NOTE: Official UPSC answer key has considered both C and D as correct.

The most appropriate responses in this situation are C and D, as both aim to address the villager's issue while managing your time as a District Magistrate.

C. Call one of your senior subordinate officers and ask him to solve the villager’s problem. This allows you to delegate the task to a trusted officer, ensuring that the issue is addressed swiftly without requiring you to sacrifice your schedule. It shows that you are ensuring the problem is handled while maintaining your commitments.

D. Quickly take the application from him, ask him a few relevant questions regarding his problem, and then proceed to the meeting. This approach shows direct personal involvement and gives immediate attention to the villager's concern. Even if you're busy, taking a few minutes to understand the issue can ensure that the villager feels supported and that his problem is prioritized.