The mean weight of 60 students in a class is 40 kg. The mean weight of boys is 50 kg while that of girls is 30 kg. Find the number of boys and girls in the class.

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Understand the Given Information
We know:
- Total number of students = 60
- Mean weight of all students = 40 kg
- Mean weight of boys = 50 kg
- Mean weight of girls = 30 kg

### Step 2: Calculate the Total Weight of All Students
Using the formula for mean:
\[ \text{Mean} = \frac{\text{Sum of weights}}{\text{Total number of students}} \]
We can rearrange this to find the total weight:
\[ \text{Sum of weights} = \text{Mean} \times \text{Total number of students} \]
Substituting the known values:
\[ \text{Sum of weights} = 40 \, \text{kg} \times 60 = 2400 \, \text{kg} \]

### Step 3: Let the Number of Boys be \( x \)
Let:
- Number of boys = \( x \)
- Number of girls = \( 60 - x \)

### Step 4: Calculate the Total Weight of Boys
Using the mean weight of boys:
\[ \text{Mean weight of boys} = \frac{\text{Sum of weights of boys}}{\text{Number of boys}} \]
This can be rearranged to find the sum of weights of boys:
\[ \text{Sum of weights of boys} = 50 \, \text{kg} \times x = 50x \]

### Step 5: Calculate the Total Weight of Girls
Using the mean weight of girls:
\[ \text{Mean weight of girls} = \frac{\text{Sum of weights of girls}}{\text{Number of girls}} \]
This can be rearranged to find the sum of weights of girls:
\[ \text{Sum of weights of girls} = 30 \, \text{kg} \times (60 - x) = 30(60 - x) = 1800 - 30x \]

### Step 6: Set Up the Equation for Total Weight
The total weight of all students is the sum of the weights of boys and girls:
\[ \text{Total weight} = \text{Sum of weights of boys} + \text{Sum of weights of girls} \]
Substituting the expressions we found:
\[ 2400 = 50x + (1800 - 30x) \]

### Step 7: Simplify the Equation
Combine like terms:
\[ 2400 = 50x + 1800 - 30x \]
\[ 2400 = 20x + 1800 \]

### Step 8: Solve for \( x \)
Subtract 1800 from both sides:
\[ 2400 - 1800 = 20x \]
\[ 600 = 20x \]
Divide both sides by 20:
\[ x = 30 \]

### Step 9: Find the Number of Girls
Using \( x \) to find the number of girls:
\[ \text{Number of girls} = 60 - x = 60 - 30 = 30 \]

### Final Answer
Thus, the number of boys is 30 and the number of girls is 30.