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organizers 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.

Given, Total number participants = 63 Total prize money distributed = Rs 3000Winner gets a prize of Rs 100 Who does not win gets a prize of Rs 25 Number of winners = ? Let the number of winners = m Since,Number of winners + Number of losers = Total number of participants Or, m + Number of losers = 63 By transposing ‘m’ to RHS, we getNumber of losers = 63 – m Now,Total Prize money distributed to winners= Number of winners X prize money distributed to each winner = m X 100 = 100m Total prize money distributed to losers = Number of losers X prize money distributed to each loser= (63 – m) X 25 = (63 x 25) – 25 m = 1575 – 25 m Now,Total Prize money of winners + Total Prize money of losers = Total prize money By substituting the total prize money distributed to winners and total prize money distributed to losers, we get100 m + 1575 – 25 m = 3000 ⇒ 100 m – 25 m + 1575 = 3000By transposing 1575 to RHS, we get100 m – 25 m = 3000 – 1575⇒75 m = 1425 After dividing both sides by 75, we get the answer.

Let the no. of winners be x & the no. of runner ups be 63-x ATQ, 100(x) + 25(63-x) = 3000 100x + 1575 - 25x = 3000 75x + 1575 = 3000 75x = 3000 - 1575 75x = 1425 x = 1425/75 x = 19 No. of winners = 19 No. of runner ups = 44.