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

Given:
Mean of boys = 52
Mean of girls = 42
Combined mean = 50
Let:
Number of boys = x
Number of girls =
Formula used:
Combined mean $$= \frac{52x + 42y}{x + y} = 50 \\$$​​

Solution:
​$$\frac{52x + 42y}{x + y} = 50 \\\Rightarrow 52x + 42y = 50x + 50y \\\Rightarrow 2x = 8y \\\Rightarrow x = 4y \\$$​​
Percentage of boys $$= \frac{x}{x + y} \times 100 = \frac{4y}{4y + y} \times 100 = \frac{4}{5} \times 100 = 80\% \\$$​​
Correct answer is (a)