Whenever a petition in conformity to the provisions of Kan. Stat. Ann. § 24-403, signed by not less than two-fifths of the taxpayers residing within the boundaries of the proposed district, or signed by the record owners of not less than fifty-one percent (51%) of the land within the boundaries of the proposed districts, shall be presented to the board of county commissioners of any county, praying that a drainage district be incorporated and organized, it shall be the duty forthwith of such board of county commissioners to fix a time for the hearing of such petition, and to cause the county clerk to give notice thereof by one publication in some newspaper published and of general circulation in the county at least five (5) days before the day fixed for the hearing.