In a class of 100 students, there are 70 boys whose average marks in a subject is 75. If the average marks of the complete class is 72, then what is the average of the girls ?

Options

A. 73
B. 65
C. 68
D. 74

Explanation

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

### Step 1: Calculate the total marks of the entire class
Given that the average marks of the entire class is 72 and there are 100 students in total, we can calculate the total marks of the class using the formula:

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

\[ \text{Total Marks of Class} = 72 \times 100 = 7200 \]

### Step 2: Calculate the total marks of the boys
We know that there are 70 boys in the class with an average mark of 75. We can calculate the total marks of the boys using the same formula:

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

\[ \text{Total Marks of Boys} = 75 \times 70 = 5250 \]

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

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

\[ \text{Total Marks of Girls} = 7200 - 5250 = 1950 \]

### Step 4: Calculate the number of girls
Since there are 100 students in total and 70 of them are boys, the number of girls in the class is:

\[ \text{Number of Girls} = 100 - 70 = 30 \]

### Step 5: Calculate the average marks of the girls
Finally, we can find the average marks of the girls using the formula:

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

\[ \text{Average Marks of Girls} = \frac{1950}{30} = 65 \]

### Conclusion
Thus, the average marks of the girls in the class is **65**.

---