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?

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Solve this multiple-choice question and choose the correct option.

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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: TD = A * (r * t) / (1 + r * t) BD = A * r * t Step-by-Step Solution: Let x = r t = 0.30 240 = A * 0.30 / 1.30 ⇒ A = 240 * 1.30 / 0.30 = ₹1040 BD = A * x = 1040 * 0.30 = ₹312 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

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?

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