An appeal to the Board of Zoning Appeals may be taken by any person aggrieved or by any office of the City affected by any decision of the Zoning inspector. Such appeal shall be taken within twenty days after the decision, filing with the Zoning Inspector and with the Board, a notice of appeal specifying the grounds thereof. The Zoning Inspector shall forthwith transmit the Board all the papers constituting the record upon which the action appealed from we. taken.