Answer: Option E. -> None of these
$$\eqalign{
& {\text{Principal}} \cr
& {\text{ = Rs}}{\text{.}}\left( {\frac{{100 \times 1000}}{{5 \times 4}}} \right) \cr
& = {\text{Rs}}{\text{. 5}}000 \cr
& {\text{Now, P = Rs}}{\text{.}}\,10000, \cr
& {\text{T = 2 years,}} \cr
& {\text{R = 5% }} \cr
& {\text{Amount}} \cr
& {\text{ = Rs}}{\text{.}}\left[ {10000 \times {{\left( {1 + \frac{5}{{100}}} \right)}^2}} \right] \cr
& = {\text{Rs}}{\text{.}}\left( {10000 \times \frac{{21}}{{20}} \times \frac{{21}}{{20}}} \right) \cr
& = {\text{Rs}}. 11025 \cr
& \therefore {\text{C}}{\text{.I}}{\text{. = }}\left( {11025 - 10000} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}. 1025 \cr} $$

Answer: Option C. -> Rs. 2522
The interest is compounded quarterly,
$$\therefore R = \frac{{20}}{4} = 5\% $$
Time = 3 quarters
$$\eqalign{
& \therefore C.I. = P\left[ {{{\left( {1 + \frac{R}{{100}}} \right)}^T} - 1} \right] \cr
& = 16000\left[ {{{\left( {1 + \frac{5}{{100}}} \right)}^3} - 1} \right] \cr
& = 16000\left[ {{{\left( {\frac{{21}}{{20}}} \right)}^3} - 1} \right] \cr
& = 16000\left( {\frac{{9261 - 8000}}{{8000}}} \right) \cr
& = 16000 \times \frac{{1261}}{{8000}} \cr
& = {\text{Rs}}{\text{.}}\,\,2522 \cr} $$

Answer: Option C. -> Rs. 16400
$$\eqalign{
& \Rightarrow {\text{C}}{\text{.I}}{\text{.}} - {\text{S}}{\text{.I}}{\text{.}} = 41 \cr
& \Rightarrow {\text{C}}{\text{.I}}{\text{.}} - {\text{S}}{\text{.I}}{\text{.}} = P{\left( {\frac{r}{{100}}} \right)^2} \cr
& \Rightarrow 41 = P\left( {\frac{{25}}{{10000}}} \right) \cr
& \Rightarrow P = 16400 \cr} $$

Answer: Option D. -> Rs. 5000
Let the total sum of money invested by Shashi be Rs. x
In scheme A money invested at simple interest for 6 years at a rate of 12% p.a.
$$\therefore \frac{2}{3}{\text{of }}x \times \frac{{12 \times 6}}{{100}} = \frac{{48x}}{{100}}....(i)$$
In scheme B money at compound interest for 2 year at a rate of 10% p.a.
$$\eqalign{
& \frac{x}{3}{\left( {1 + \frac{{10}}{{100}}} \right)^2} - \frac{x}{3} \cr
& \Rightarrow \frac{x}{3}{\left( {1 + \frac{{10}}{{100}}} \right)^2} - \frac{x}{3} = \frac{{7x}}{{100}} \cr} $$
According to given information we get
$$\eqalign{
& \Rightarrow \frac{{48x}}{{100}} + \frac{{7x}}{{100}} = 2750 \cr
& \Rightarrow 55x = 2750 \times 100 \cr
& \Rightarrow x = \frac{{2750 \times 100}}{{55}} \cr
& \Rightarrow x = Rs.\,5000 \cr} $$

Answer: Option C. -> Rs. 500
$$\eqalign{
& 10\% = \frac{1}{{10}} \cr
& {\text{Let P}} = {\text{ }}{\left( {10} \right)^2} = 100 \cr
& {\text{Total CI = 21 unit = 525}} \cr
& {\text{1 unit = 25}} \cr
& {\text{P}} = {\text{ 100 unit }} \cr
& {\text{ = 100}} \times {\text{25}} = {\text{2500}} \cr
& {\text{New Time = 4 years}} \cr
& {\text{and new rate = 5}}\% \cr
& {\text{SI = }}\frac{{2500 \times 4 \times 5}}{{100}}{\text{ }} \cr
& {\text{SI = Rs. 500}} \cr} $$

Answer: Option B. -> Rs. 2000
$$\eqalign{
& {\text{R}}\% {\text{ = }}\frac{{2662 - 2420}}{{2420}} \times 100 \cr
& = \frac{{242}}{{2420}} \times 100 \cr
& = 10\% \cr
& {\text{2 years CI}}\% \cr
& {\text{ = 10 + 10 + }}\frac{{10 \times 10}}{{100}} \cr
& = 21\% \cr
& {\text{So, 121}}\% {\text{ = 2420}} \cr
& \Rightarrow {\text{100}}\% {\text{ = 2000}} \cr} $$

