The banker's discount and the true discount on a sum of money due 8 months hence are Rs. 120 and Rs. 110 respectively. Find the rate percent.

$$\eqalign{ & {\text{Sum}} = \frac{{B.D. \times T.D.}}{{B.D. - T.D.}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,\frac{{120 \times 110}}{{120 - 110}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,1320 \cr} $$
Since B.D. is S.I. on sum due, so S.I. on Rs. 1320 for 8 months is Rs. 120.
$$\eqalign{ & {\text{Rate}} = \frac{{100 \times 120}}{{1320 \times \frac{2}{3}}}\,\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{150}}{{11}}\,\% \cr} $$