Question

In a class of 60 students, 60% are boys. The average of marks of the boys is 68 and that of the girls is 72. What are the average marks of the whole class?

• A. 68.8
• B. 69.3
• C. 69.6
• D. 70.1

Hint:

To find the average marks of the whole class, use the weighted average formula: \[ \text{Average} = \frac{\text{Total marks of boys} + \text{Total marks of girls}}{\text{Total number of students}} \]

Answer 1

The Correct Option is C

We are given: - Total students = 60 - Percentage of boys = 60% - Average marks of boys = 68 - Average marks of girls = 72 ### Step 1: Number of boys and girls Number of boys = 60% of 60 = \( 0.60 \times 60 = 36 \) Number of girls = 40% of 60 = \( 0.40 \times 60 = 24 \) ### Step 2: Total marks of boys and girls Total marks of boys = Average marks of boys \( \times \) Number of boys = \( 68 \times 36 = 2448 \) Total marks of girls = Average marks of girls \( \times \) Number of girls = \( 72 \times 24 = 1728 \) ### Step 3: Total marks of the whole class Total marks of the whole class = Total marks of boys + Total marks of girls \[ 2448 + 1728 = 4176 \] ### Step 4: Average marks of the whole class Average marks of the whole class = Total marks of the whole class \( \div \) Total number of students \[ \frac{4176}{60} = 69.6 \] Thus, the average marks of the whole class is \( \boxed{69.6} \).