True Discount known (8 months) → Banker’s Discount: The true discount on a bill of Rs. 1860 due after 8 months is Rs. 60. Find the banker's discount.

Introduction / Context:
Given True Discount (TD) on a known face value F for a given time, we can back out x = r * t using TD = F * x / (1 + x). With x, we find Banker's Discount via BD = F * x.

Given Data / Assumptions:

• F = Rs. 1860.
• t = 8 months ⇒ t = 8/12 years = 2/3 years.
• TD = Rs. 60; simple interest.

Concept / Approach:
Let x = r * t. From TD relation, solve for x and compute BD.

Step-by-Step Solution:
TD = F * x / (1 + x) ⇒ 60 = 1860 x / (1 + x).1860 x = 60 + 60 x ⇒ 1800 x = 60 ⇒ x = 1/30.BD = F * x = 1860 * (1/30) = Rs. 62.

Verification / Alternative check:
P = F − TD = 1860 − 60 = 1800; also P = F / (1 + x) = 1860 / (1 + 1/30) = 1860 / (31/30) = 1800, consistent.

Why Other Options Are Wrong:
Rs. 52 and Rs. 60 do not satisfy BD = F * x with x = 1/30; "None of these" is unnecessary.

Common Pitfalls:
Solving for r instead of x = r * t; arithmetic slips when isolating x.

Final Answer:
Rs . 62