Question

the organizers of a maths quiz decided that each winner in the competition should get a prize of Rs.500 and each participant who does not win should get a participation prize of Rs.100 if the total money distributed is Rs.11,100 and the total number of participants is 63, then find the number of winners in the competition.

Answer 1

Let the number of winners be x.
Then, number of losers=(63-x)
Total prize=Rs.11100
Total prize given to winners=500*x=500x
Total prize given to losers=100(63-x)=6300-100x
Given 500x+6300-100x=11100
or,400x=11100-6300=4800
or,x=4800/400=12
Therefore, number of winners=12 .

Answer 2

Winner gets Rs 500.        Others get Rs 100.
Let there be W winners.      Then 63-W are not winners (other participants)

So  total money distributed = 500 W + (63-W) 100 = 11,100
          5 W + 63 - W = 111
               4 W = 48
                  W = 12
SO there are 12 winners in the competition.