Every officer, elective or appointive, before entering upon the duties of his office, shall qualify by taking his oath of office prescribed for public officers by the Constitution of the State, and by filing the oath with the Clerk, together with any bond required by statute, by this Charter or by the Council. In case of failure to comply with the provisions of this section within ten days from the date he is notified in writing of his election or appointment, such officer shall be deemed to have declined the office and such office shall thereupon become vacant unless the Council shall, by resolution, extend the time in which such officer may qualify as above set forth.