Present worth is Rs. 576 and banker's gain is Rs. 16. Find the true discount.

Given data

• Present worth (PW) = Rs. 576
• Banker's gain (BG) = Rs. 16
• True discount (TD) = ?

Concept/ApproachKey relation: BG = TD² / PW  ⇒  TD = √(BG × PW)

Step-by-step calculationTD = √(16 × 576)= √(9216) = Rs. 96

Verification/AlternativeBG should equal TD² / PW = 96² / 576 = 9216 / 576 = 16 (matches).

Common pitfallsConfusing banker's discount (BD) with banker's gain (BG); BG = BD − TD, not BD itself.

Final AnswerRs. 96