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Question -

The organisers of an essay competition decide that a winner in the competition gets a prize of тВ╣100 and a participant who does not win gets a prize of тВ╣25. The total prize money distributed is тВ╣3,000. Find the number of winners, if the total number of participants is 63.



Answer -

Let the numbers of winner be x.
Then, the number of participants who didnтАЩt win = 63 тАУ x
Total money given to the winner = x ├Ч 100 = 100x
Total money given to participant who didnтАЩt win = 25├Ч(63-x)
According to the question,
100x + 25├Ч(63-x) = 3,000
тЗТ 100x + 1575 тАУ 25x = 3,000
тЗТ 75x = 3,000 тАУ 1575
тЗТ 75x = 1425
тЗТ x = 1425/75
тЗТ x = 19
Therefore, the numbers of winners are 19.

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