The mayor and aldermen of any city of not less than twenty and not more than fifty thousand inhabitants may establish in such city a board of police commissioners, which shall consist of five members including the mayor, a majority of whom shall be a quorum for the transaction of business. With the exception of the mayor no member of such board shall be a member of the city council. The mayor shall serve on such board for a term coequal with his term of office, unless his office is sooner vacated by him, and until his successor is elected and qualified. The members of the board shall serve without compensation.