Question

The organizer of an essay competition decides that the winner in the competition gets a prize of Rs100 and a participant who does not win gets a prize of Rs25. The total prize money distributed is Rs3000. Find the number of winners, if the total number of participants is 63.

Answer 1

Hint- Since the total prize money that is distributed is given to us thus if we consider the total winners as a variable and use conditions of question given to find this variable then we will get the answer.
Now let the total number of winners = p
The organizer of the essay competition is giving the winner a prize money of 100 rupees.
Hence Total amount of prize money will be the total number of winners multiplied with prize money given to a winner.
$\therefore $Amount of prize money = $100 \times p = 100p$……………………. (1)
Now the total number of participants given is 63.
In these 63 participants p are the winners hence the number of people who are not winners will be $63 - p$
It is given in question that the organizer is giving Rs25 to people who don't win.
Hence amount of money paid to such people who are on non- winning side will be $25 \times \left( {63 - p} \right)$…………….. (2)
Now the total amount of money that needs to be distributed is given as Rs3000 in the question……………… (3)
However
Total money to be distributed = Amount of prize money to winners + Amount of prize money to non-winners
$ \Rightarrow $Equation (3) = equation (1) + equation (2)
On substituting the values from the above equations we get
$3000 = 100p + 25 \times \left( {63 - p} \right)$
$
  3000 = 100p + 1575 - 25p \\
   \Rightarrow 3000 = 75p + 1575 \\
   \Rightarrow 75p = 1425 \\
    \\
 $
Thus on solving for p we get $p = 19$
Hence the total number of winners is equal to 19.

Note- Whenever we face such type of problems the important step is to make sure that the total money that need to be distributed by the organizer is divided amongst the total winners as per their winning price decided by the organizer and the non-winners or the participants as per their winning price decided by the organizer .This concept will help you to reach to the right answer required in the question.