The average weight of 120 student in the second year class of college is 56kg. If the average weight of boys and that of girls in the class are 60kg and 50 kg respectively,then the number of boys and girls in the class are respectively,

Options

A. 72,64
B. 38,64
C. 72,48
D. 62,58

Answer

To solve the problem step by step, we will find the number of boys and girls in the class based on the given average weights.

### Step 1: Understand the Information Given
We know:
- Total number of students = 120
- Average weight of all students = 56 kg
- Average weight of boys = 60 kg
- Average weight of girls = 50 kg

### Step 2: Set Up the Variables
Let:
- Number of boys = \( x \)
- Number of girls = \( 120 - x \) (since the total number of students is 120)

### Step 3: Calculate Total Weight of All Students
The total weight of all students can be calculated using the average weight:
\[ \text{Total weight of all students} = \text{Average weight} \times \text{Total number of students} = 56 \, \text{kg} \times 120 = 6720 \, \text{kg} \]

### Step 4: Calculate Total Weight of Boys and Girls
The total weight of boys and girls can be expressed as:
- Total weight of boys = \( 60 \, \text{kg} \times x \)
- Total weight of girls = \( 50 \, \text{kg} \times (120 - x) \)

### Step 5: Set Up the Equation
The total weight of all students is equal to the total weight of boys plus the total weight of girls:
\[ 60x + 50(120 - x) = 6720 \]

### Step 6: Simplify the Equation
Now, simplify the equation:
\[ 60x + 6000 - 50x = 6720 \]
Combine like terms:
\[ 10x + 6000 = 6720 \]

### Step 7: Solve for \( x \)
Subtract 6000 from both sides:
\[ 10x = 6720 - 6000 \]
\[ 10x = 720 \]
Now divide by 10:
\[ x = 72 \]

### Step 8: Find the Number of Girls
Now that we have the number of boys, we can find the number of girls:
\[ \text{Number of girls} = 120 - x = 120 - 72 = 48 \]

### Final Answer
Thus, the number of boys and girls in the class are:
- Number of boys = 72
- Number of girls = 48