Question

In a Mathematics test, the average marks of boys is $x\%$ and the average marks of girls is $y\%$ with $x\ne y$. If te average marks of all students is $z\%$ the ratio of the number of girls to the total number of students is?

• A. $\frac{z-x}{y-x}$
• B. $\frac{z-y}{y-x}$
• C. $\frac{z+y}{y-x}$
• D. $\frac{z+x}{y-x}$

Answer 1

The correct option is A $\frac{z-x}{y-x}$

Let total number of boys and girls are $a$ and $b$ respectively, then

$(a+b)z=ax+by$ (as given in the question)

$z=\frac{a}{a+b}x+\frac{b}{a+b}y$

Suppose ratio of the number of girls to the total number of students is $r$, then ratio of the number of boys to the total number of students will be $1-r$.

$\therefore z=(1-r)x+ry\Rightarrow r=\frac{z-x}{y-x}$