True discount on a bill of Rs. 540 is Rs. 90. Find the banker's discount.

Given data

• Face value A = Rs. 540
• TD = Rs. 90
• BD = ?

Concept/Approach
Present worth PW = A − TD. Also TD / PW = r t / 100. Once r t is known, BD = A × r t / 100.

Step-by-step calculation
PW = 540 − 90 = 450r t / 100 = TD / PW = 90 / 450 = 0.2 ⇒ r t = 20BD = A × 20 / 100 = 540 × 0.20 = Rs. 108

Verification/Alternative
BG = BD − TD = 108 − 90 = 18; also BG = TD² / PW = 8100 / 450 = 18 (checks).

Common pitfalls
Computing BD on PW rather than on A; BD is always on the face value.

Final Answer
Rs. 108