The present worth of a bill is ₹ 1500. If the true discount on the bill is ₹ 75, find the banker’s discount (simple interest on face value for the term).

Introduction / Context:
This question contrasts true discount (TD) and banker’s discount (BD). Given present worth (P) and TD, we can compute BD using a standard identity.

Given Data / Assumptions:

• P = 1500
• TD = 75
• Face value F = P + TD = 1575

Concept / Approach:
Banker’s discount is SI on face value: BD = F * r * t. True discount is SI on present worth: TD = P * r * t. Using r*t = TD/P, we obtain: BD = TD + (TD^2)/P.

Step-by-Step Solution:
Compute banker’s gain BG = BD − TD = (TD^2)/P = 75^2 / 1500 = 5625 / 1500 = 3.75. Hence BD = TD + BG = 75 + 3.75 = 78.75.

Verification / Alternative check:
If r*t = TD/P = 75/1500 = 0.05, then BD = F * 0.05 = 1575 * 0.05 = 78.75, matching the result.

Why Other Options Are Wrong:
77.75 and 76.75 do not match the identity; 82.75 and 80.00 misapply the formula.

Common Pitfalls:
Confusing BD with TD; forgetting BD − TD = (TD^2)/P; or using face value instead of present worth in the TD expression.

Final Answer:
₹ 78.75