Answer: Option B. -> Rs. 3
$$\eqalign{
& {\text{S}}{\text{.I}}{\text{.}}\, = Rs.\,\left( {\frac{{1200 \times 5 \times 2}}{{100}}} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,120 \cr
& {\text{C}}{\text{.I}}{\text{.}} = Rs.\,\left[ {1200 \times {{\left( {1 + \frac{5}{{100}}} \right)}^2} - 1200} \right] \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,123 \cr
& \therefore {\text{Difference}} = Rs.\,\left( {123 - 120} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,3 \cr} $$

Answer: Option A. -> Rs. 51.25
$$\eqalign{
& {\text{Sum}} = Rs.\,\left( {\frac{{50 \times 100}}{{2 \times 5}}} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,500 \cr
& {\text{Amount}} = Rs.\,\left[ {500 \times {{\left( {1 + \frac{5}{{100}}} \right)}^2}} \right] \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left( {500 \times \frac{{21}}{{20}} \times \frac{{21}}{{20}}} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,551.25 \cr
& \therefore {\text{C}}{\text{.I}}{\text{.}} = Rs.\,\left( {551.25 - 500} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,51.25 \cr} $$

Answer: Option A. -> Rs. 5000
$${\text{Rate 8% = }}\frac{2}{{25}}$$
Principal   
   Amount
25
27
25
27
625
729
↓ × 8
↓ × 8
5000
5832
Hence required sum = Rs. 5000

Answer: Option A. -> Rs. 874.75
$$\eqalign{
& {\text{Amount after }}{{\text{1}}^{{\text{st}}}}{\text{ year}} \cr
& {\text{ = Rs}}{\text{. }}\left[ {4000\left( {1 + \frac{{15}}{{100}}} \right) - 1500} \right] \cr
& = {\text{Rs}}{\text{. }}\left[ {\left( {4000 \times \frac{{23}}{{20}}} \right) - 1500} \right] \cr
& = {\text{Rs}}{\text{. }}\left( {4600 - 1500} \right) \cr
& = {\text{Rs}}{\text{. }}3100 \cr
& {\text{Amount after }}{{\text{2}}^{{\text{nd}}}}{\text{ year}} \cr
& {\text{ = Rs}}{\text{. }}\left[ {3100\left( {1 + \frac{{15}}{{100}}} \right) - 1500} \right] \cr
& = {\text{Rs}}{\text{. }}\left[ {\left( {3100 \times \frac{{23}}{{20}}} \right) - 1500} \right] \cr
& = {\text{Rs}}{\text{. }}\left( {3565 - 1500} \right) \cr
& = {\text{Rs}}{\text{. }}2065 \cr
& {\text{Amount after }}{{\text{3}}^{{\text{rd}}}}{\text{ year}} \cr
& {\text{ = Rs}}{\text{. }}\left[ {2065\left( {1 + \frac{{15}}{{100}}} \right) - 1500} \right] \cr
& = {\text{Rs}}{\text{. }}\left[ {\left( {2065 \times \frac{{23}}{{20}}} \right) - 1500} \right] \cr
& = {\text{Rs}}{\text{. }}\left( {2374.75 - 1500} \right) \cr
& = {\text{Rs}}{\text{. }}874.75 \cr} $$

Answer: Option C. -> Rs. 930
$$\eqalign{
& {\text{Principal = Rs 6000}} \cr
& {\text{Rate }}\% {\text{ = 10}}\% \cr
& {\text{Time (t) = 1}}\frac{1}{2}{\text{ years}} \cr} $$
$$\eqalign{
& {{\text{2}}^{{\text{nd}}}}{\text{ year CI = 660}} \cr
& {\text{6 months }}{{\text{2}}^{{\text{nd}}}}{\text{ year CI}} \cr
& {\text{ = }}\frac{{660}}{2}{\text{ = 330}} \cr
& {\text{Total CI}} \cr
& {\text{ = }}\left( {600 + 330} \right) \cr
& \,\, = 930 \cr} $$

Answer: Option C. -> 8%
$$\eqalign{
& {\text{SI for 1 year}} \cr
& {\text{ = Rs 260}} \cr
& {\text{SI for 2 year}} \cr
& {\text{ = 260}} \times {\text{2}} \cr
& {\text{ = Rs}}{\text{. 520 }} \cr
& {\text{Difference in (CI}} - {\text{SI)}} \cr
& \left( {540.80 - 520} \right){\text{ = Rs 20}}{\text{.8}} \cr
& {\text{Required rate % }} \cr
& {\text{ = }}\frac{{20.8}}{{260}} \times {\text{100}} \cr
& {\text{ = 8% }} \cr} $$

