The present worth (PW) of a bill is ₹800 and the true discount (TD) is ₹36. Determine the banker’s discount (BD).

Introduction / Context:
Given PW and TD, compute x from TD = x * PW. Then use BD = (1 + x) * TD to find banker’s discount. This method remains valid irrespective of the underlying rate and time split, as long as simple-interest discounting is assumed.

Given Data / Assumptions:

• PW = ₹800.
• TD = ₹36.

Concept / Approach:
Compute x = TD / PW. Then BD = (1 + x) * TD = TD + x * TD. This yields a small increment over TD equal to BG = x * TD.

Step-by-Step Solution:

Verification / Alternative check:
BG = BD − TD = 37.62 − 36 = ₹1.62. Also BG = x * TD = 0.045 * 36 = ₹1.62; consistent.

Why Other Options Are Wrong:
₹37, ₹34.38, and ₹38.98 do not equal 1.045 * 36.

Common Pitfalls:
Using BD = PW * x (incorrect; that gives TD). BD multiplies face value, not PW.

Final Answer:
Rs. 37.62