In a school with 600 students, the average age of the boys is 12 years and that of the girls is 11 years. If the average age of the school is 11 years and 9 months, then the number of girls in the school is:

Options

A. 450
B. 150
C. 250
D. 350

Answer

To solve the problem, we need to find the number of girls in the school given the average ages of boys and girls, as well as the total number of students.

### Step-by-Step Solution:

1. **Define Variables:**
Let the number of boys be \( b \) and the number of girls be \( g \). We know that:
\[ b + g = 600 \]

2. **Average Age Calculations:**
The average age of boys is 12 years, so the total age of boys can be expressed as:
\[ \text{Total age of boys} = 12b \]
The average age of girls is 11 years, so the total age of girls can be expressed as:
\[ \text{Total age of girls} = 11g \]

3. **Total Age of All Students:**
The average age of the entire school is given as 11 years and 9 months. We convert this into years:
\[ 11 \text{ years} + 9 \text{ months} = 11 + \frac{9}{12} = 11.75 \text{ years} \]
Therefore, the total age of all students is:
\[ \text{Total age of all students} = 11.75 \times 600 \]

4. **Calculate Total Age of All Students:**
\[ \text{Total age of all students} = 11.75 \times 600 = 7050 \text{ years} \]

5. **Set Up the Equation:**
Now, we can set up the equation for the total age:
\[ 12b + 11g = 7050 \]

6. **Substitute for \( b \):**
From the first equation \( b + g = 600 \), we can express \( b \) in terms of \( g \):
\[ b = 600 - g \]
Substitute this into the total age equation:
\[ 12(600 - g) + 11g = 7050 \]

7. **Simplify the Equation:**
\[ 7200 - 12g + 11g = 7050 \]
\[ 7200 - g = 7050 \]

8. **Solve for \( g \):**
\[ -g = 7050 - 7200 \]
\[ -g = -150 \]
\[ g = 150 \]

9. **Find the Number of Boys:**
Using \( g \) to find \( b \):
\[ b = 600 - g = 600 - 150 = 450 \]

### Final Answer:
The number of girls in the school is \( \boxed{150} \).