Hide answer & extension
Represent each player by a compass point. Let B, D, A and S represent Messrs. Banker, Dentist, Apothecary and Scrivener respectively and b, d, a and s represent the four jobs.
Mr. Banker (B) partners the scrivener (s). Let B sit at West. This means s sits at East. As no other player can also be B or s, the table looks like this:
The dentist (d) sits on Mr. Scrivener's (S) right. East cannot be S, so North cannot be d. East cannot be d, so South cannot be S.
By elimination, only North can be S. This means that d must sit to the right of North (at West):
A and a are partners. This is only possible if A is South and a is North:
Therefore, Mr. Banker the dentist sits to the left of the banker.
Extension
If each person is partnered with their job namesake, how many possible combinations of names and jobs are possible?
