# Q.16 The organisers 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.

Let the no. of winners be x.

Since total no. of participants is 63, thus no. of participants who does not win = 63 - x

According to the question, equation becomes:

x(100) + (63-x)(25) = 3000

or                100x + 1575 - 25x = 3000

or                 75x + 1575 = 3000

Transposing 1575 to the RHS :

75x = 3000 - 1575

or              75x = 1425

Dividing both sides by 75, we get

x = 19

Therefore no. of winners = 19

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