Answer: Option A. -> Rs. 1575.20
$$\eqalign{
& {\text{ = Rs}}.10000\left[ {\left( {1 + \frac{4}{{100}}} \right)\left( {1 + \frac{5}{{100}}} \right)\left( {1 + \frac{6}{{100}}} \right)} \right] \cr
& = {\text{Rs}}.\left( {10000 \times \frac{{26}}{{25}} \times \frac{{21}}{{20}} \times \frac{{53}}{{50}}} \right) \cr
& = {\text{Rs}}.\left( {\frac{{57876}}{5}} \right) = {\text{Rs}}.11575.20 \cr
& {\text{C}}{\text{.I}}{\text{. = Rs}}{\text{.}}\left( {11575.20 - 10000} \right) \cr
& \,\,\,\,\,\,\,\,\, = {\text{Rs}}.1575.20 \cr} $$

Answer: Option C. -> Rs. 4641
$$\eqalign{
& {\text{P = Rs}}.10000, \cr
& {\text{R}} = 20\% \,p.a. \cr
& \,\,\,\,\,\,\, = 10\% \,{\text{per}}\,{\text{half year}} \cr
& T = 2\,{\text{years}} = 4\,{\text{half}}\,{\text{years}} \cr
& {\text{Amount}} \cr
& {\text{ = Rs}}.\left[ {10000 \times {{\left( {1 + \frac{{10}}{{100}}} \right)}^4}} \right] \cr
& = {\text{Rs}}.\left( {10000 \times \frac{{11}}{{10}} \times \frac{{11}}{{10}} \times \frac{{11}}{{10}} \times \frac{{11}}{{10}}} \right) \cr
& = {\text{Rs}}.14641 \cr
& \therefore {\text{C}}{\text{.I}}{\text{. = Rs}}.\left( {14641 - 10000} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}.\,4641 \cr} $$

Answer: Option C. -> Rs. 625
Interest on 650 for one year = 676 - 650 = 26
$$\eqalign{
& 26 = \frac{{650 \times r \times 1}}{{100}} \cr
& r = 4\% \cr
& 650 = P\left[ {1 + \frac{4}{{100}}} \right] \cr
& \Rightarrow 650 = P \times \frac{{26}}{{25}} \cr
& \Rightarrow p = \frac{{650 \times 25}}{{26}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,625 \cr} $$

Answer: Option B. -> Rs. 121
$$\eqalign{
& {\text{ = Rs}}.\left[ {1600 \times {{\left( {1 + \frac{5}{{2 \times 100}}} \right)}^2} + 1600 \times \left( {1 + \frac{5}{{2 \times 100}}} \right)} \right] \cr
& {\text{ = Rs}}.\left[ {1600 \times \frac{{41}}{{40}} \times \frac{{41}}{{40}} + 1600 \times \frac{{41}}{{40}}} \right] \cr
& {\text{ = Rs}}.\left[ {1600 \times \frac{{41}}{{40}}\left( {\frac{{41}}{{40}} + 1} \right)} \right] \cr
& {\text{ = Rs}}.\left( {\frac{{1600 \times 41 \times 81}}{{40 \times 40}}} \right) \cr
& {\text{ = Rs}}.\,3321 \cr
& \therefore {\text{C}}{\text{.I}}{\text{. = Rs}}.\left( {3321 - 3200} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}.\,121 \cr} $$

Answer: Option C. -> 4% per annum
Difference in CI and SI for 2 years
$$\eqalign{
& = \left( {40.80 - 40} \right) \cr
& = {\text{Rs 0}}{\text{.80}} \cr
& {\text{SI for first year }} \cr
& {\text{ = }}\frac{{40}}{2} = {\text{Rs}}{\text{.}}\,20 \cr
& {\text{Required Rate }}\% \cr
& {\text{ = }}\frac{{0.80}}{{20}} \times 100 = 4\% \cr} $$

Answer: Option C. -> Rs. 9040
$$\eqalign{
& {\text{Amount}} \cr
& {\text{ = Rs}}.\left[ {20000{{\left( {1 + \frac{{10}}{{100}}} \right)}^2}\left( {1 + \frac{{20}}{{100}}} \right)} \right] \cr
& = {\text{Rs}}.\left( {20000 \times \frac{{11}}{{10}} \times \frac{{11}}{{10}} \times \frac{6}{5}} \right) \cr
& = {\text{Rs}}.29040 \cr
& {\text{C}}{\text{.I}}{\text{. = Rs}}.\left( {29040 - 20000} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}. 9040 \cr} $$

