Notwithstanding the provisions of § 40-49-20, in every city with a population of over eighty-six thousand, according to the latest official United States census, there shall be a board of plumbing examiners consisting of five members as follows: Two master plumbers with at least four years’ experience, one journeyman plumber with at least four years’ experience, and two other members. The members of such board shall be appointed by the mayor of the city for terms of four years and until their successors are appointed and qualify; except, that of the members first appointed, one shall be appointed for a term of one year, one for a term of two years, one for a term of three years and two for terms of four years or until their successors are appointed and qualify. In the event of a vacancy on the board, such vacancy shall be filled by appointment of the mayor and such appointee shall hold office for the unexpired term of his predecessor and until his successor is appointed and qualifies. All other provisions of this article shall apply to any such city.