In a city with a population of more than thirty thousand persons and fewer than fifty thousand persons, according to the most recent official United States Census, in addition to the commissioners of public works to be elected as provided in § 5-31-210, the mayor and the chairman of the committee on water supply, if there be such a committee, shall be ex officio commissioners of public works, if requested by a resolution approved by seventy-five percent or more of the commissioners of public works and authorized by an ordinance approved by seventy-five percent or more of the members of the municipal council of the municipality. The board of commissioners of public works in any such city shall fill any vacancy occurring in the commission by appointment for the unexpired term, appointment to be made by the remaining commissioners, except in the case of an ex officio member of the commission.