Question

6. 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.​

Answer 1

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.

Answer 2

Answer:

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.