## Solution

Did the question confuse you? That was the sole purpose - to confuse you. Otherwise, there is hardly any substance in the question.

In the present case, there is a single Rs 500 counterfeit note in circulation. So the loss suffered by the receiver can neither be more nor less than Rs 500. The loss has to be Rs 500.

Let's look at the question differently - we change the chronology of events slightly which, however, does not change the complexion of the question.

First, the customer enters the shop, hands over the Rs 500 note, and buys the pen. Let's assume that the shop-keeper has enough change to satisfy this transaction. Therefore, he hands over the pen and Rs 300 to the customer. The cheat goes away with the pen and the money. The shop-keeper is unaware that the 500-rupee note is fake. But, the note is a fake and the shop-keeper has suffered a loss of Rs 500 (Rs 200 worth pen and Rs 300 in cash).

Now, in anticipation of more customers, the shop-keeper needs change. He, therefore, goes to the neighbouring shop-keeper and requests for change. He hands over the 500-rupee note to the neighbour who gives him five 100-rupee notes (or whatever change) in exchange. But even before the shop-keeper can walk out of the shop, the neighbour has doubts and examines the 500-rupee note, and finds it to be fake.

"Hey, this is fake," the neighbour tells. He returns the fake note to the shop-keeper and takes back his five 100-rupee notes. It was as though this transaction had never occurred! It was as if the shop-keeper had not met his neighbour at all - the fake 500-rupee note continues to remain in his possession, and the neighbour has the five 100-rupee notes as though he had never parted with them! The poor shop-keeper has lost 500 rupees - Rs 200 worth pen and Rs 300 in cash.

• Union Public Service Commission - www.upsc.gov.in
• IIT-Kharagpur - www.iitkgp.ac.in
• Indian Statistical Institute - www.isical.ac.in
• Indian Institute of Technology Madras - www.iitm.ac.in
• Indian Institute of Management, Ahmedabad - www.iimahd.ernet.in
• Indian Institute of Mass Commission - www.iimc.nic.in
• IIT Bombay - www.iitb.ac.in