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.

Dear Student

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
⇒x = 1425/75
⇒x=19
Therefore, the numbers of winners are 19.

Thanks