§ 82. Expense; how borne. The proportion of the total cost of work performed on any project, in addition to such elements thereof as are not subject to federal aid, which shall be borne by the state of New York shall be the difference between the funds contributed for such work by the federal government and the actual cost thereof except as provided in section two hundred and thirty, and less any amount which may be provided by any municipality in accordance with the provisions of this chapter.