The true discount (TD) on a certain sum due 6 months hence at 15% p.a. is ₹240. What is the banker’s discount (BD) on the same sum for the same time and rate?

Introduction / Context:
Given TD and (rate × time), BD is just a simple multiplier away. The ratio BD/TD equals 1 + x where x = r * t. We leverage this direct relation for a quick computation.

Given Data / Assumptions:

• TD = ₹240.
• t = 6 months = 0.5 year; r = 15% p.a. ⇒ x = 0.075.

Concept / Approach:
Identity: BD = (1 + x) * TD. No need to find the face value explicitly. Compute x, multiply TD by (1 + x).

Step-by-Step Solution:

Verification / Alternative check:
If TD = 240 and x = 0.075, then BD − TD = x * TD = 18 ⇒ BD = 258, consistent.

Why Other Options Are Wrong:
₹228, ₹248, and ₹278 do not equal 1.075 * 240.

Common Pitfalls:
Forgetting to convert months to years before computing x; mixing up BD and BG.

Final Answer:
Rs. 258