In all cities located in counties in which both a public county and city hospital are being conducted under separate supervision and management, such cities are hereby authorized and directed, when consolidation is completed under this chapter and upon the recommendation of the board of hospital trustees, to sell the property now owned and used by such cities for hospital purposes, both real and personal, at public or private sale, the proceeds of such sale to be used, first, for the retirement and payment of any outstanding bonds issued in connection with the purchase of such hospital property, and the remainder, if any, shall be turned into the county public hospital fund.