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Question

Question 16
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 3, 000. Find the number of winners, if the total number of participants is 63.

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Solution

Total sum of money = 3000
Let the number of winners of 100 be x.
Total participants =63
therefore no. of participant who does not win = 63-x

According to the question,
100×x+25×(63x)=3000
100x+157525x=3000
75x+1575=3000
75x+15751575=30001575 [Subtracting 1575 from both sides]
75x=1425
75x75=142575 [Dividing both sides by 75]
x=19
Hence the number of winner is 19.

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