On the day fixed for hearing or any day to which the hearing is adjourned, the board shall hear and consider any objections presented to the annexation of the territory. After the hearing of objections, if it shall be determined by a vote of two-thirds (23) of all the members of the board that the territory proposed to be annexed will be benefited by such annexation, the board shall proceed to fix and determine the boundaries of the territory to be annexed to the district.