The cost of preparation and distribution of the statement setting forth the arguments in favor of, and those opposed to, the recommendations of the county board, and the cost of any election held pursuant to this article shall be a charge against the general fund of the county. If such district is situated in more than one county, the cost of the election shall be prorated against each county in the same proportion as the assessed valuation of the territory of the proposed new district lying in such county bears to the total assessed valuation of the proposed new districts.