The organisers of an essay competition decided 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 rs3000 . find the number of winners , lf the total number of participants is 63 .
Answers
Answer:
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.
Given,
winner gets a prize =100 Rs
Who doesn't get = 25 Rs
Total Prize money = 3000 Rs
Total no of participants = 63
To find,
Number of winners = ??
Solution,
Let,
No of winner = x
no of participants who doesn't win = (63-x)
now,
Prize money got by Winner participants
= 100x Rs
Prize money got by those who doesn't win
= 25(63-x) Rs
Given,
Total prize money = 3000 Rs
prize money(who win) + prize money (who
doesn't win) = 3000 Rs
100x + 25 (63-x) = 3000
100x + 25×63 - 25x = 3000
100x-25x = 3000 - 25×63
75x = 3000 - 1575
75x = 1425
x = 1425/75 = 19
hence,
Number of winners = x = 19
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