Question

the organiser of competition decided that a winner in the competition gets a price of Rs25 the total prize distributed is Rs3000.find the number of winner,if the total number of participants is 63​

Answer 1

Given, Total number participants = 63

Total prize money distributed = Rs 3000

Winner gets a prize of Rs 100

Loser 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 get

Number of losers `= 63 – m`

Now, Total Prize money distributed to winners

= Number of winners X prize money distributed to each winner `= m xx 100 = 100m`

Total prize money distributed to losers

= Number of losers X prize money distributed to each loser

`= (63 – m) xx 25 = (63 xx 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 = 3000`

By transposing 1575 to RHS, we get

`100 m – 25 m = 3000 – 1575`

`⇒75 m = 1425`

After dividing both sides by 75, we get

`(75m)/(75)=(1425)/(75)`

Or, `m=19`

Thus, number of winners = 19 Answer