Any portion of an abatement district which will not be reasonably benefited by remaining within such district may be withdrawn as in this section provided. Upon receiving a petition signed by fifty (50) or more landowners within the portion desired to be withdrawn from any abatement district, or by a majority of such landowners, if there are less than one hundred (100) landowners within the portion sought to be withdrawn, requesting the withdrawal of such portion from the district on the ground that such portion will not be reasonably benefited by remaining in said district, the board of county commissioners shall fix a time for hearing on such petition and for hearing protests to the continuance of the remaining territory as an abatement district. The hearing shall not be less than ten (10) days nor more than thirty (30) days after the receipt thereof. The board shall, at least one (1) week prior to the time so fixed, publish notice of such hearing by one (1) publication in a newspaper of general circulation in the district, which the board deems most likely to give notice to the inhabitants thereof, of the proposed withdrawal.