The average weight of a class of 50 students Is 48.6 kg. If the average weight of the 20 boys is I 54 kg, then find the average weight (in kg.) of the girls in the class.

Options

A. 40
B. 46
C. 45
D. 42

Answer

To find the average weight of the girls in the class, we can follow these steps:

### Step 1: Calculate the total weight of the class
The average weight of the class of 50 students is given as 48.6 kg. To find the total weight of the class, we can use the formula:

\[ \text{Total Weight} = \text{Average Weight} \times \text{Number of Students} \]

Substituting the values:

\[ \text{Total Weight} = 48.6 \, \text{kg} \times 50 = 2430 \, \text{kg} \]

### Step 2: Calculate the total weight of the boys
The average weight of the 20 boys is given as 54 kg. Using the same formula:

\[ \text{Total Weight of Boys} = \text{Average Weight of Boys} \times \text{Number of Boys} \]

Substituting the values:

\[ \text{Total Weight of Boys} = 54 \, \text{kg} \times 20 = 1080 \, \text{kg} \]

### Step 3: Calculate the total weight of the girls
Now, we can find the total weight of the girls by subtracting the total weight of the boys from the total weight of the class:

\[ \text{Total Weight of Girls} = \text{Total Weight of Class} - \text{Total Weight of Boys} \]

Substituting the values:

\[ \text{Total Weight of Girls} = 2430 \, \text{kg} - 1080 \, \text{kg} = 1350 \, \text{kg} \]

### Step 4: Calculate the number of girls in the class
The total number of students in the class is 50, and there are 20 boys. Therefore, the number of girls is:

\[ \text{Number of Girls} = \text{Total Students} - \text{Number of Boys} = 50 - 20 = 30 \]

### Step 5: Calculate the average weight of the girls
Finally, we can find the average weight of the girls using the total weight of the girls and the number of girls:

\[ \text{Average Weight of Girls} = \frac{\text{Total Weight of Girls}}{\text{Number of Girls}} \]

Substituting the values:

\[ \text{Average Weight of Girls} = \frac{1350 \, \text{kg}}{30} = 45 \, \text{kg} \]

### Final Answer
The average weight of the girls in the class is **45 kg**.

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