The organizers of an essay competition decide that a winner in the competition gets a prize of Rs 100 and a participant
The organizers of an essay competition decide 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 Rs 3000. Find the number of winners, if the total number of participants is 63.
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Let the number of winners be x. Therefore, the number of participants who did not win will be 63 − x.
Amount given to the winners = Rs (100 × x) = Rs 100x
Amount given to the participants who did not win = Rs [25(63 − x)] = Rs (1575 − 25x)
According to the given question,
100x + 1575 − 25x = 3000
On transposing 1575 to R.H.S, we obtain
75x = 3000 − 1575
75x = 1425
On dividing both sides by 75, we obtain
75x/75 = 1425/75
x = 19
Hence, number of winners = 19
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