Question

The organisers of an essay competition decide that a winner in the competition gets prize of Rs 100 and the 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

Answer 1

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 = 3000
By 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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