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Simple classic puzzle on profit


Bill sold his motor scooter to Tom for $100.  After driving it around for a few days Tom discovered it was in such a broken-down condition that he sold it back to Bill for $80.  The next day Bill sold it to Herman for $90.  What is Bill's total profit?

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4 answers to this question

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I've not heard this one...but I'll take a stab:


Let X be the amount Bill originally bought the scooter for.

Bill's total profit (or loss) = $110 - X

Example: If he originally bought it for $100, then:

  1. Bill buys for $100 (total profit = -$100)
  2. Bill sells to Tom for $100 (total profit = $0)
  3. Tom sells to Bill for $80 (total profit = -$80)
  4. Bill sells to Hermon for $90 (total profit = $10)

So unless we know what he originally bought the scooter for, we can't really calculate his total profit.


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Pickett makes a good point about not knowing the original price that Bill paid, but based on the data as presented



Bill acquired this for some value X in the past. 

Bill  sold to [$100] and bought from [$80] Tom for a net profit of $20 

Bill bought from Tom [$80] sold to Herman [$90] for a net profit of $10

For these 3 transactions the net profit is $30

Since we don't know X Bill's profit will be affected by the cost of Acquisition

If it cost Bill

  • $100 [X = $100] then his total profit would be $30
  • $130 [X = $130] then his total profit would = $30 - $30 = 0
  • $50 [X =$50] then his total profit would = $30 + $50 = $80

Therefore Bill's total profit = X - $100 + $30



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