# The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the

21 views

closed
The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is
1. 80%
2. 60%
3. 40%
4. 20%

by (24.2k points)
selected

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%