Appeals to the board of adjustment may be taken by any person aggrieved or by any officer, department, board or bureau of the county affected by any decision of the administrative officer. Such appeal shall be taken within a reasonable time, as provided by the rules of the board of adjustment, by filing with the officer from whom the appeal is taken and with the board of adjustment a notice of appeal specifying the grounds thereof. The officer from whom the appeal is taken shall forthwith transmit to the board of adjustment all the papers constituting the record upon which the action appealed from was taken.