Question

A candidate scored $25\%$ marks and failed by $30$ marks and another candidate scored $50\%$ marks and got $20$ marks more than the minimum marks required to pass. Find the maximum marks and the passing mark.

Answer 1

Let $x$ and $y$ be the passing marks and maximum marks respectively.

Therefore,

$\frac{25}{100}y=x-30$

$\frac{y}{4}=x-30$

$\Rightarrow x=\frac{y}{4}+30.....\left(1\right)$

Also,

$\frac{50}{100}y=x+20$

$\frac{y}{2}=x+20$

$\Rightarrow \frac{y}{2}=\frac{y}{4}+30+20\left(\text{From}\left(1\right)\right)$

$\Rightarrow \frac{y}{2}-\frac{y}{4}=50$

$\Rightarrow \frac{y}{2}=50$

$\Rightarrow y=50\times 2=100$

Substituting the value of $y$ in equation $\left(1\right)$, we have

$x=\frac{200}{4}+30=50+30=80$

Hence the minimum passing marks are $80$ and the maximum marks are $200$.