A sum of money lent at compound interest for 2 yr at 20 % pa would fetch ₹ 964 more, if the interest was payable half-yearly than if it was payable annually. What is the sum?

Let the sum be ₹ P .
Then, CI when compounded half - yearly = [P x (1 + 10/100)⁴ - P] = 4641P/10000
CI when compounded annually = [ P x (1 + 20/100)² - P] = 11P/25
According to the question, 4641P/10000 - 11P/25 = 964
⇒ [(4641 - 4400)/10000] x P = 964
∴ P = (964 x 10000)/241
= ₹ 40000