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  • 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.

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.

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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 = \frac{1425}{75} = 19

                 x = 19

Therefore no. of winners = 19

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Divya Prakash Singh

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