Present worth is Rs. 1600 and true discount is Rs. 160. Find the banker's gain.

Given data

• PW = Rs. 1600
• TD = Rs. 160
• BG = ?

Concept/ApproachUse the identity BG = TD² / PW.

Step-by-step calculationBG = 160² / 1600 = 25,600 / 1600 = Rs. 16

Verification/AlternativeAlso, BD = TD + BG = 160 + 16 = 176; consistency checks can be made with the implied rate-time if needed.

Common pitfallsApplying BG = BD − TD without first finding BD; the squared relation is faster here.

Final AnswerRs. 16