Answer: Option C. -> Rs. 16000
$$\eqalign{
& {\text{Rate of interest = 5}}\% {\text{ p}}{\text{.c}}{\text{.p}}{\text{.a}}{\text{.}} \cr
& {\text{If time 3 years than CI}} - {\text{SI}} \cr
& {\text{ = }}P\left[ {{{\left( {\frac{R}{{100}}} \right)}^3} + 3{{\left( {\frac{R}{{100}}} \right)}^2}} \right] \cr
& \Rightarrow 122 = P\left[ {{{\left( {\frac{5}{{100}}} \right)}^3} + 3{{\left( {\frac{5}{{100}}} \right)}^2}} \right] \cr
& \Rightarrow 122 = P\left( {\frac{{125}}{{1000000}} + \frac{{75}}{{10000}}} \right) \cr
& \Rightarrow 122 = P\left[ {\frac{{125 + 7500}}{{1000000}}} \right] \cr
& \Rightarrow 122 = P\left[ {\frac{{7525}}{{1000000}}} \right] \cr
& \Rightarrow P = \frac{{122 \times 1000000}}{{7625}} \cr
& \Rightarrow P = {\text{Rs}}{\text{. 16000}} \cr} $$

Answer: Option A. -> Rs. 10000
Interest for 2 years at the rate of 15%
$$\eqalign{
& {\text{ = 15 + 15 + }}\frac{{15 \times 15}}{{100}} \cr
& = 32.25\% \cr
& {\text{According to question,}} \cr
& {\text{32}}{\text{.25}}\% {\text{ = 3225}} \cr
& {\text{100}}\% {\text{ = }}\frac{{3225}}{{32.25}} \times 100 \cr
& = 100 \times 100 = 10000 \cr} $$

Answer: Option A. -> Rs. 1856.40
$$\eqalign{
& {\text{10}}\% {\text{ = }}\frac{1}{{10}} \cr
& {\text{Principal}}\,\,\,\,\,\,\,{\text{Amount}} \cr
& \,\,\,\,\,\,\,{\text{10}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,11 \cr
& \,\,\,\,\,\,\,{\text{10}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,11 \cr
& \,\,\,\,\,\,\,{\text{10}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,11 \cr
& \,\,\,\,\,\,\,{\text{10}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,11 \cr
& \underbrace {\overline {\,\,\,10000\,\,\,\,\,\,{\text{:}}\,\,\,\,\,{\text{14641}}\,\,\,} }_{{\text{CI = 4641}}} \cr
& \because {\text{Principal = 10000 units}} \cr
& {\text{ = Rs}}{\text{. 4000 (given)}} \cr
& {\text{1 unit = }}\frac{2}{5} \cr
& {\text{CI = 4641 unit}} \cr
& {\text{ = Rs}}{\text{. }}\left( {\frac{2}{5} \times 4641} \right) \cr
& = {\text{Rs}}{\text{. }}1856.40 \cr} $$

Answer: Option B. -> 4 years
$$\eqalign{
& {\text{Let principal = P}} \cr
& {\bf{Case (I)}} \cr
& {\text{Time = 3 years,}} \cr
& {\text{Amount = 8P}} \cr
& \Rightarrow 8{\text{P = P}}{\left( {1 + \frac{{\text{R}}}{{100}}} \right)^3} \cr
& \Rightarrow {\left( 2 \right)^3} = {\left( {1 + \frac{{\text{R}}}{{100}}} \right)^3} \cr
& {\text{Taking cube root of both sides,}} \cr
& \Rightarrow {\text{2 = }}\left( {1 + \frac{{\text{R}}}{{100}}} \right) \cr
& \Rightarrow {\text{R = 100 }}\% \cr
& {\bf{Case (II)}} \cr
& {\text{Let after t years it will be 16 times}} \cr
& \Rightarrow 16{\text{P = P}}{\left( {1 + \frac{{\text{R}}}{{100}}} \right)^{\text{t}}} \cr
& \Rightarrow 16 = {\left( 2 \right)^{\text{t}}} \cr
& \Rightarrow {\left( 2 \right)^4} = {\left( 2 \right)^{\text{t}}} \cr
& \Rightarrow {\text{t}} = 4 \cr
& {\text{Hence required time}} \cr
& {\text{(t) = 4 years}} \cr} $$