The organisers 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.

Let the numbers of winner be x.

Then, the number of participants who didn't win = 63 - x

Total money given to the winner = x × 100 = 100x

Total money given to participant who didn't win = 25×(63-x)

According to the question,

100x + 25×(63-x) = 3,000

⇒ 100x + 1575 - 25x = 3,000

⇒ 75x = 3,000 - 1575

⇒ 75x = 1425

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

⇒ x = 19

∴, the numbers of winners are 19.