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
🎥 Video solution / Text Solution of this question is given below:
Given averages: Boys = 52, Girls = 42, Combined = 50.
Let the proportion of boys be \(p\) (so girls = \(1-p\)).
Weighted mean gives:
$$52p + 42(1-p) = 50$$
$$52p + 42 - 42p = 50 \Rightarrow 10p = 8 \Rightarrow p = 0.8.$$
Percentage of boys \(= 0.8 \times 100\% = \boxed{80\%}\).