A shopkeeper sells a file and a notebook... A shopkeeper sells a file and a notebook for Rs. 27 to the first customer, a notebook and a pen for Rs. 31 to a second customer, and a pen and a file for Rs. 29 to a third customer. The prices of the items are rounded in rupees. Which of the following inference is correct? 1. The pen is the costliest of the three. 2. The file is the costliest of the three. 3. The notebook is the costliest of the three. 4. The shopkeeper sold the items to different customers at different rates. My problem : question is correct and I think that if I fix any price for some item then that will not satisfy the equations so I think 4th option is correct. I don't know which tag will be appropriate.

If the question is saying that each item costs a whole number of rupees (is this what "rounded in rupees" means?) then you are right, it is not possible for the shopkeeper to have charged the same prices to each customer (so the fourth option is correct).

This is because in total he has sold two of each item, but he has charged a total of Rs $87$. If he had charged $a$ for each file, $b$ for each notebook and $c$ for each pen then we would have $87=2(a+b+c)$, but $87$ is odd so this is impossible.