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Question

The organisers Orphan essay competition decide the winner in the competition gets the price of rupees hundred and the participant who does not win gets a price of rupees 25 the total prize money distributed is rupees 3000 find the number of winner if the total number of participants 63

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Solution

Given, Total number participants = 63

Total prize money distributed = Rs 3000

Winner 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 get

Number 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 get 100 m + 1575 – 25 m = 3000

⇒ 100 m – 25 m + 1575 = 3000

By transposing 1575 to RHS, we get

100 m – 25 m = 3000 – 1575

⇒75 m = 1425

After dividing both sides by 75, we get the answer. m = 1425/75 = 19

Thus, number of winners = 19

Total prize money distributed = Rs 3000

Winner 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 get

Number 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 get 100 m + 1575 – 25 m = 3000

⇒ 100 m – 25 m + 1575 = 3000

By transposing 1575 to RHS, we get

100 m – 25 m = 3000 – 1575

⇒75 m = 1425

After dividing both sides by 75, we get the answer. m = 1425/75 = 19

Thus, number of winners = 19

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