The Prakrit name for present-day Rajgir in Bihar was Rajagaha.

Explanation:
Rajgir is a city and a notified area in Nalanda district in the Indian state of Bihar. It is located in a valley surrounded by seven hills. Rajgir was the capital of the Magadha Empire during the reign of Ajatshatru. The city has a rich history and cultural heritage. In ancient times, it was known as Rajagaha in Prakrit language.

Prakrit Language:
Prakrit is a group of Middle Indo-Aryan languages that were spoken in ancient India. It was the language of the common people and was widely used in the Maurya and Gupta empires. The Prakrit language is considered the precursor of modern Indian languages like Hindi, Bengali, and Marathi.

Rajagaha:
Rajagaha was the capital of the Magadha Empire during the reign of Ajatshatru. It was an important political and cultural center of ancient India. Many important events of the Buddha's life took place in Rajagaha. The city was also the site of the first Buddhist council, which was held after the Buddha's death.

Conclusion:
In conclusion, the Prakrit name for present-day Rajgir in Bihar was Rajagaha. The city has a rich history and cultural heritage and was an important political and cultural center of ancient India.

Because rajagaha was the houses of the king