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.
Answers
Answer:
∴ The number of winners is 19.
Step-by-step explanation:
Let x be the number of the winners. So, the number of participants who does not win (63−x).
Prize money given to x winners = Rs. (100×x)= Rs. 100x
and prize money given to (63−x) participants = Rs. 25(63−x)
Given, total prize money distributed = Rs. 3000
∴100x+25(63−x)=3000
⇒4x+(63−x)=120 ...[On dividing both sides by 25]
⇒3x+63=120
⇒3x=120−63 ...[Transposing 63 to RHS]
⇒3x−57⇒x=
3
57
=19
∴ The number of winners is 19.
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.