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# Simple classic puzzle on profit

## Question

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?

## 4 answers to this question

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

Spoiler

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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Spoiler

18 %

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Spoiler

No, I lie! Surely not 18%, but 10, 20 or 30 %, depending on the way you interpret the question.

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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

Spoiler

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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