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

Answer: Option D. -> Rs. 50
$$\eqalign{
& T.D. = \frac{{B.G. \times 100}}{{R \times T}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{10 \times 100}}{{10 \times 2}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,50 \cr} $$

Answer: Option B. -> 320
$$\eqalign{
& {\text{Amount}}\,{\text{Due}} \cr
& = \frac{{B.D. \times T.D.}}{{B.D. - T.D.}} \cr
& = \frac{{80 \times 64}}{{80 - 64}} \cr
& = {\text{Rs}}{\text{.}}\,320 \cr} $$

Answer: Option B. -> 7
$$\eqalign{
& {\text{Banker's}}\,{\text{Gain}} \cr
& = \frac{{{{\left( {T.D.} \right)}^2}}}{{P.W.}} \cr
& = \frac{{{{\left( {120} \right)}^2}}}{{2400}} \cr
& = \frac{{14400}}{{2400}} \cr
& = {\text{Rs}}{\text{.}}\,6 \cr} $$

Answer: Option C. -> Rs. 120
Present Worth (P.W.) = 840 - 105 = Rs. 735
Therefore, S.I. on Rs. 735 = Rs. 105
S.I. on Rs. 8400
= $$\frac{{105 \times 840}}{{735}}$$
= Rs. 120

Answer: Option C. -> $$13\frac{1}{3}\,\% $$
Let amount of the bill = Rs. 100. Money deducted = Rs. 10
Money received by the holder of the bill = Rs. (110 - 10) = Rs. 90
∴ S.I. on Rs. 90 for 10 months = Rs. 10
$$\eqalign{
& \therefore {\text{Rate}} = \left( {\frac{{100 \times 10}}{{90 \times \frac{{10}}{{12}}}}} \right)\% \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 13\frac{1}{3}\,\% \cr} $$

Answer: Option A. -> Rs. 200
$$\eqalign{
& TD = \frac{{BG \times 100}}{{TR}} \cr
& \,\,\,\,\,\,\,\,\,\,\, = \frac{{20 \times 100}}{{10}} \cr
& \,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,200 \cr} $$

Answer: Option D. -> Rs. 200
$$\eqalign{
& F = \frac{{BD \times TD}}{{BD - TD}} \cr
& \,\,\,\,\,\,\,\, = \frac{{200 \times 100}}{{200 - 100}} \cr
& \,\,\,\,\,\,\,\, = \frac{{200 \times 100}}{{100}} \cr
& \,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,200 \cr} $$

Answer: Option C. -> Sum = Rs. 400 and Time = 2.5 years
$$\eqalign{
& BD = {\text{Rs}}.100 \cr
& TD = {\text{Rs}}{\text{.}}\,80 \cr
& R = 10\% \cr
& F{\text{ = }}\frac{{BD \times TD}}{{(BD - TD)}} \cr
& \,\,\,\,\,\,\, = \frac{{100 \times 80}}{{(100 - 80)}} \cr
& \,\,\,\,\,\,\, = \frac{{100 \times 80}}{{20}} \cr
& \,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,400 \cr} $$
BD = Simple Interest on the face value of the bill for unexpired time = $$\frac{{FTR}}{{100}}$$
$$\eqalign{
& \Rightarrow 100 = \frac{{400 \times T \times 10}}{{100}} \cr
& \Rightarrow 100 = 4 \times T \times 10 \cr
& \Rightarrow 10 = 4 \times T \cr
& \Rightarrow T = \frac{{10}}{4} = 2.5{\text{years}} \cr} $$

Answer: Option A. -> Rs. 400
$$\eqalign{
& {\text{T}} = 3\,{\text{year}} \cr
& {\text{R}} = {\text{10}}\% \cr
& {\text{TD = }}\frac{{{\text{BG}} \times 100}}{{{\text{TR}}}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\, = \frac{{36 \times 100}}{{3 \times 10}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\, = 12 \times 10 \cr
& \,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}120 \cr
& {\text{TD = }}\frac{{{\text{PW}} \times {\text{TR}}}}{{100}} \cr
& \Rightarrow 120 = \frac{{{\text{PW}} \times 3 \times 10}}{{100}} \cr
& \Rightarrow 1200 = {\text{PW}} \times 3 \cr
& {\text{PW}} = \frac{{1200}}{3} \cr
& \,\,\,\,\,\,\,\,\,\,{\text{ = Rs}}{\text{.}}400 \cr} $$