The average age of 25 boys in a class decreases by 6 months, when a new boy takes the place of a 20 yr old boy. Find out the age of new boy.

Answer

To solve the problem, we need to find the age of the new boy who replaces a 20-year-old boy, which causes the average age of 25 boys to decrease by 6 months.

### Step-by-Step Solution:

1. **Calculate the Total Age of the 25 Boys Before Replacement:**
Let the average age of the 25 boys be \( A \) years. The total age of the 25 boys can be expressed as:
\[ \text{Total Age} = 25A \]

2. **Determine the New Average Age After Replacement:**
When the new boy replaces the 20-year-old boy, the average age decreases by 6 months. Since 6 months is equal to \( \frac{1}{2} \) years, the new average age becomes:
\[ A - \frac{1}{2} \]

3. **Calculate the Total Age of the 25 Boys After Replacement:**
The total age of the 25 boys after the new boy replaces the 20-year-old boy can be expressed as:
\[ \text{Total Age After Replacement} = 25 \left( A - \frac{1}{2} \right) \]

4. **Set Up the Equation:**
The total age after replacement can also be calculated by subtracting the age of the old boy and adding the age of the new boy:
\[ \text{Total Age After Replacement} = 25A - 20 + \text{Age of New Boy} \]
Setting the two expressions for total age equal gives us:
\[ 25 \left( A - \frac{1}{2} \right) = 25A - 20 + \text{Age of New Boy} \]

5. **Simplify the Equation:**
Expanding the left side:
\[ 25A - 12.5 = 25A - 20 + \text{Age of New Boy} \]
Now, we can simplify this equation:
\[ -12.5 = -20 + \text{Age of New Boy} \]

6. **Solve for the Age of the New Boy:**
Rearranging gives:
\[ \text{Age of New Boy} = -12.5 + 20 \]
\[ \text{Age of New Boy} = 7.5 \]

### Conclusion:
The age of the new boy is **7.5 years**.