Solution:
$$\eqalign{
& {\text{Let}}\,{\text{Banker's}}\,{\text{Discount}} \cr
& = {\text{Rs}}{\text{.}}\,10 \cr
& {\text{Then,}}\,{\text{Banker's}}\,{\text{Gain}} \cr
& = {\text{Rs}}{\text{.}}\,\frac{1}{5} \times 10 \cr
& = {\text{Rs}}{\text{.}}\,2 \cr
& T.D. = \left( {B.D. - B.G.} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = \left( {10 - 2} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,8 \cr
& {\text{Sum}} = \frac{{10 \times 8}}{{10 - 8}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{80}}{2} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,40 \cr} $$
S.I. on Rs. 40 for 2.5 year is Rs. 10
$$\eqalign{
& {\text{Therefore,}} \cr
& {\text{Rate}} = \frac{{100 \times 10}}{{40 \times 2.5}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = 10\% \cr} $$
