( A \). Therefore, the total age of the 30 women can be expressed as:
\[ \text{Total Age} = 30A \]

4. **New Average After Replacement**:
When the 25-year-old woman is replaced by Priyanka, the new average age becomes:
\[ A - \frac{1}{4} \]
The total age with Priyanka included can be expressed as:
\[ \text{Total Age with Priyanka} = 30A - 25 + P \]
where \( P \) is Priyanka's age.

5. **Setting Up the Equation**:
Since the number of women remains the same (30), we can set up the equation based on the new average:
\[ 30A - 25 + P = 30 \left( A - \frac{1}{4} \right) \]

6. **Expanding the Right Side**:
Expanding the right side gives:
\[ 30A - 25 + P = 30A - \frac{30}{4} \]
Simplifying \( \frac{30}{4} \) gives:
\[ \frac{30}{4} = 7.5 \]
Thus, the equation becomes:
\[ 30A - 25 + P = 30A - 7.5 \]

7. **Cancelling Terms**:
We can cancel \( 30A \) from both sides:
\[ -25 + P = -7.5 \]

8. **Solving for Priyanka's Age**:
Rearranging the equation to find \( P \):
\[ P = -7.5 + 25 \]
\[ P = 17.5 \]

9. **Conclusion**:
Therefore, Priyanka's age is \( 17.5 \) years.

### Final Answer:
Priyanka's age is **17.5 years**.