Find banker’s discount from true discount: The true discount on a bill due 24 months hence at 24% per annum is ₹144. What is the banker’s discount for the same bill?

Introduction / Context:
Given TD and the time/rate, we can back out the face value and then compute BD directly. TD is on present worth; BD is on face value for the same time.

Given Data / Assumptions:

• t = 24 months = 2 years
• r = 24% = 0.24 per annum
• TD = ₹144

Concept / Approach:
Use:

Step-by-Step Solution:

Verification / Alternative check:
Compute PW = A − TD = 444 − 144 = ₹300. Interest on PW for 2 years at 24% is 300 * 0.24 * 2 = ₹144 (matches TD).

Why Other Options Are Wrong:
They do not satisfy both TD and BD relations simultaneously with the same A and x = 0.48.

Common Pitfalls:
Using TD = A * r * t (incorrect), or mixing A with PW during substitutions.

Final Answer:
₹ 213.12