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THE ORGANISER OF AN ESSAY COMPETITION DECIDE THAT A WINNER IN THE COMPETITION GETS RS 100 AND A PARTICIPANT WHO DOES NOT WIN GETS RS 25. THE TOTAL PRIZE MONEY DISTRIBUTED IS RS 3,000.FIND THE NUMBER OF WINNERS, IF THE TOTAL NUMBER OF PARTICIPANTS IS 63.
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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.
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