The true discount on a bill due 10 months hence at 6% per annum is Rs. 26.25. Find the amount of the bill (face value).

Introduction / Context: With true discount, we can recover the face value by inverting the TD formula using the given time and rate.

Given Data / Assumptions:

• TD = 26.25
• t = 10 months = 10/12 years
• r = 6% per annum

Concept / Approach: TD = F * (r * t) / (1 + r * t). Solve F = TD * (1 + r * t) / (r * t).

Step-by-Step Solution: t = 10/12 = 5/6; r * t = 0.06 * 5/6 = 0.05. F = 26.25 * (1 + 0.05)/0.05 = 26.25 * 1.05 / 0.05 = 26.25 * 21 = 551.25.

Verification / Alternative check: Present worth P = F/(1 + 0.05) = 551.25/1.05 = 525; TD = 551.25 − 525 = 26.25, consistent.

Why Other Options Are Wrong: 550.00, 551.50, 550.25 do not yield TD = 26.25 when substituted into the formula.

Common Pitfalls: Not converting months to years; mixing TD with SI on face value.

Final Answer: Rs. 551.25