Following public notice and hearing, the Board of Appeals may reverse or affirm, wholly or partly, or may modify the order, requirement, decision or determination appealed from and shall make such order, requirement, decision or determination as, in its opinion, ought to be made in the premises and, to that end, shall have all the power of the Building Inspector. If the action by the Board of Appeals is to reverse the action of the Building Inspector in whole, the filing fee shall be refunded to the appellant. The Board of Appeals shall decide the same within 60 days following the final hearing.