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# The organisers 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. 3,000 . Find the number of winners, if the total number of participants is $ 63 . $

Given :

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 3,000.

The total number of participants $= 63$.

To find :

We have to find the number of winners.

Solution :

Let the number of winners be $x$.

This implies, that the number of people who did not win $= 63 - x$

Therefore,

$Rs. x(100)+ Rs. (63-x)(25) = Rs. 3000$

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

$(100-25)x + 1575 = 3000$

$75x = 3000 - 1575$

$75x = 1425$

$x=\frac{1425}{75}$

$x=\frac{57}{3}$

$x=19$

The number of winners is 19.

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