Answer: Option B. -> $${\text{7}}\frac{4}{9}$$ %
Principal = Rs. 12000
Rate % = 10%
Interest paid by the person in 5 years
$$\eqalign{
& = \frac{{12000 \times 10 \times 5}}{{100}} \cr
& = {\text{Rs}}{\text{. 6000}} \cr} $$
Interest received by the person after 3 years
$$\eqalign{
& = {\text{Rs}}{\text{. }}\left( {6000 - 3320} \right) \cr
& = {\text{Rs}}{\text{. 2680}} \cr
& {\text{By using formula,}} \cr
& {\text{Rate}}\% \cr
& {\text{ = }}\frac{{2680}}{{12000}} \times \frac{{100}}{3} \cr
& = \frac{{67}}{9} \cr
& = 7\frac{4}{9}\% \cr
& {\text{Hence required rate}}\% \cr
& {\text{ = 7}}\frac{4}{9}\% \cr} $$

Answer: Option A. -> $$3\frac{1}{3}$$ %
$$\eqalign{
& {\text{Let sum}} = x \cr
& {\text{Then,}} \cr
& {\text{S}}{\text{.I}}{\text{.}} = \frac{x}{9}. \cr
& {\text{Let rate}} = {\text{R}}\% \,{\text{and}} \cr
& {\text{time}} = {\text{R}}\,{\text{years}}{\text{.}} \cr
& \therefore \left( {\frac{{x \times {\text{R}} \times {\text{R}}}}{{100}}} \right) = \frac{x}{9} \cr
& \Rightarrow {{\text{R}}^2} = \frac{{100}}{9} \cr
& \Rightarrow {\text{R}} = \frac{{10}}{3} = 3\frac{1}{3} \cr
& {\text{Hence, rate}} = 3\frac{1}{3}\% \cr} $$

Answer: Option B. -> 5%
Let rate of interest = R%
According to the question,
$$\eqalign{
& \frac{{500 \times 4 \times {\text{R}}}}{{100}} + \frac{{600 \times 3 \times {\text{R}}}}{{100}} = 190 \cr
& \Rightarrow 20{\text{R + 18R = 190}} \cr
& \Rightarrow 38{\text{R = 190}} \cr
& \Rightarrow {\text{R = 5% }} \cr} $$
Hence required rate % = 5%
Alternate
Note : In such type of questions to save your valuable time follow the given below method.
Let rate of interest = 1%
$$\eqalign{
& {\text{Case (I): Interest (}}{{\text{I}}_1}{\text{)}} \cr
& {\text{ = }}\frac{{500 \times 4 \times 1}}{{100}} \cr
& = 20 \cr
& {\text{Case (II): Interest (}}{{\text{I}}_2}{\text{)}} \cr
& {\text{ = }}\frac{{{\text{600}} \times 3 \times 1}}{{100}} \cr
& = 18 \cr} $$
According to the question,
Interest    
    Rate %
  38  
  1  
  ↓×5  
  ↓×5  
  190  
  5%  
Hence required rate % = 5%

Answer: Option D. -> 12 years
$$\eqalign{
& {\text{P}} + \frac{{P \times {\text{r}} \times {\text{t}}}}{{100}} = 3{\text{P}} \cr
& \Rightarrow 1 + \frac{{rt}}{{100}} = 3 \cr
& \Rightarrow \frac{{{\text{rt}}}}{{100}} = 2 \cr
& \Rightarrow {\text{r}} = \frac{{2 \times 100}}{8} = 25\% \cr
& {\text{so, }}\,\left( {1 + \frac{{{\text{rt}}}}{{100}}} \right) = 4 \cr
& \Rightarrow \frac{{{\text{rt}}}}{{100}} = 3 \cr
& \Rightarrow {\text{t}} = \frac{{3 \times 100}}{{25}} \cr
& \Rightarrow {\text{t}} = 12\,{\text{years}} \cr} $$

