Mike wanted to buy a bike, and he found one he liked at $20, so he bought it. The next day, a friend saw it and offered $30 dollars for it so Mike agreed. He later bought it back for $40. Again someone saw it and offered $50 and again Mike sold it. Mike finally rebought the bike for good for $60. Mike then took it to a bike show where a man told him the bike was worth $40.

Deciding to keep it, did Mike gain or lose money on the transactions? Count the bikes worth in the problem.

Of the five transactions, the first two are paired and the second two are paired. Only the last is unpaired.

In each of the two buy/sell pairs Mike has gained $10 without permanently affecting his non-ownership of the bike, and therefore at that point is $20 ahead (after the two buy/sell pairs).

Finally he buys a bicycle worth $40 but pays $60 for it. So counting the worth of the bicycle as $40, he has overpaid on this one transaction $20.

That exactly offsets the $20 he came out ahead for basically nothing, and therefore Mike is exactly even.

Posted by Charlie on 2003-07-26 04:50:59