Question

In an examination , the average marks obtained by students who passed was $x$ $\%$, while the average of those who failed was $y$ $\%$. The average marks of student taking the exam was $z$ $\%$. Find in terms of $x,y$ and $z$ the percentage of students taking the exam who failed ?

• A. $\frac{(z-x)}{(y-x)}$
• B. $\frac{(x-z)}{(y-z)}$
• C. $\frac{(y-x)}{(z-y)}$
• D. $\frac{(y-z)}{(x-z)}$
• E. None of these

Answer 1

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

Let pass $=b$, fall $=c$ and total $=a$

Thus, $b\times x+c\times y=a\times z$ ....(1)

$\Rightarrow a=b+c$

$\Rightarrow ax=bx+cx$ ....(2)

From (1) and (2), we have

$c(y-x)=a(z-x)$

$\Rightarrow \frac{c}{a}=\frac{z-x}{y-x}$

Hence, option A is correct.