The true discount on a bill due in 9 months at 4% per annum (simple interest) is ₹ 150. Find the amount of the bill (face value).

Introduction / Context:
We use the true discount formula to back-calculate the face value from TD, rate, and time. This is a direct application of TD with simple interest.

Given Data / Assumptions:

• TD = 150
• r = 4% per annum
• t = 9 months = 0.75 years

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

Step-by-Step Solution:
r * t = 0.04 * 0.75 = 0.03. F = 150 * (1 + 0.03) / 0.03 = 150 * 1.03 / 0.03 = 5150.

Verification / Alternative check:
Present worth P = F/(1 + r t) = 5150/1.03 = 5000. TD = F − P = 150, which matches the given data.

Why Other Options Are Wrong:
Values other than 5150 do not yield TD = 150 when substituted into TD = F * 0.03/1.03.

Common Pitfalls:
Forgetting to convert months into years or miscomputing r*t; treating TD as SI on face value instead of using the correct denominator.

Final Answer:
₹ 5150