The average weight of a class of 15 boys and 10 girls is 38.4 kg . If the average weight of the boys is 40 kg, then what is the average weight of the girls ?

Options

A. 36.5 kg
B. 35kg
C. 36kg
D. 35.6kg

Answer

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

### Step 1: Calculate the total weight of the class
The average weight of the class is given as 38.4 kg, and the total number of students in the class is 15 boys + 10 girls = 25 students.

Using the formula for average:
\[ \text{Average} = \frac{\text{Total Weight}}{\text{Number of Students}} \]
We can rearrange this to find the total weight:
\[ \text{Total Weight} = \text{Average} \times \text{Number of Students} \]
Substituting the values:
\[ \text{Total Weight} = 38.4 \, \text{kg} \times 25 = 960 \, \text{kg} \]

### Step 2: Calculate the total weight of the boys
The average weight of the boys is given as 40 kg, and there are 15 boys in total.

Using the same formula for average:
\[ \text{Total Weight of Boys} = \text{Average Weight of Boys} \times \text{Number of Boys} \]
Substituting the values:
\[ \text{Total Weight of Boys} = 40 \, \text{kg} \times 15 = 600 \, \text{kg} \]

### 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:
\[ \text{Total Weight of Girls} = 960 \, \text{kg} - 600 \, \text{kg} = 360 \, \text{kg} \]

### Step 4: 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:
\[ \text{Average Weight of Girls} = \frac{360 \, \text{kg}}{10} = 36 \, \text{kg} \]

### Conclusion
The average weight of the girls is **36 kg**.

---