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: Determine the total marks of the boys
We know that there are 70 boys in the class and their average marks are 75. Therefore, we can calculate the total marks obtained by the boys.

\[ \text{Total marks of boys} = \text{Number of boys} \times \text{Average marks of boys} = 70 \times 75 = 5250 \]

### Step 2: Determine the total marks of the class
The average marks of the entire class of 100 students is given as 72. We can find the total marks obtained by all students in the class.

\[ \text{Total marks of class} = \text{Total number of students} \times \text{Average marks of class} = 100 \times 72 = 7200 \]

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

\[ \text{Total marks of girls} = \text{Total marks of class} - \text{Total marks of boys} = 7200 - 5250 = 1950 \]

### Step 4: Determine the number of girls
Since there are 100 students in total and 70 of them are boys, we can find the number of girls.

\[ \text{Number of girls} = \text{Total number of students} - \text{Number of boys} = 100 - 70 = 30 \]

### Step 5: Calculate the average marks of the girls
Finally, we can find the average marks of the girls by dividing the total marks of the girls by the number of girls.

\[ \text{Average marks of girls} = \frac{\text{Total marks of girls}}{\text{Number of girls}} = \frac{1950}{30} = 65 \]

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

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