(A) The members of a Board holding office at the time this chapter becomes effective shall continue in office until the expiration of their respective terms and until their respective successors are appointed or elected, and qualified, as the case may be.
(B) One of the Board members appointed by the Mayor shall serve for one year beginning on the second Tuesday in May after the city comes within the provisions hereof. The other appointed member shall serve for two years beginning on the same date. The successors to any of the appointed members of such Boards shall serve for two years each or until their successors are appointed and qualified.
(`79 Code, § 32.110)