Let's analyze both statements in the context of Article 315 of the Constitution:
Statement I: Article 315(1) directly states, "Subject to the provisions of this article, there shall be a Public Service Commission for the Union and a Public Service Commission for each State." This statement is correct.
Statement II: Article 315(4) provides for this exact situation. It says, "The Public Service Commission for the Union, if requested so to do by the Governor of a State may, with the approval of the President, agree to serve all or any of the needs of the State." This statement is also correct.
Since both statements accurately reflect the provisions of Article 315, the correct option is (c).