The organisers of an essay competition …

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

Let the number of winners =x
 

∴  Number of participants who are not winners = (63 - x)
 

∴  Prize money given to:                Winners = xRs 100 = Rs 100 x

                 Non-winner participants = Rs 25  (63-x)

                                                = Rs 25 63 - Rs 25x

                                                 = Rs 1575 - Rs 25x

According to the condition, we have

                                100x + 1575 - 25x = 3000

or                                          75x = 3000 - 1575       [Transposing 1575 to RHS]

or                                           75x = 1425

or                                              x = 1425 75 = 19

    Thus, the number of winners = 19