The true discount on a bill of Rs. 540 is Rs. 90. The banker's discount is:

$$\eqalign{ & {\text{P}}{\text{.W}}{\text{.}} = Rs.\,\left( {540 - 90} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,450 \cr & \therefore {\text{S}}{\text{.I}}{\text{.}}\,{\text{on}}\,Rs.\,450 = Rs.\,90 \cr & {\text{S}}{\text{.I}}{\text{.}}\,{\text{on}}\,Rs.\,540 \cr & = Rs.\,\left( {\frac{{90}}{{450}} \times 540} \right) \cr & = Rs.\,108 \cr & \therefore {\text{B}}{\text{.D}}. = Rs.\,108 \cr} $$