Convert true discount to banker’s discount: The true discount on a certain sum due 1 year hence at 30% per annum is ₹240. What is the banker’s discount for the same time and rate?

Introduction / Context:
With TD known, recover the face value A and then compute BD. This is a straightforward application of TD and BD formulas for simple interest over one year.

Given Data / Assumptions:

• t = 1 year
• r = 30% = 0.30 per annum
• TD = ₹240

Concept / Approach:

Step-by-Step Solution:

Verification / Alternative check:
PW = A − TD = 1040 − 240 = ₹800. Interest on ₹800 for 1 year at 30% is ₹240 (matches TD); BD = ₹312 as computed.

Why Other Options Are Wrong:
They contradict the consistent A, PW, TD trio defined by x = 0.30.

Common Pitfalls:
Using BD = TD or adding/subtracting incorrectly when recovering A from TD.

Final Answer:
₹ 312