The organisers 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
3,000. Find the number of winners, if the total number of participants is 63.
Answers
Answer:
Ncert solutions
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Mathematics
Science
Chapters in NCERT Solutions - Mathematics , Class 8
Exercises in Linear Equations in One Variable
Question 31
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 ₹3,000. Find the number of winners, if the total number of participants is 63.
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Let the numbers of winner be x.
Then, the number of participants who didn't win = 63 - x
Total money given to the winner = x × 100 = 100x
Total money given to participant who didn't win = 25×(63-x)
According to the question,
100x + 25×(63-x) = 3,000
⇒ 100x + 1575 - 25x = 3,000
⇒ 75x = 3,000 - 1575
⇒ 75x = 1425
\Rightarrow x=\frac{1425}{75}⇒x=
75
1425
⇒ x = 19
∴, the numbers of winners are 19.
Answer:
Let x be the number of winners.
Then the number of participants who do not win is given as (63 – x)
The prize money given to x winners = Rs ( 100x)
The prize money given to (63 – x) participants is = Rs 25(63 – x)
According to the given data, the total prize money distributed = Rs 3000
Therefore, 100x + 25(63 – x) = 3000
4x + (63 – x) = 120
3x + 63 = 120
x = 19
Therfore , the number of winners is 19