Question

The organisers of an essay competition decide that a winner in the competition gets a prize of Rs $100$ and a participant who does not win gets a prize of Rs $25$. The total prize money distributed is Rs $3,000$. Find the number of winners, if the total number of participants is $63$.

Answer 1

Total number of participants = 63

Let the participants not winning are $\Rightarrow x$

and winner be $=63-x$

$\therefore$ The linear equation looks like :-

$(63-x)100+\left(x\right)25=3000$

$6300-x\times 100+x\times 25=3000$

$6300-3000=75\times x$

$3300=75\times x$

or $x=\frac{3300}{75}$

$x=44$

$\therefore$ No. of winners are $\Rightarrow 63-x\Rightarrow 63-44$

$\Rightarrow 19$