Upon a petition filed with the county auditor at least ninety days in advance of any countywide election signed by not less than ten percent of the qualified electors of the county as determined by the total number of votes cast for the office of governor at the last general election, asking that an election be held on the question of the adoption of one of the forms of county managership and specifying which of the forms is to be submitted, the board of county commissioners shall submit the question at the next regular primary or general election.