The simple interest and the true discount on a certain sum for the same time and rate are ₹85 and ₹80. What is the sum due (face value)?

Concept / Approach The given 'simple interest' here is effectively the Banker's Discount (BD) because it is computed on the sum due (face value). The True Discount (TD) is the difference between the face value and the present worth. For the same time and rate with simple interest: BD = A × R,   TD = A × R / (1 + R) which implies a handy result: A = (BD × TD) / (BD − TD) where A is the face value (sum due) and R is the time–rate product.

Step-by-step calculation BD = ₹85,   TD = ₹80 A = (BD × TD) / (BD − TD) = (85 × 80) / (85 − 80) = 6800 / 5 = ₹1,360

Verification Compute present worth (PW) and the effective R to check consistency: PW = A − TD = 1360 − 80 = ₹1,280 R = TD / PW = 80 / 1280 = 0.0625 = 6.25% Then BD should be A × R: BD = 1360 × 0.0625 = ₹85 which matches the given value.

Common pitfalls

• Confusing BD with TD—BD is on face value; TD equals the interest on present worth.
• Forgetting to use the identity A = (BD × TD)/(BD − TD) for quick computation.
• Mixing up present worth with face value while plugging numbers.

Final Answer ₹1,360