The mean weight of 150 students in a certain class in 60kg. The mean weight of boys in the class is 70 kg and that of the girls as 55kg. What is the number of boys in the class.
(a)50
(b)55
(c)60
(d)100

Options

A. 50
B. 55
C. 60
D. 100

Answer

To find the number of boys in the class, we can follow these steps:

### Step 1: Understand the given information
We know:
- Total number of students = 150
- Mean weight of all students = 60 kg
- Mean weight of boys = 70 kg
- Mean weight of girls = 55 kg

### Step 2: Set up the equations
Let:
- The number of boys = \( b \)
- The number of girls = \( g \)

From the information given, we can write:
1. \( b + g = 150 \) (Equation 1)

### Step 3: Calculate the total weight of students
The total weight of all students can be calculated using the mean:
\[ \text{Total weight of all students} = \text{Mean weight} \times \text{Total number of students} = 60 \times 150 = 9000 \text{ kg} \]

### Step 4: Calculate the total weight of boys and girls
The total weight of boys and girls can also be expressed as:
\[ \text{Total weight of boys} = 70b \]
\[ \text{Total weight of girls} = 55g \]

Thus, we can write:
\[ 70b + 55g = 9000 \text{ (Equation 2)} \]

### Step 5: Substitute \( g \) from Equation 1 into Equation 2
From Equation 1, we can express \( g \) in terms of \( b \):
\[ g = 150 - b \]

Substituting this into Equation 2:
\[ 70b + 55(150 - b) = 9000 \]

### Step 6: Simplify the equation
Expanding the equation:
\[ 70b + 8250 - 55b = 9000 \]
Combining like terms:
\[ 15b + 8250 = 9000 \]

### Step 7: Solve for \( b \)
Subtract 8250 from both sides:
\[ 15b = 9000 - 8250 \]
\[ 15b = 750 \]
Now, divide by 15:
\[ b = \frac{750}{15} = 50 \]

### Conclusion
The number of boys in the class is \( 50 \).