All get Equal Share
An old and crafty mathematician had n children, not all of the same sex, none of whom were of the same age. His will was short and sweet. It said :
"My property should be distributed among my children, starting from the eldest to youngest. The i -th child gets $ 1 0 0 0 × i + 1 0 % of what that remains ."
However, in spite of the apparent inequality in distribution, everyone got an equal share. If all the children gave 0 . 5 % of their inheritance as tax. What was the total amount of tax collected from the n children?
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2 solutions
Let the total be 90,000 and 9 children. Then each childs share is 10,000.
1st child gets : 1000 + 10%(90,000-1000) = 1000 + 8900 = 9900 (not 10,000)
Money left after this = 90000-9900 = 80100 2nd child : 2000 + 10%(80100-2000) = 2000 + 7810 = 9810
It is obvious that everyone does not get the same share.
Let the total amount of money be T and the number of children be n . Then each child's share is T / n .
The first child gets : 1 0 0 0 + ( T − 1 0 0 0 ) / 1 0 = T / 1 0 + 9 0 0
Amount left after 1st person's share = T − T / 1 0 − 9 0 0 = 9 / 1 0 T − 9 0 0
Second child gets : 2 0 0 0 + ( 9 / 1 0 T − 9 0 0 − 2 0 0 0 ) / 1 0 = 9 T / 1 0 0 + 1 7 1 0
The last child (n-th) gets : 1 0 0 0 n = T / n or n = 1 0 0 0 T
All three quantities are equal.
To get T : T / 1 0 + 9 0 0 = 9 T / 1 0 0 + 1 7 1 0 Thus, T = 8 1 0 0 0 and n = 9 .
The tax is 0.5% of all shares. Effectively, 0.5% of the total property = 0 . 5 % × 8 1 0 0 0 = 4 0 5
I guess it should be 450. 9 children and each gets $10,000. First son gets 1000+10% of 90K=10K 2nd son 1000×2+10% of 80K =10K
So a tax of $50 for each hence $450.