Banker's discount is Rs. 72 and true discount is Rs. 60 for the same sum and time. Find the sum due (face value).

Given data

• BD = Rs. 72
• TD = Rs. 60
• Sum due A = ?

Concept/ApproachRatio BD / TD = (100 + r t) / 100 ⇒ find r t. Then use TD = A × r t / (100 + r t) to get A.

Step-by-step calculationBD / TD = 72 / 60 = 6 / 5 = 1.2 ⇒ (100 + r t) / 100 = 1.2 ⇒ r t = 20TD = A × 20 / 120 = A / 660 = A / 6 ⇒ A = Rs. 360

Verification/AlternativeBD = A × 20 / 100 = 360 × 0.2 = 72 (matches).

Common pitfallsSubtracting BD − TD to get A; remember A = PW + TD, and formulas above are cleaner.

Final AnswerRs. 360