Question

It is given that, the true discount on a bill of ${\text{Rs}}.540$ is ${\text{Rs}}.90.$The bankerâ€™s discount is:${\text{A}}{\text{. Rs}}{\text{. 60}} \\ {\text{B}}{\text{. Rs}}{\text{. 108}} \\ {\text{C}}{\text{. Rs}}{\text{. 110}} \\ {\text{D}}{\text{. Rs}}{\text{. 112}} \\$

Hint: The interest on the present value is called the true discount $\left( {{\text{TD}}} \right)$.bankerâ€™s discount is the simple interest on the face value of the debt for the time period between the legally due date and the date on which the bill is discounted.

Present worth $\left( {{\text{P}}{\text{.W}}{\text{.}}} \right)$=Face value-true discount
Here in this question face value is ${\text{Rs}}{\text{. = 540}}$ and true discount is ${\text{Rs}}{\text{. = 90}}$
${\text{P}}{\text{.W}}{\text{. = Rs}}{\text{.}}\left( {540 - 90} \right) = {\text{Rs}}{\text{.450}}$
Simple interest on present worth is a true discount.
$\because$ SI on ${\text{Rs}}{\text{.450 = Rs}}{\text{.90}}$
$\therefore$SI on ${\text{Rs}}{\text{.1 = }}\dfrac{{{\text{Rs}}{\text{.90}}}}{{{\text{Rs}}{\text{.540}}}}$

Hence SI on ${\text{Rs}}{\text{.540 = Rs}}{\text{.}}\dfrac{{90 \times 540}}{{450}} = {\text{Rs}}{\text{.108}}$

And here ${\text{Rs}}{\text{.540}}$ is face value and we know simple interest on face value is a banker's discount.

Therefore, the banker's discount =${\text{Rs}}{\text{.108}}$.

Hence option ${\text{B}}$ is the correct option.

Note: Whenever you get this type of question the key concept of solving is you should know the terms present worth, true discount, face value, bankerâ€™s discount and also knowledge that simple interest on present worth is true discount and simple interest on face value is bankerâ€™s discount.