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.
(In reply to Answer
by K Sengupta)
Before Mike bought the bike for the first time, let the amount in his possession br x dollars.
Now, the total amount spent by Mike = 20+40+60 = 120 dollars, and the total amount received by Mike = 30+50 = 80 dollars.
Thus, the total amount with Mike at the end of the series of transactions = (x+80-120) = x-40 dollars.
Accordingly, at the end of the series of transactions, Mike had 40 dollars less than what he had at the start.
We also note that at the conclusion of the said transactions, Mike had gained the possession of the bike, whose price is pricisely 40 dollars.
Consequently, Mike neither gained nor lost in the transaction.