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Question

The organizers 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 ’3000‘. Find the number of winners, if the total number of participants is ’63'.


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Solution

Let the number of winners be ‘W

The number of participants who didn’t win=63-W

Total money given to the winners=Totalnumberofwinners×Prizegiventoeachwinner

=W×100

=100W

Total money given to participants who didn’t win=Totalnumberofparticipantswhodidn'twin×Prizegiventoeachparticipantwhodidn'twin

=63-W×25

According to the given details, the equation becomes:

100W+63-W×25=3000100W+1575-25W=300075W=3000-157575W=1425W=142575W=19

Therefore, the total number of winners is'19'


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