The average marks of 50 students in a class is 72. The average marks of boys and girls in that subject are 70 and 75 respectively. The number of boys in the class is:

Options

A. 20
B. 35
C. 25
D. 30

Answer

To solve the problem step by step, we will use the concept of averages and the relationship between the total marks, average marks, and the number of students.

### Step-by-Step Solution:

1. **Understand the Information Given**:
- Total number of students = 50
- Average marks of all students = 72
- Average marks of boys = 70
- Average marks of girls = 75

2. **Calculate Total Marks of All Students**:
- Total marks of all students = Average marks × Total number of students
- Total marks = 72 × 50 = 3600

3. **Let the Number of Boys be \( b \)**:
- Therefore, the number of girls = Total students - Number of boys = \( 50 - b \)

4. **Set Up the Equation for Total Marks**:
- Total marks of boys = Average marks of boys × Number of boys = \( 70b \)
- Total marks of girls = Average marks of girls × Number of girls = \( 75(50 - b) \)
- The total marks of all students can also be expressed as the sum of the total marks of boys and girls:
\[ 70b + 75(50 - b) = 3600 \]

5. **Expand and Simplify the Equation**:
- Expanding the equation:
\[ 70b + 3750 - 75b = 3600 \]
- Combine like terms:
\[ -5b + 3750 = 3600 \]

6. **Solve for \( b \)**:
- Rearranging the equation:
\[ -5b = 3600 - 3750 \]
\[ -5b = -150 \]
\[ b = \frac{-150}{-5} = 30 \]

7. **Conclusion**:
- The number of boys in the class is **30**.