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, Prof. Usman, Prof. Rathor and Prof. Purohit are facing South.
Hence, option C is the correct answer.