Find rate when BG is a fraction of BD: The banker’s gain on a sum due 2.5 years hence is (3/23) of the banker’s discount. Find the annual simple interest rate.

Introduction / Context:
Relating BG and BD directly yields r t. Then, dividing by t gives the annual rate. This pattern is common in banker’s discount questions.

Given Data / Assumptions:

• BG / BD = 3/23
• t = 2.5 years

Concept / Approach:
Identity:

Step-by-Step Solution:

Verification / Alternative check:
BG/BD = 0.15 / 1.15 = 3/23 (exact), confirming the calculation.

Why Other Options Are Wrong:
5% would imply x = 0.125; other unusual options do not satisfy the given BG/BD ratio for 2.5 years.

Common Pitfalls:
Using BD/BG instead of BG/BD or failing to isolate x properly.

Final Answer:
6%