The mean weight of 150 students in a certain class is 60kg. The mean weight of boys is 70kg and that of girls is 55kg. What are the number of boys and girls respectively in the class.
(a)75and75
(b)50and100
(c)70and80
(d)100and50

Options

A. 75and75
B. 50and100
C. 70and80
D. 100and50

Answer

To solve the problem, we need to find the number of boys and girls in the class based on the given mean weights and total number of students.

### Step-by-Step Solution:

1. **Understand the Given Information:**
- Total number of students = 150
- Mean weight of all students = 60 kg
- Mean weight of boys = 70 kg
- Mean weight of girls = 55 kg

2. **Set Up the Variables:**
- Let the number of boys be \( b \).
- Let the number of girls be \( g \).
- We know that \( b + g = 150 \) (Equation 1).

3. **Calculate Total Weights:**
- Total weight of all students = Mean weight × Total number of students = \( 60 \times 150 = 9000 \) kg.
- Total weight of boys = Mean weight of boys × Number of boys = \( 70b \) kg.
- Total weight of girls = Mean weight of girls × Number of girls = \( 55g \) kg.

4. **Set Up the Weight Equation:**
- The total weight of boys and girls combined equals the total weight of all students:
\[ 70b + 55g = 9000 \quad \text{(Equation 2)} \]

5. **Substitute \( g \) in Terms of \( b \):**
- From Equation 1, we can express \( g \) as:
\[ g = 150 - b \]
- Substitute this into Equation 2:
\[ 70b + 55(150 - b) = 9000 \]

6. **Simplify the Equation:**
- Distributing the 55:
\[ 70b + 8250 - 55b = 9000 \]
- Combine like terms:
\[ 15b + 8250 = 9000 \]
- Subtract 8250 from both sides:
\[ 15b = 9000 - 8250 \]
\[ 15b = 750 \]
- Divide by 15:
\[ b = 50 \]

7. **Find the Number of Girls:**
- Substitute \( b \) back into Equation 1 to find \( g \):
\[ g = 150 - 50 = 100 \]

8. **Conclusion:**
- The number of boys is 50 and the number of girls is 100.

### Final Answer:
The number of boys and girls respectively in the class is **50 and 100**.