The organizers of an essay competition decide that a winner gets a prize of Rs.100 and who does not win gets a prize of Rs.25. The total prize money distributed is 3000. Find the no. of winners if no. of participants is 63.
Answer: The number of winners who received a prize of Rs.100 is 19 where the total number of participants in the essay competition is 63.
Let's look into the stepwise solution
Given: Total number of participants = 63
Total prize money distributed = Rs.3000
Let the number of winners be x.
According to the question,
The amount won by winners will be Rs.100 x
The number of people who do not win = (63 - x)
So, the amount received by the participants who don't win = Rs. 25 × (63 - x)
Amount won by winners + Amount received by the participants who don't win = 3000
⇒ 100 x + 25 × (63 - x) = 3,000
⇒ 100 x + 1,575 - 25 x = 3,000
⇒ 100 x - 25 x = 3,000 - 1,575
⇒ 75 x = 1,425
⇒ x = 1,425 / 75
⇒ x = 19
Thus, the number of winners who won Rs.100 as a prize is 19.