Upon the inclusion of any drainage ditch constructed under the provisions of sections 31-101 to 31-134, or of any drainage district which shall have been dissolved, which benefits an area in part within or adjacent to the boundaries of a drainage district organized under the provisions of Chapter 31, article 3 or 4, the board of directors of the district to which such transfer shall have been made shall operate and maintain the ditch so transferred in the same manner as the ditches originally constructed by such district and shall have the power to levy taxes upon the lands benefited thereby in the same manner as in the case of the ditch or ditches constructed by such district.