A recount of the votes cast at any City election for any office or upon any proposition may be had in accordance with election statutes. Unless otherwise required by statute (a) the petition for a recount of the votes cast at any City election shall be filed with the Clerk by 4:00 p.m. on the second full day on which the Clerk's office is open for business after the Board of Canvassers has made its official report of the result of the election at which such votes were cast, (b) any counter petition shall be filed by 4:00 p.m. of the next full day thereafter on which the Clerk's office is open for business and (c) no officer shall be qualified to take office until final determination of any recount of the votes cast for such office.