# An annoying puzzle

A puzzle is making rounds on the internet for quite sometime now and driving people crazy as there is no consensus about the correct answer. Before moving further, here is the puzzle.

A lady goes to a shop and buys goods worth Rs. 200(shopkeeper selling goods with zero profit). The lady pays with a 1000 rupee note to the shopkeeper. He gets change from the next shop and keeps Rs. 200 for himself & returns Rs. 800 to the lady. After sometime the neighbor returns the Rs. 1000 note saying it is fake and takes his money back. How much loss did the shopkeeper suffer?

Now there are various answers doing rounds, all of which seem to make sense. Some of them can be found on Quora and Stack Exchange. I will try to answer it in a different way and it is up to the reader to decide whether it makes sense. So here goes..

Initially, everyone is at an **even state** i.e no profit and no loss. The shopkeeper may have the product worth Rs. 200, but he must have paid the said Rs. 200 to procure it since the problem says he sells it for ‘zero profit’. So even he is at an **even state**.

The lady comes to buy the product and pays with a fake note. The value of this note is obviously Rs. 0. Due to lack of change, the shopkeeper approaches a neighbor and asks him for a change of Rs. 1000, giving him the fake note. The neighbor gives the shopkeeper real money in exchange for nothing.

Here is the important part. It seems that the shopkeeper got Rs. 1000 for free. That is, he gave a piece of paper with no value and got Rs. 1000 in return. So the shopkeeper is in profit, right? WRONG. He is in a **debt** of Rs. 1000. So, to break even again, the shopkeeper must return Rs. 1000 to the neighbor.

From this loaned amount, the shopkeeper pays Rs. 800 to the lady. So now, the lady has Rs. 1000 worth money/goods without having to pay anything. So she is at a profit of Rs. 1000. By the same logic, the shopkeeper just lost Rs. 1000 worth money/goods. But remember that, Rs. 800 of the Rs. 1000 is the debt taken from the neighbor. So he is actually at a loss of just Rs. 200 and not Rs. 1000.

The shopkeeper is now left with Rs. 200 which he received as **debt** from his neighbor. To return the loan in its full, the shopkeeper has to add Rs. 800 from his own pocket. This, again is loss. So the total loss becomes, ~~Rs. 1000~~ Rs. 200 (money/goods lost to the lady) + Rs. 800 (money lost from his own pocket as part of the loan repayment) = ~~Rs. 1800~~**Rs. 1000.**

This according to me, is the right answer. Please critique.