Answer: Option B. -> 3 years
$$\eqalign{
& {\text{By using formula }} \cr
& \Leftrightarrow \frac{{{\text{3000}} \times 12 \times {\text{T}}}}{{100}} = 1080 \cr
& \Leftrightarrow {\text{T = }}\frac{{108}}{{36}}{\text{ = 3 years}} \cr} $$

Answer: Option D. -> $$12\frac{1}{2}$$ %
Money is double itself means interest is equal to money.
$$\eqalign{
& {\text{P = }}\frac{{{\text{P}} \times {\text{8}} \times {\text{r}}}}{{100}} \cr
& \Rightarrow {\text{r = }}\frac{{100}}{8} \cr
& \Rightarrow {\text{r = 12}}\frac{1}{2}\% \cr} $$

Answer: Option B. -> 8%
$$\eqalign{
& {\bf{Case - I:}} \cr
& {\text{SI}}\% = {\text{R}}\% \times {\text{t}} \cr
& {\text{SI}}\% = {\text{5}}\% \times {\text{8}} \cr
& = {\text{40}}\% \cr
& {\bf{Case - II:}} \cr
& {\text{SI}}\% = {\text{5}} \times {\text{r}}\% {\text{ }} \cr
& {\text{According to the question}} \cr
& \Rightarrow {\text{40}}\% = {\text{5}} \times {\text{r}}\% \cr
& \Rightarrow {\text{r}}\% = {\text{8}}\% \cr} $$

Answer: Option C. -> 5 years
$$\eqalign{
& {\text{Let principal and SI is}} \cr
& {\text{ = }}10x,{\text{ }}3x{\text{ }} \cr
& {\text{and time is = }}t \cr
& \Rightarrow 3x = \frac{{10x \times 6 \times t}}{{100}} \cr
& \Rightarrow t = 5\,{\text{years}} \cr} $$

Answer: Option C. -> 10%
  Let Sum be Rs. x and Let S.I. = Rs. x
$$\eqalign{
& {\text{Time}} = 10\,{\text{years}} \cr
& \therefore {\text{Rate}} = \frac{{{\text{S}}{\text{.I}}{\text{.}} \times {\text{100}}}}{{{\text{Principal}} \times {\text{Time}}}} \cr
& = \frac{{x \times 100}}{{x \times 10}} \cr
& = 10\% \,{\text{per}}\,{\text{annum}}{\text{.}} \cr} $$

Answer: Option B. -> 12%
$$\eqalign{
& {\text{Rate}} = \frac{{{\text{S}}{\text{.I}}{\text{.}} \times {\text{100}}}}{{{\text{Principal}} \times {\text{Time}}}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{5400 \times 100}}{{15000 \times 3}} \cr
& = 12\% \,{\text{Per annum}}{\text{.}} \cr} $$

Answer: Option A. -> $${\text{21}}\frac{3}{7}$$ %
$$\eqalign{
& {\text{S}}{\text{.I}}{\text{. of 2}}{\text{.5 years}} \cr
& {\text{ = 5500}} - {\text{4000}} \cr
& {\text{ = 1500}} \cr
& {\text{S}}{\text{.I}}{\text{. of 2 years}} \cr
& {\text{ = }}\frac{{1500}}{{2.5}} \times {\text{2}} \cr
& {\text{ = 1200}} \cr
& {\text{So, Principal}} \cr
& {\text{ = 4000}} - {\text{SI of 2 years}} \cr
& \Rightarrow {\text{Principal = 4000}} - 1200 \cr
& \Rightarrow {\text{Principal = 2800}} \cr
& {\text{r}}\% {\text{ = }}\frac{{1200}}{{2800 \times 2}} \times {\text{100}} \cr
& \,\,\,\,\,\,\,\,{\text{ = 21}}\frac{3}{7}\% \cr} $$

Answer: Option C. -> Rs. 3882
S.I for 1 year = 5832 – 5182 = Rs. 650
S.I for 2 years = Rs. 1300
P = 5182 – 1300
= Rs. 3882

Answer: Option A. -> Rs. 1200
Let the amount invested in scheme A be Rs. x and that in B be Rs. 3x.
Then,
$$\eqalign{
& = \frac{{x \times 4 \times 8}}{{100}} + \frac{{3x \times 2 \times 13}}{{100}} = 1320 \cr
& or,\,\frac{{32x}}{{100}} + \frac{{78x}}{{100}} = 1320 \cr
& or,\,\frac{{110x}}{{110}} = 1320 \cr
& \therefore x = \frac{{1320 \times 100}}{{110}} \cr
& = {\text{Rs}}{\text{. 1200}}. \cr} $$

Answer: Option B. -> Rs. 137745.02
Let Ram get Rs. x and
Shyam get Rs. (260200 - x)
Then Amount get by Ram after 3 years
$${\text{ = }}x \times {\left( {1 + \frac{4}{{100}}} \right)^3}$$
and Amount get by Shyam after 6 years
$$ = \left( {260200 - x} \right) \times {\left( {1 + \frac{4}{{100}}} \right)^6}$$
But both get equal amount
$$\therefore x \times {\left( {1 + \frac{4}{{100}}} \right)^3} = \left( {260200 - x} \right) \times $$       $${\left( {1 + \frac{4}{{100}}} \right)^6}$$
$$\eqalign{
& \Rightarrow \frac{x}{{2600200 - x}} = \frac{{17576}}{{15625}} \cr
& \Rightarrow 15625x = 4573275200 - 17576x \cr
& \Rightarrow 33201x = 4573275200 \cr
& \Rightarrow x = 137745.022 \cr} $$
So, Ram will get Rs. 137745.022