True Discount given (16 months) → Banker’s Gain: The true discount on a bill of ₹ 7440 due 16 months hence is ₹ 240. Find the banker's gain.

Introduction / Context:
Once TD is given, we can solve for x = r * t using TD = F * x / (1 + x). Banker's Discount is BD = F * x, and Banker's Gain is BG = BD − TD.

Given Data / Assumptions:

• F = ₹ 7440.
• t = 16 months = 16/12 years = 4/3 years.
• TD = ₹ 240.

Concept / Approach:
Let x = r * t. Solve for x from the TD equation, then compute BD and BG.

Step-by-Step Solution:
TD = 7440 x / (1 + x) = 240 ⇒ 7440 x = 240 + 240 x ⇒ 7200 x = 240 ⇒ x = 1/30.BD = 7440 * (1/30) = ₹ 248.BG = BD − TD = 248 − 240 = ₹ 8.

Verification / Alternative check:
P = F − TD = 7440 − 240 = 7200; also P = F / (1 + x) = 7440 / (31/30) = 7200, consistent.

Why Other Options Are Wrong:
10, 6, 4, 12 do not match BG once x = 1/30 is established.

Common Pitfalls:
Arithmetic slips when isolating x; forgetting BG = BD − TD.

Final Answer:
₹ 8