Answer: Option A. -> Rs. 5624.32
$$\eqalign{
& {\text{C}}{\text{.I}}{\text{. earned during }}{{\text{1}}^{{\text{st}}}}{\text{ year}} \cr
& {\text{= }}\,{\text{Rs}}{\text{.}}\left[ {5000\left( {1 + \frac{5}{{100}}} \right) - 5000} \right]{\text{ }} \cr
& = {\text{Rs}}{\text{. }}\left( {5250 - 5000} \right) \cr
& = {\text{Rs}}{\text{. 250}} \cr
& {\text{Amount after }}{{\text{1}}^{{\text{st}}}}{\text{ year}} \cr
& = {\text{Rs}}{\text{. }}\left( {5250 - 20\% {\text{ of }}250} \right) \cr
& = {\text{Rs}}{\text{.}}\left( {5250 - 50} \right){\text{ }} \cr
& {\text{= }}\,{\text{Rs}}{\text{.}}\,{\text{5200 }} \cr
& {\text{C}}{\text{.I}}{\text{. earned during }}{{\text{2}}^{{\text{nd}}}}{\text{ year}} \cr
& = {\text{Rs}}{\text{.}}\left[ {5200\left( {1 + \frac{5}{{100}}} \right) - 5200} \right]{\text{ }} \cr
& = {\text{Rs}}{\text{. }}\left( {5460 - 5200} \right) \cr
& = {\text{Rs}}{\text{.260 }} \cr
& {\text{Amount after }}{{\text{2}}^{{\text{nd}}}}{\text{ year}} \cr
& {\text{= Rs}}{\text{. }}\left( {5460 - 20\% {\text{ of }}260} \right) \cr
& {\text{= Rs}}{\text{. }}\left( {5460 - 52} \right) \cr
& = {\text{Rs}}{\text{.}}\,{\text{5408 }} \cr
& {\text{C}}{\text{.I}}{\text{. earned during }}{{\text{3}}^{{\text{rd}}}}{\text{ year}} \cr
& {\text{= Rs}}{\text{. }}\left[ {5408\left( {1 + \frac{5}{{100}}} \right) - 5408} \right] \cr
& = {\text{Rs}}{\text{. }}\left( {5678.40 - 5408} \right) \cr
& = {\text{Rs}}{\text{.}}\,{\text{270}}{\text{.40 }} \cr
& {\text{Amount after }}{{\text{3}}^{{\text{rd}}}}{\text{ year}} \cr
& = {\text{Rs}}{\text{. }}\left( {5678.40 - 20\% \,{\text{of }}270.40} \right) \cr
& = {\text{Rs}}{\text{. }}\left( {5678.40 - 54.08} \right) \cr
& = {\text{Rs}}{\text{. 5624}}{\text{.32}} \cr} $$

Answer: Option B. -> Rs. 1655
$$\eqalign{
& {\text{Principal = Rs. 5000}} \cr
& {\text{Time = 3 years}} \cr
& {\text{Rate = 10}}\% {\text{ = }}\frac{1}{{10}} \cr
& {\text{Principal}}\,\,\,\,\,\,\,{\text{Amount}} \cr
& \,\,\,\,\,\,\,\,\,\,{\text{10}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{11}} \cr
& \,\,\,\,\,\,\,\,\,\,{\text{10}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{11}} \cr
& \,\,\,\,\,\,\,\,\,\,{\text{10}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{11}} \cr
& \underbrace {\overline {\,\,\,\,\,\,1000\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{1331}}\,\,\,\,\,} }_{331{\text{ units}}} \cr
& \Rightarrow 1000{\text{ units = Rs 5000}} \cr
& \Rightarrow 1{\text{ units = Rs 5}} \cr
& \Rightarrow 331{\text{ units = 331}} \times {\text{5}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = Rs. 1655}} \cr} $$

Answer: Option A. -> Rs. 2400
$$\eqalign{
& {\text{Rate = 12}}\% \cr
& {\text{Time = 2 years}} \cr
& {\text{Effective rate of CI for 2 years}} \cr
& {\text{ = 12 + 12 + }}\frac{{12 \times 12}}{{100}} \cr
& = 25.44\,\% \cr
& {\text{Effective rate of SI for 2 years}} \cr
& {\text{ = 12}} \times 2{\text{ = 24}}\,\% \cr
& {\text{According to question,}} \cr
& {\text{Required SI}} \cr
& {\text{ = }}\frac{{2544}}{{25.44}} \times {\text{24}} = {\text{ Rs. 2400}} \cr
& {\text{Required sum}} \cr
& {\text{ = Rs. 2400}} \cr} $$

Answer: Option A. -> 45 years
$$\eqalign{
& P{\left( {1 + \frac{{\text{R}}}{{100}}} \right)^{15}} = 2P \cr
& \Rightarrow {\left( {1 + \frac{{\text{R}}}{{100}}} \right)^{15}} = 2 \cr
& {\text{Let }}P{\left( {1 + \frac{{\text{R}}}{{100}}} \right)^n} = 8P \cr
& \Rightarrow {\left( {1 + \frac{{\text{R}}}{{100}}} \right)^n} = 8 = {2^3} = {\left\{ {{{\left( {1 + \frac{{\text{R}}}{{100}}} \right)}^{15}}} \right\}^3} \cr
& \Rightarrow {\left( {1 + \frac{{\text{R}}}{{100}}} \right)^n} = {\left( {1 + \frac{{\text{R}}}{{100}}} \right)^{45}} \cr
& \Rightarrow n = 45 \cr
& \therefore {\text{Required time = 45 years}} \cr} $$