Q.The present value of a bill is ₹1,500 and its true discount is ₹60. Find

With the present value and true discount known, the banker's gain follows from BG = TD²/PV, and the banker's discount is then TD + BG.

Given $PV = 1500$ and $TD = 60$.

1. Banker's gain:

   $BG = \dfrac{TD^{2}}{PV} = \dfrac{60^{2}}{1500} = \dfrac{3600}{1500} = 2.40.$

2. Banker's discount: $BD = TD + BG = 60 + 2.40 = 62.40.$ …

Alternatively, since $BG = TD\cdot rt/100$ and $TD = PV\cdot rt/100$, the ratio $BG/TD = TD/PV = 60/1500 = 0.04 …

Writing $BG = TD^2/F$ instead of $TD^2/PV$, or adding TD to PV to …