We are given that,
Prof. Rathor gets a south facing flat which is next to Prof. Usman’s flat
Thus, Rathor's and Usman's flat are facing South.
Prof. Sawant and Prof. Usman get their flats which are diagonally opposite to each other
Thus, Sawant's flat is North facing and his flat and Usman's flat are at the opposite ends.
Prof. Rathor gets a south facing flat which is next to Prof. Usman’s flat
Thus, Rathod's flat is facing South.
Thus, Purohit's flat is facing North and so is Tripathy's
The condition is as shown below:-
Thus, If the flats of Prof. Tripathy and Prof. Purohit are interchanged, Prof. Rathor flat will be next to that of Prof.Usman.
Hence, option A is the correct answer.