Question

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.

Answer 1

Given, Total number participants = 63
Total prize money distributed =
Rs 3000Winner 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 getNumber 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 get100 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.

Thus, number of winners = 19 Answer

Answer 2

Let the no. of winners be x
& the no. of runner ups be 63-x
ATQ,
100(x) + 25(63-x) = 3000
100x + 1575 - 25x = 3000
75x + 1575 = 3000
75x = 3000 - 1575
75x = 1425
x = 1425/75
x = 19
No. of winners = 19
No. of runner ups = 44.

Hope dis Helps u