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?

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  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

    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

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  2. Thankyou!

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