Question

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

Answer 1

Let the number of winners be $x$

and, the number of runner-ups (does not win) be $(63-x)$.

Each Winner will get $Rs.100$

and, each runner-up will get $Rs.25$

From the given condition, we have

$\therefore 100\times$(no. of winners) $+25\times$(no. of runner-ups) $=3000$

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

$\Rightarrow 100x+1575-25x=3000$

$\Rightarrow 75x+1575=3000$

$\Rightarrow 75x=3000-1575$

$\Rightarrow 75x=1425$

$\Rightarrow x=\frac{1425}{75}$

$\therefore x=19$

Hence,the number of winners is $19$.