2 roommates - Arjun and Bishan - rent a house with two rooms for a month. One room is 700 sqft in size and the other 300 sqft.
Let's say that the rent is Rs. 100 for 1 month for both rooms combined. The roomates decide that Arjun would stay in the larger room for half the month after which they would swap and Bishan would stay in the 700 sqft room. After half the month, Arjun decides that he does not want to move to the smaller room and asks Bishan if they can come to a compromise.
Bishan proposes the following: He says that he will continue to let Arjun stay in the 700 sqft room for the remaining half of the month. In exchange for allowing this, Bishan wants Arjun to pay Rs. 70 of the total Rs.100 because Arjun's room is 70% of the apartment (when they are due the bill at the end of the month).
Arjun agrees that rent must be payed proportional to the area of the room. However, he claims that as per the original agreement, they were both entitled to stay in each room for half a month each. So, Arjun claims, Bishan only deserved the larger room for half the month, and so, Arjun only needs to compensate Bishan for the 2nd half of the month. Thus, says Arjun, that he will pay 70% of the rent of 2nd half of the month - i.e., 70% of Rs 50 (2nd half's rent) which is Rs.35.
As per the method proposed by Bishan, the total rent payable by Arjun is Rs.70 (ie., 70% of Rs.100).
As per the method proposed by Arjun, the total rent payable by himself is Rs.60 (ie., Rs.25 for the 1st half of the month and Rs. 35 for the next half)
What should they do?