Answer: Option B. -> 20 years
$$\eqalign{
& {\text{Let sum}} = {\text{Rs}}{\text{. }}x \cr
& {\text{Then,}} \cr
& {\text{S}}{\text{.I}}{\text{.}} = 30\% \,{\text{of}}\,{\text{Rs}}{\text{.}}\,x \cr
& \,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\frac{{3x}}{{10}} \cr
& {\text{Time}} = 6\,{\text{years}}{\text{.}} \cr
& \therefore {\text{Rate}} = \left( {\frac{{100 \times 3x}}{{10 \times x \times 6}}} \right)\% \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 5\% \cr
& {\text{Now, sum}} = {\text{Rs}}{\text{. }}x \cr
& {\text{S}}{\text{.I}}{\text{.}} = {\text{Rs}}{\text{. }}x \cr
& {\text{Rate}} = 5\% \cr
& \therefore {\text{Time}} = \left( {\frac{{100 \times x}}{{x \times 5}}} \right){\text{years}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 20\,{\text{years}} \cr} $$

Answer: Option C. -> 21 years
$$\eqalign{
& \frac{{\left( {n - 1} \right)}}{{{t_1}}} = \frac{{\left( {m - 1} \right)}}{{{t_2}}} \cr
& \frac{1}{7} = \frac{3}{{{t_2}}} \cr
& {t_2} = 21{\text{ years}} \cr} $$

Answer: Option D. -> 6 : 3 : 2
Let the three amounts be Rs. x, Rs. y and Rs. z,
Then,
$$\eqalign{
& \frac{{x \times 10 \times 6}}{{100}} = \frac{{y \times 12 \times 10}}{{100}} = \frac{{z \times 15 \times 12}}{{100}} \cr
& \Rightarrow 60x = 120y = 180z \cr
& \Rightarrow x = 2y = 3z = k(say) \cr
& \Rightarrow x = k,y = \frac{k}{2},z = \frac{k}{3} \cr
& \Rightarrow x:y:z = k:\frac{k}{2}:\frac{k}{3} \cr
& \Rightarrow x:y:z = 1:\frac{1}{2}:\frac{1}{3} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 6:3:2 \cr} $$

Answer: Option B. -> 6% per year
$$\eqalign{
& {\text{Let sum = }}x \cr
& {\text{Interest = }}\frac{3}{4}x{\text{ }} \cr
& {\text{Interest = }}\frac{{{\text{PTR }}}}{{100}} \cr
& \Rightarrow \frac{3}{4}x = \frac{{x \times {\text{R}} \times 12.5}}{{100}} \cr
& {\text{R = 6}}\% \cr} $$

Answer: Option C. -> 12%
$$\eqalign{
& {\text{t}} = {\text{1 month = }}\frac{1}{{12}}{\text{year}} \cr
& {\text{SI = 1 paisa = Rs}}{\text{. }}\frac{1}{{100}} \cr
& {\text{r}}\% = \frac{{{\text{SI}} \times {\text{100}}}}{{{\text{P}} \times {\text{T}}}} = \frac{{1 \times 100 \times 12}}{{100 \times 1 \times 1}} \cr
& {\text{r}}\% = 12\% \cr} $$

Answer: Option C. -> Rs. 6600
Let total capital be Rs. x
Then,
  $$ \Rightarrow \left( {\frac{x}{3} \times \frac{7}{{100}} \times 1} \right) + \left( {\frac{x}{4} \times \frac{8}{{100}} \times 1} \right) + $$       $$\left( {\frac{{5x}}{{12}} \times \frac{{10}}{{100}} \times 1} \right)$$    $$ = 561$$
$$\eqalign{
& \Rightarrow \frac{{7x}}{{300}} + \frac{x}{{50}} + \frac{x}{{24}} = 561 \cr
& \Rightarrow 51x = \left( {561 \times 600} \right) \cr
& \Rightarrow x = \left( {\frac{{561 \times 600}}{{51}}} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = 6600 \cr} $$