Correct Answer - Option 1 : 80%
Concept:
The average marks = \(\rm \text{Sum of marks of all the students}\over \text{Total number of students}\)
Calculation:
Given the avg. marks of boys = 52 and that of girls = 42
Let the no. of boys be x and of girls be y
Sum of marks of boys = 52 x
Sum of marks of girls = 42 y
According to the question, if 50 is the combined average;
⇒ 52x + 42y = 50(x + y)
⇒ 52x + 42y = 50x + 50y
⇒ 2x = 8y
∴ x = 4y
Total number of students in the class = x + y = 4y + y = 5y
% of boys = \(\rm \frac{\text{No of boys}}{\text{Total No. of students}} \times 100\)
= \(\rm \frac{4y}{5y} \times 100\)
= 80%