Assertion: At the time of the Independence of India, Princely states covered one-third of the land area of the British Indian Empire.
Reason: The Princely states were powerful and were able to maintain their sovereignty.

The Assertion is correct but the Reason is incorrect.

Prior to Independence, the British announced that with the end of their rule, the paramountcy of the British crown over the Princely States would also end.
This meant that the Princely States, numbering 565, would become legally independent and could choose to join India, and Pakistan, or remain independent.

At the time of the Independence of India, Princely states covered one-third of the land area of the British Indian Empire.
The decision of joining India or Pakistan was left to the princely rulers, rather than being determined by the people.
This posed a significant challenge as it could potentially lead to the fragmentation of India and threatened the unity of the newly formed nation. Several large and small states ruled by princes, called the Princely States, enjoyed some form of control over their internal affairs as long as they accepted British supremacy. This was called paramountcy or suzerainty of the British crown.