Compute banker’s discount and banker’s gain: The present worth of a bill is ₹2200 and the true discount is ₹220. Find the banker’s discount and the banker’s gain.

Introduction / Context:
From present worth (PW) and true discount (TD) we can find face value and r t. Then BD and BG follow mechanically. A key identity: TD / PW = r t.

Given Data / Assumptions:

• PW = ₹2200
• TD = ₹220
• A = PW + TD = ₹2420

Concept / Approach:
Use:

Step-by-Step Solution:

Verification / Alternative check:
TD = A * (r t) / (1 + r t) = 2420 * 0.10 / 1.10 = ₹220 (checks).

Why Other Options Are Wrong:
They mis-order BG and BD magnitudes or break the relation TD/PW = r t = 0.10.

Common Pitfalls:
Using face value instead of PW when computing r t from TD, or swapping BG and BD definitions.

Final Answer:
BG = ₹ 22 and BD = ₹ 242