Variations and exceptions from the design and dimensional standards and improvement requirements of this title may be made by the ZBA in cases where, owing to exceptional conditions, there are extreme difficulties or hardships in the way of carrying out the strict letter hereof. Resubdivision of a single lot of a platted block of an old subdivision shall be considered as an exceptional condition meriting departure from the strict letter of this title. No variation or exception shall be made that will be detrimental to the public welfare or that will affect adversely the official plan, and no variation shall be allowed without a public hearing before the ZBA, in accordance with the procedure for public hearings provided for in the zoning title; however, no additional fee shall be charged. (1985 Code § 10-1-8)