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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answer is B.

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Detailed Solution

It is given that total the number of participants is 63.
Prize given to the Winner is Rs.100 and prize given to the participants who did not win is Rs.25
Total prize money is Rs.3,000.
Let the number of winners be x. Calculate using the given data.
Total number of participants = Number of winners + Number of participants who did not win .
63=x+ Number of participants who did not win.
Solving above equation,
Number of participants who did not win= 63-x.
Making equation for total amount given to the winning participants.
Total amount given to winners = Number of winners

×

Amount given to 1 winner

= x × 100 = 100 x

Make an equation for the total amount given to non-winning participants,
Total amount given to participants who did not win = Number of participants who did not win

×

Amount given to 1 participant.
Substituting values in above equation,

= (63 − x) × 25 = 63 × 25 − x × 25 = 1575 − 25 x

The number of winners will be,
Total prize money = Total amount given to winners + Total amount given to participants who did not win.
Substituting the values of each in above equation,