Step 1: Understand what privy purses were.
Privy purses were annual payments made by the Government of India to former rulers of princely states after their accession in 1947; they were constitutionally guaranteed as compensation for giving up sovereignty and merging with India.
Step 2: Identify when they were abolished.
Indira Gandhi's government abolished privy purses as part of socialist economic policy; this was achieved through the 26th Constitutional Amendment Act, 1971, which deleted Articles 291 and 362 that had guaranteed these payments.
Step 3: Confirm the answer.
The 26th Amendment (1971) is the correct answer; this move eliminated special privileges for former royalty and was widely seen as a major step toward a more egalitarian and unified India.
\[ \boxed{\text{26th Constitutional Amendment, 1971}} \]