Banker’s discount and gain application: A bill is due in 9 months at a simple rate of 4% per annum. The banker’s gain on discounting this bill is ₹2.25. Find the face value (sum due at maturity) of the bill.

Introduction / Context:
This question tests core ideas in bill discounting: banker’s discount (BD), true discount (TD), present worth (PW), and banker’s gain (BG). BG is the excess of BD over TD, and it equals the simple interest on the true discount for the unexpired time. Using these relationships, we can back out both TD and the face value of the bill due at maturity.

Given Data / Assumptions:

• Time to maturity t = 9 months = 0.75 year.
• Rate r = 4% per annum (simple).
• Banker’s gain BG = ₹2.25.
• Standard banking convention for simple discounting and no grace days unless stated.

Concept / Approach:
Use the identity BG = (TD * r * t) / 100, i.e., banker’s gain equals simple interest on the true discount. Once TD is obtained, present worth PW follows from TD = (PW * r * t) / 100. Face value (sum due) = PW + TD.

Step-by-Step Solution:

Verification / Alternative check:
Compute BD and TD explicitly for a face value of ₹2575 at 4% for 0.75 year. Their difference equals ₹2.25, confirming the calculation.

Why Other Options Are Wrong:
₹2500 is the present worth, not the face value; ₹2250, ₹2525, ₹3250 do not satisfy BG = ₹2.25 at the stated r and t.

Common Pitfalls:
Confusing face value with present worth; forgetting that BG is simple interest on TD, not on PW or face directly.

Final Answer:
₹2575