All city elections held for the purpose of electing officers shall be non-partisan and shall be so designated on the official ballot. No candidate shall run for a city office under the name or designation of any of the political parties. Nominations of candidates for city offices shall be selected by the qualified electors at a municipal primary election to be held twenty-one days preceding the regular municipal election. Any person desiring to file as a candidate for any office at the primary election shall do so not more than thirty days and not less than fifteen days before the date of the primary election. All declarations of candidacy for the primary election shall be filed with the City Comptroller by the candidate, and such person filing a declaration shall pay to the City Comptroller to be turned in to the City Treasurer a filing fee of $5.00 for Councilman and $25.00 for all other offices. The names of all candidates who file for an office shall be placed on the official ballot for the primary election, which shall be conducted as nearly as may be in conformity with the general primary election laws. The two candidates receiving the highest number of votes for the offices of Mayor, City Treasurer, City Comptroller and Councilman shall be deemed nominated and their names alone shall be placed on the official ballot for the ensuing municipal election: Provided, however, that if one candidate for any one of these offices shall receive a majority of all of the votes cast for all candidates for such office, the person so receiving a majority shall be deemed elected to the office in question, and his name alone for that office shall be placed on the official ballot. In the case of Councilman, where there are two Councilmen to be elected for one ward, the four candidates for Councilmen receiving the highest number of votes at the primary election shall be deemed nominated for those offices and their names only shall be placed upon the official ballot of the ensuing municipal election. Voters for the primary election shall have the same qualifications as voters for the general city election.