Under contracts as authorized by the preceding section, the rate of payment per patient day to be paid by the county to any hospital, receiving state aid under the hospital in-patient program of the state health department, shall be established at a computed rate of twenty (20) percent of the average patient day cost to the hospital for care as such cost is computed anddetermined by audit procedures approved by the state department of health; provided, that the liability of the county for cost of care shall not exceed the above twenty (20) percent of such patient day cost whether or not the hospital is paid by the state or other source for the remaining eighty (80) percent of care cost. (Mont. Co. Code 1965, § 89-57.)