Question

A TOTAL of rs. 80 000 is to be distributed among 200 persons as prizes. A prize is either of rs 500 or rs 100. Find the number of each prize.

Answer 1

lets consider x as no. of people for rs 100 and y as no. of people for rs 500

x+y =200
100x+500y = 80000

solving simultaneously
100x + 100y =20000
100x + 500y = 80000
from the above y =150
and x = 50

Answer 2

let number of 500 rs prize and number of 100 rs prize be distributed between x and y respectively
so
x+y= 200
or, y= 200-x
now
x persons get 500× x = 500x rs
and y persons get 100× y=100y rs
so, 500x+ 100y= 80000
or, 5x+y = 800
or, 5x+ (200-x) = 800
[ as y=200-x]

or, 5x+ 200- x= 800
or, 4x = 600
or, x= 600/4= 150
now y= 200-150= 50

number of 500 rs prize and number of 100 rs prize be distributed between 150 and 50 persons respectively