Question

The organissers of an essay competition decide that a winner in the competition gets a prize of Rs.100.00 and a participant who does not win gets a prize of Rs.25. the total prize money distributed is Rs.3000.00 . Find the no of winners in the total no of participants are 63

Answer 1

Let the number of winners be x and the rest be y.
So, x+y= total participants
or, x+y = 63 
or, x = 63 - y (i) 

Now the total prize money was 3000
So we can write it as 100x + 25y = 3000
Now substituting the value of x in (i)  in this equation we get,
= 100(63-y) + 25y = 3000
= 6300 - 100y + 25y = 3000
= -100y + 25y = 3000 - 6300
= -75y = -3300
= y = -3300/-75 
= y = 44

Now x+y=63
So, x + 44 = 63
= x = 63 - 44
= x = 19
Thus the total number of winners are 19.

Hope that helps !!

Answer 2

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The organizers of an essay competition decide that a winner gets a prize of rs.100 and who doesn't wins get a prize of rs.25 the total prize money distributed is 3000 find the no. Of winners if no. Of participants is 63

Let x be the number of winners.

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✿Then the number of participants who do not win is given as (63 – x)

✿The prize money given to x winners = Rs ( 100x)

The prize money given to (63 – x) participants is = Rs 25(63 – x)

✿According to the given data, the total prize money distributed = Rs 3000

Therefore, 100x + 25(63 – x) = 3000

4x + (63 – x) = 120

3x + 63 = 120

x = 19

✿Therefore, the number of winners is 19.

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