The council of every city subject to the provisions of this act and the acts to which this act is amendatory, upon petition to them of 50 or more registered electors of the city praying that an election of the qualified voters of the city be called to determine whether the board of public works in the city shall be abolished, shall, by resolution, submit the question of abolishing the board of public works to the qualified electors of the city at the city election held in the month of April next following. The board of public works in the city shall not be abolished unless a majority of the electors voting on the proposition shall by ballot so determine.