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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Answers
Answer:
19 winners.
Step By Step Explanation:
Given, Total number participants = 63
Total prize money distributed = 3000₹
Winner gets a prize of 100₹
Who does not win gets a prize of 25₹
Number of winners = ?
Let the number of winners = m
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 = 3000By transposing 1575 to RHS, we get100 m – 25 m = 3000 – 1575⇒75 m = 1425
After dividing both sides by 75, we get the answer 19
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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
⇒ x = 1425/75
⇒ x = 19
Therefore, the numbers of winners are 19.