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Question

The organizers of an essay competition decide that a winner in the competition gets a prize of rupees 100 and a participant who does not win gets a prize of rupees 25. The total prize money distributed is rupees 3000. Find the number of winners, if the total number of participants is 63 ?


Solution

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.

Thus, number of winners = 19 Answer

 

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