On the third Monday after the annexation or consolidation takes effect, a committee consisting of three members of the governing body of the county from which the annexed territory is taken and three members of the governing body of the county to which the territory is annexed shall be appointed by said governing bodies in the manner otherwise provided by law for appointments thereof.
The committee shall meet at the courthouse of the county from which the territory is taken, at 10:00 a. m. on the Monday following their appointment.