Banker's gain on a bill due 1 year hence at 12% p.a. is Rs. 6. Find the true discount.

Given data

• t = 1 year, r = 12% ⇒ r t = 12
• BG = Rs. 6
• TD = ?

Concept/ApproachUse the relation BG / TD = r t / 100 ⇒ TD = BG × 100 / (r t).

Step-by-step calculationTD = 6 × 100 / 12 = Rs. 50

Verification/AlternativeWith TD = 50 and r t = 12, BG should be 50 × 12/100 = 6 (matches).

Common pitfallsUsing BD instead of BG in the ratio with TD; only BG/TD equals r t / 100.

Final AnswerRs. 50