Answer: Option C. -> Rs. 250
$$\eqalign{
& 4\% = \frac{1}{{25}} \cr
& \,\,\,\,\,\,\,\,\, = \frac{{26 \to {\text{Amount}}}}{{25 \to {\text{Principal}}}} \cr
& {\text{Time = 2 years}} \cr
& {\text{Principal}}\,\,\,\,\,{\text{Amount}} \cr
& \,\,\,\,\,\,\,\,\,{\text{25}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{26}} \cr
& \,\,\,\,\,\,\,\,\,{\text{25}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{26}} \cr
& \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \cr
& \,\,\,\,\,\,\,\,625\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,676 \cr
& \,\,\,\, \downarrow \times 0.4\,\,\,\,\,\, \downarrow \times 0.4 \cr
& \,\,\,\,\,\,\,\,\,250\,\,\,\,\,\,\,\,\,\,\,\,270.40 \cr
& {\text{Hence required principal}} \cr
& {\text{ = Rs.250}} \cr} $$

Answer: Option B. -> 10%
Let the sum be Rs. P and rate of interest be R% per annum. Then,
$$\eqalign{
& P{\left( {1 + \frac{R}{{100}}} \right)^2} = 9680\,.....\,\left( 1 \right) \cr
& P{\left( {1 + \frac{R}{{100}}} \right)^3} = 10648\,.....\,\left( 2 \right) \cr} $$
On dividing equation (2) by (1) :
$$\eqalign{
& 1 + \frac{R}{{100}} = \frac{{10648}}{{9680}} \cr
& \Rightarrow \frac{R}{{100}} = \frac{{10648}}{{9680}} - 1 \cr
& \Rightarrow \frac{R}{{100}} = \frac{{10648 - 9680}}{{9680}} \cr
& \Rightarrow \frac{R}{{100}} = \frac{{968}}{{9680}} \cr
& \Rightarrow \frac{R}{{100}} = \frac{1}{{10}} \cr
& \Rightarrow R = \frac{1}{{10}} \times 100 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = 10\% \cr} $$

Answer: Option D. -> $${\text{Rs}}{\text{.}}\,\frac{{P{R^2}}}{{{{\left( {100} \right)}^2}}}$$
$$\eqalign{
& {\text{S}}{\text{.I}}{\text{. = Rs}}{\text{.}}\left( {\frac{{P \times R \times 2}}{{100}}} \right) \cr
& \,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\left( {\frac{{2PR}}{{100}}} \right) \cr
& {\text{C}}{\text{.I}}{\text{. = Rs}}{\text{.}}\left[ {P \times {{\left( {1 + \frac{R}{{100}}} \right)}^2} - P} \right] \cr
& \,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\left[ {\frac{{P{R^2}}}{{{{\left( {100} \right)}^2}}} + \frac{{2PR}}{{100}}} \right] \cr
& \therefore {\text{Difference}} \cr
& {\text{ = Rs}}{\text{.}}\left[ {\left\{ {\frac{{P{R^2}}}{{{{\left( {100} \right)}^2}}} + \frac{{2PR}}{{100}}} \right\} - \frac{{2PR}}{{100}}} \right] \cr
& = {\text{Rs}}{\text{.}}\left[ {\frac{{P{R^2}}}{{{{\left( {100} \right)}^2}}}} \right] \cr} $$

Answer: Option B. -> Rs. 2400
Time (t) = 2 years
Rate % = 4%
Effective rate of CI of 2 years
$$\eqalign{
& {\text{ = 4 + 4 + }}\frac{{4 \times 4}}{{100}} \cr
& = 8.16\% \cr} $$
Effective Rate of SI for 2 years = 8%
According to the question
$$\eqalign{
& {\text{8}}{\text{.16% of sum}} \cr
& {\text{ = Rs. 2448}} \cr
& {\text{1% of sum}} \cr
& {\text{ = Rs. }}\frac{{2448}}{{8.16}} \cr
& {\text{8% of sum}} \cr
& {\text{ = }}\frac{{2448}}{{8.16}} \times {\text{8}} \cr
& {\text{ = Rs. 2400 }} \cr} $$