Question

16. 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 1

Answer:

Question :-

The organisers 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 ₹ 3000. Find the number of winners, if the total number of participants is 63.

Answ€r :-

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

Let the number of winners be $\bold{x}$

To find :-

Number of winners

_________________________

Since, Number of winners + Number of losers = Total number of participants

Or, x + Number of participants who did not win = 63

Therefore, the number of participants who did not win will be 63 − x

Now, Total Prize money distributed to winners= Number of winners X prize money distributed to each winner = Amount given to the winners = ₹ (100 × x)

= ₹ 100x

Total prize money distributed to losers = Number of participants who did not win X prize money distributed to each participants who did not win = Amount given to the participants who did not win = ₹ 25(63 − x)

= ₹ (1575 − 25x)

♣ $\rm \red{\bold{According \: to \: the \: condition,}\underline{given}}$

Now, Total Prize money of winners + Total Prize money of losers = Total prize money

♣ $\rm \red{\underline{substituting \: the \: value \: we \: get :-}}$

100x + (1575 − 25x) = 3000

⇒75x + 1575 = 3000

On transposing 1575 to RHS, we get

⇒75x = 3000 − 1575

⇒75x = 1425

On dividing both sides by 75, we get

⇒x = $\frac{1425}{75}$ = $\mathfrak \green{\underline{19}}$

• Therefore, the number of winners = 19

_____________________

Answer 2

let x be the number of winners.

so, the no. participants who doesn't win (63-x)

price money to x winners = rs100x

and price money given to (63-x) participant = rs25(63-x)

given ,

total price money distributed = 3000rs

Therefore 100x + 25(63-x) = 3000

4x +( 63-x) = 120 [on dividing both sides by 25]

3x = 120-63

( transposing 63 to rhs)

3x - 57 = x= 57/3 = 19

no. of winners is 19

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