Appeals from the decision of the zoning officer may be made to the Board of Adjustment by any person aggrieved or by an officer of the City or member of the Council. The applicant shall file with the zoning officer and with the Board of Adjustment a notice of appeal specifying the grounds thereof. The zoning officer shall forthwith transmit to the Board all papers constituting the record upon which the action appealed from was taken. Such appeal shall be taken within a reasonable time as provided by the rules of the Board.