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The 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.

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Engineering graduate from NIT Calicut, Rank holder (#47) in State Entrance Examination.

From the given question, we can obtain the following data. prize of winner=100 Rupees prize of a participant who doesn't win=25 Rupees Total prize money=3000 total number of participant=63 Let number of winners=x number of participant who doesn't win=y total number of participant =x+y=63............(1) total...
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From the given question, we can obtain the following data.

prize of winner=100 Rupees

prize of a participant who doesn't win=25 Rupees

Total prize money=3000

total number of participant=63

Let number of winners=x

number of participant who doesn't win=y

total number of participant =x+y=63............(1)

total prize money=x*100+y*25=3000............(2)

from (1)

x+y=63

y=63-x.........(3)

substitute (3) into (2)

x*100+y*25=3000

100x+25(63-x)=3000

100x-25x+25*63=3000

75x=3000-25*63=3000-1575=1425

x=1425/75=19

ie number of winners=19

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Engineering graduate from NIT Calicut, Rank holder (#47) in State Entrance Examination.

From the given question, we can obtain the following data. prize of winner=100 Rupees prize of a participant who doesn't win=25 Rupees Total prize money=3000 total number of participant=63 Let number of winners=x number of participant who doesn't win=y total number of participant =x+y=63............(1) total...
read more

From the given question, we can obtain the following data.

prize of winner=100 Rupees

prize of a participant who doesn't win=25 Rupees

Total prize money=3000

total number of participant=63

Let number of winners=x

number of participant who doesn't win=y

total number of participant =x+y=63............(1)

total prize money=x*100+y*25=3000............(2)

from (1)

x+y=63

y=63-x.........(3)

substitute (3) into (2)

x*100+y*25=3000

100x+25(63-x)=3000

100x-25x+25*63=3000

75x=3000-25*63=3000-1575=1425

x=1425/75=19

ie number of winners=19

read less
Comments

Let the number of winners be x. Therefore, the number of participants who did not win will be 63 − x. Amount given to the winners = Rs (100 × x) = Rs 100x Amount given to the participants who did not win = Rs = Rs (1575 − 25x) According to the given question, 100x + 1575 − 25x...
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Let the number of winners be x. Therefore, the number of participants who did not win will be 63 − x.

Amount given to the winners = Rs (100 × x) = Rs 100x

Amount given to the participants who did not win = Rs [25(63 − x)]

= Rs (1575 − 25x)

According to the given question,

100x + 1575 − 25x = 3000

On transposing 1575 to R.H.S, we obtain

75x = 3000 − 1575

75x = 1425

On dividing both sides by 75, we obtain

x = 19

Hence, number of winners = 19

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Comments

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