math

There are 10 children (aged 1 to 10 years) who have equal amounts of money. In the first transaction the eldest child gives one rupee to every child younger to him. In the second transaction, the second eldest child gives one rupee to every child younger to him. This type of distribution continues for the next two transactions. In the end the total sum with the children who have given money to other children is half the sum of money with the children who did not give any money.what was the original amount with EACH child?

Can we able to form an equation to find the amount each child had? Please help

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  1. If I understand correctly there would have been 4 transactions.

    let the amount that each child has originally be x

    first transaction:
    1st child -- x-9
    each of remaining 9 children has x+1

    2nd transaction:
    1st child -- x-9
    2nd child -- x+1 - 8 = x-7
    each of remaining 8 children has x+2

    3rd transaction:
    1st chld -- x-9
    2nd child -- x-7
    3rd child -- x+2 - 7 = x-5
    each of the remaining 7 children has x+3

    4th transaction:
    1st child -- x-9
    2nd child -- x-7
    3rd child -- x-5
    4th child -- x+3 - 6 = x-3
    each of the remaining children --- x+4

    "In the end the total sum with the children who have given money to other children is half the sum of money with the children who did not give any money"
    ---- x-9 + x-7 + x-5 + x-3 = (1/2)(6)(x+4)
    4x - 24 = 3x+12
    x = 36

    each had 36

    check:

    distribution of money after each round

    0: 36 36 36 36 ... 36
    1: 27 37 37 37 ... 37
    2: 27 29 38 38 ... 38
    3: 27 29 31 39 39 ... 39
    4: 27 29 31 33 40 40 .. 40

    sum of those that gave money = 27+29+31+33 = 120
    sum of those that received money = 6x40 = 240
    so 120 = 1/2 of 240
    All checks out

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  2. Last step didn't understand

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