# How many acres of land did the farmer originally have?

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As per the will of a late farmer, his property would have to be divided in the following way.
The eldest got half of the land and an added 2 acres. Second son received half of the remaining land plus 2 acres. Third son got half of the remaining +2 acres. But as the fourth son took half of the remaining plus 2 acres of land, there was nothing left for the fifth son.

How many acres of land did the farmer originally have?

posted Sep 11, 2015

60 acres
Total land = x acres
1st son = 1/2 * x + 2 acres......................................................Left = 1/2 * x - 2
2nd son = 1/2 * (1/2 x - 2) + 2 = 1/4 * x + 1 acres................Left = 1/4 * x - 3
3rd son = 1/2 * (1/4 * x - 3) + 2 = 1/8 * x + 0.5 acres...........Left = 1/8 * x -3.5
4th son = 1/2 * (1/8 * x - 3.5) + 2 = 1/16 * x + 0.25 acres...Left = 1/16 * x -3.75 = 0
Thus, x = 3.75 * 16 = 60 acres

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