In the half yearly examination of class IX of a school, the mean marks scored by the boys is 52 and the mean marks scored by the girls is 48. If on the whole, the mean marks of the calss is 50.5, find the ratio of the number of boys to the number of girls in the class.

Answer

To solve the problem, we will use the formula for the mean and the information provided about the mean marks of boys, girls, and the overall class.

### Step-by-Step Solution:

1. **Let the number of boys and girls be defined:**
- Let the number of boys be \( m \).
- Let the number of girls be \( n \).

2. **Write down the mean marks for boys and girls:**
- The mean marks scored by boys is 52.
- The mean marks scored by girls is 48.

3. **Calculate the total marks for boys and girls:**
- Total marks scored by boys = \( 52m \) (since mean = total marks/number of students).
- Total marks scored by girls = \( 48n \).

4. **Write down the overall mean marks for the class:**
- The overall mean marks of the class is given as 50.5.
- Therefore, the total marks for the whole class can be expressed as:
\[ \text{Total Marks} = \text{Total Marks of Boys} + \text{Total Marks of Girls} = 52m + 48n \]
- The total number of students in the class is \( m + n \).

5. **Set up the equation using the overall mean:**
- According to the formula for mean:
\[ \text{Mean} = \frac{\text{Total Marks}}{\text{Total Number of Students}} \]
- Substituting the values we have:
\[ 50.5 = \frac{52m + 48n}{m + n} \]

6. **Cross-multiply to eliminate the fraction:**
\[ 50.5(m + n) = 52m + 48n \]

7. **Expand and rearrange the equation:**
\[ 50.5m + 50.5n = 52m + 48n \]
\[ 50.5m + 50.5n - 52m - 48n = 0 \]
\[ -1.5m + 2.5n = 0 \]

8. **Rearranging gives us:**
\[ 2.5n = 1.5m \]
\[ \frac{m}{n} = \frac{2.5}{1.5} = \frac{5}{3} \]

9. **Finding the ratio of boys to girls:**
- Therefore, the ratio of the number of boys to the number of girls is:
\[ \text{Ratio of boys to girls} = \frac{m}{n} = \frac{5}{3} \]

### Final Answer:
The ratio of the number of boys to the number of girls in the class is \( 5:3 \).