Statement 1 is incorrect because the minimum age prescribed for a person to be a member of a Panchayat is 21 years, not 25 years, as per Article 243 of the Indian Constitution. Statement 2 is correct; when a Panchayat is reconstituted after premature dissolution, it indeed serves for the remainder of the original term, ensuring continuity in local governance. This understanding highlights the structure and functionality of grassroots democracy in India, crucial for effective local governance as outlined in various governance and polity texts referred to in UPSC preparations.