The banker’s discount (BD) and the true discount (TD) on a sum due 8 months hence are ₹52 and ₹50, respectively. Find (i) the sum due (face value) and (ii) the annual rate percent.

Introduction / Context:Given BD and TD for the same time and rate, their ratio gives x = r * t. With t known (in years), r follows. Then the face value F can be computed from BD = F * x. This chain uses only standard discounting identities.

Given Data / Assumptions:

• BD = ₹52, TD = ₹50.
• Time = 8 months = 8/12 = 2/3 year.
• Simple-interest bill-discounting setting.

Concept / Approach:Use BD/TD = 1 + x ⇒ x = BD/TD − 1. Then r = x / t. Next, BD = F * x gives F. Finally sanity-check TD via TD = F * x / (1 + x).

Step-by-Step Solution:

Verification / Alternative check:Compute TD: TD = F * x / (1 + x) = 1300 * 0.04 / 1.04 = 52 / 1.04 = ₹50, consistent.

Why Other Options Are Wrong:Other pairs do not satisfy both BD/TD = 26/25 and BD = F * x with t = 8 months.

Common Pitfalls:Failing to convert months to years; mixing BD and BG.

Final Answer:Rs. 1300, 6%