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Question
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.
Solution
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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