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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. $3000$ . Find the number of winners, if the total number of participants is $63$ .

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14

16

19

12

answer is C.

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Detailed Solution

It is given 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

and total prize money distributed is Rs.

3000

.
Let x be the number of the winners.
So, the number of participants who does not win

(63 - x)

.
Prize money given to

x

winners = Rs.

(100 \times x) =

Rs.

100 x

Prize money given to

(63 - x)

participants = Rs.

25 (63 - x)

According to the question,
Total prize money distributed = Rs.

3000

100 x + 25 (63 - x) = 3000

\Rightarrow 4 x + (63 - x) = 120

\Rightarrow 3 x + 63 = 120

\Rightarrow 3 x = 120 - 63

\Rightarrow 3 x - 57

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

\Rightarrow x = 19

Therefore, the number of winners is

19

.
Hence, the correct option is 3.

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