After incorporation of a city or town located in more than one county, all purposes essential to the maintenance, operation, and administration of the city or town whenever any action is required or may be performed by the county, county legislative authority, or any county officer or board, such action shall be performed by the respective county, county legislative authority, officer, or board of the county of that part of the city or town in which the largest number of inhabitants reside as of the date of the incorporation of the proposed city or town except as provided in RCW 35.02.240, and all costs incurred shall be borne proportionately by each county in that ratio which the number of inhabitants residing in that part of each county forming a part of the proposed city or town bears to the total number of inhabitants residing within the whole of the city or town.