Formal:
* किं त्वं क्षुधार्तः असि? (kim tvam kṣudhārtḥ asi?) - This is a grammatically correct and formal way to ask. It literally translates to "Are you hungry?"
* त्वं क्षुधा ग्रस्तः असि? (tvam kṣudhā grastaḥ asi?) - This translates to "Are you consumed by hunger?" and is slightly more emphatic.
Informal:
* क्षुधार्तः असि? (kṣudhārtḥ asi?) - This is a shorter, more informal way to ask, simply meaning "Are you hungry?"
* भोजनं करिष्यसि? (bhojanam kariṣyasi?) - This translates to "Will you eat?" and is a more casual way to ask if someone is hungry.
Other options:
* त्वं क्षुत् अनुभवति? (tvam kṣut anubhavati?) - This translates to "Do you feel hunger?" and is a more poetic way to ask.
The best choice for you will depend on the context and your desired level of formality.