Question

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. $45\%$

Answer 1

Answer: (A)

Let $n(G)$ and $n(B)$ be the number of girls and boys in a class respectively and $m(G)$ and $m(B)$ be the total marks scored by girls and boys respectively.
$\therefore \frac{m\left(G\right)+m\left(B\right)}{n\left(G\right)+n\left(B\right)}=53\dots \left(i\right)$
Also, $m\left(G\right)=55n\left(G\right)$, $m\left(B\right)=50n\left(B\right)\dots \left(ii\right)$
From $\left(i\right)$ and $\left(ii\right)$, we get
$\frac{55n\left(G\right)+55n\left(B\right)}{n\left(G\right)+n\left(B\right)}=53$
$\Rightarrow n\left(B\right)=\frac{2}{3}n\left(G\right)$
$\therefore$ Percentage of girls
$=\frac{n\left(G\right)}{n\left(B\right)+n\left(G\right)}\times 100$
$=\frac{n\left(G\right)}{\left(\frac{2}{3}+1\right)n\left(G\right)}\times 100=60\%$