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.
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Let x be the number of winners.
Then the number of participants who do not win is given as (63 – x)
The prize money given to x winners = Rs ( 100x)
The prize money given to (63 – x) participants is = Rs 25(63 – x)
According to the given data, the total prize money distributed = Rs 3000
Therefore, 100x + 25(63 – x) = 3000
4x + (63 – x) = 120
3x + 63 = 120
x = 19
Therefore, the number of winners is 19.
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