Q. Mean marks scored by the students of a class is 53. The mean marks of the girls is 55 and the mean marks of the boys is 50. What is the percentage of girls in the class?
A) 60%
B) 40%
C) 50%
D) 45%
Explanation
(a)
Let numbers of boys are $x$ and numbers of girls are$y$.
$\therefore$ $53(x + y) = 55y + 50x$
$\Rightarrow$ $3x = 2y$
$\Rightarrow$ $x = \frac{2y}{3}$
$\therefore$ total number of students $= x + y = \frac{2y}{3} + y = \frac{5}{3}\ y$
Hence, required percentage
$= \frac{y}{\frac{5y}{3}} \times 100\% = \frac{3}{5} \times 100\% = 60\%$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.