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. $(z-x)/(y-x)$
• B. $(x-z)/(y-z)$
• C. $(y-x)/(z-y)$
• D. None of these

Answer 1

The correct option is A $(z-x)/(y-x)$

Let Pass, fail and total $b,c,a$ respectively

$\therefore b\times x+c\times y=a\times z$

and $a=b+c$

$⟹ax=bx+cx$

solving above two equations

we get, $c(y-x)=a(z-x)$

$⟹\frac{c}{a}=\left(\frac{z-x}{y-x}\right)$