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.
Answers
Answer:
19
Step-by-step explanation:
Let no. of winners be x
Let no. of other participants be y
1 winner gets 100 1 loser gets 25
=> x winners get (100)x => y losers get (25)y
ATQ
x + y = 63 ---(1)
100x + 25y = 3000 ---(2)
multiply (1) by 100
100x + 100y = 6300
100x + 25y = 3000
(1) - (2)
=> 75y = 3300
=> y = 44
placing value of y in (1)
x + 44 = 63
=> x = 63-44
=> x = 19
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.