Question

A certain amount of money is equally divided between some persons .If there were 8 persons more each would have got one rupee less. The number of the person and the amount are?

Answer 1

let the amount of money be m
let the number of people sharing be x
let each persons share be y

then xy = m

second case:
number of people = x+8
share of each person = y-1
then m = (x+8)(y-1)
= xy + 8y - x - 8

thus:
xy+8y-x-8 = xy
x = 8y - 8 , where y > 0 , and y is a natural number

form the following table:
y x m
1 0 0 ---- not likely
2 8 16
3 16 48
4 24 96
5 32 160
... etc

let's test 2 8 16
number of people is 8
amount of money = 16
share for each person = 2
had there been 8 more people or 16 people, each would get 1, which is 1 peso less

testing 5 32 160
number of people = 32
amount of money = 160
share per person = 5
had there been 8 more people or 40 people, each would get 4, which is 1 peso less

There will be an infinite number of solutions as you can see

Answer 2

Thankyou!