Answer: Option A. -> Rs. 400
$$\eqalign{
& T.D. = \frac{{B.D. \times 100}}{{100 + \left( {R \times T} \right)}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\left[ {\frac{{420 \times 100}}{{100 + \left( {15 \times \frac{1}{3}} \right)}}} \right] \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left( {\frac{{420 \times 100}}{{105}}} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,400 \cr} $$

Answer: Option B. -> 4 months
$$\eqalign{
& {\text{S}}{\text{.I}}{\text{.}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{1600 = T}}{\text{.D}}{\text{.}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{1680}}{\text{.}} \cr
& \therefore {\text{Rs}}{\text{.}}\,{\text{1600}}\,{\text{is}}\,{\text{the}}\,{\text{P}}{\text{.W}}{\text{.}}\,{\text{of}}\,{\text{Rs}}{\text{.}}\,{\text{1680,}}\,{\text{i}}{\text{.e}}{\text{.,}} \cr
& {\text{Rs}}{\text{.}}\,{\text{80}}\,{\text{is}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{1600}}\,{\text{at}}\,{\text{15}}\% . \cr
& \therefore {\text{Time}} = \left( {\frac{{100 \times 80}}{{1600 \times 15}}} \right){\text{year}} \cr
& = \frac{1}{3}{\text{year}} = 4\,{\text{months}}{\text{.}} \cr} $$

Answer: Option C. -> Rs. 600
$$\eqalign{
& T.D. = {\frac{{B.G. \times 100}}{{Rate \times Time}}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left( {\frac{{24 \times 100}}{{10 \times 2}}} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,120 \cr
& \therefore P.W. = \frac{{100 \times T.D.}}{{Rate \times Time}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left( {\frac{{100 \times 120}}{{10 \times 2}}} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,600 \cr} $$

Answer: Option C. -> 12%
$$\eqalign{
& {\text{B}}{\text{.D}}{\text{.}}\,{\text{for}}\frac{3}{2}{\text{years}} = Rs.\,558 \cr
& {\text{B}}{\text{.D}}{\text{.}}\,{\text{for 2}}\,{\text{years}} \cr
& = Rs.\left( {558 \times \frac{2}{3} \times 2} \right) \cr
& = Rs.\,744 \cr
& {\text{T}}{\text{.D}}{\text{.}}\,{\text{for}}\,{\text{2}}\,{\text{years}} = Rs.\,600 \cr
& \therefore {\text{Sum}} = \frac{{B.D. \times T.D.}}{{B.D. - T.D.}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left( {\frac{{744 \times 600}}{{144}}} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,3100 \cr
& {\text{Thus,}}\,{\text{Rs}}{\text{.}}\,{\text{744}}\,{\text{is}}\,{\text{S}}{\text{.I}}{\text{.}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{3100}}\,{\text{for}}\,{\text{2}}\,{\text{years}}{\text{.}} \cr
& \therefore {\text{Rate}} = \left( {\frac{{100 \times 744}}{{3100 \times 2}}} \right)\% \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 12\% \cr} $$

Answer: Option C. -> Rs. 1020
$$\eqalign{
& T.D. = {\frac{{B.G. \times 100}}{{R \times T}}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left( {\frac{{270 \times 100}}{{12 \times 3}}} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,750 \cr
& \therefore B.D. = Rs.\left( {750 + 270} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,1020 \cr} $$

Answer: Option D. -> Rs. 96
$$\eqalign{
& T.D. = \sqrt {P.W. \times B.G.} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = \sqrt {576 \times 16} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = 96 \cr} $$

Answer: Option B. -> Rs. 108
$$\eqalign{
& {\text{P}}{\text{.W}}{\text{.}} = Rs.\,\left( {540 - 90} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,450 \cr
& \therefore {\text{S}}{\text{.I}}{\text{.}}\,{\text{on}}\,Rs.\,450 = Rs.\,90 \cr
& {\text{S}}{\text{.I}}{\text{.}}\,{\text{on}}\,Rs.\,540 \cr
& = Rs.\,\left( {\frac{{90}}{{450}} \times 540} \right) \cr
& = Rs.\,108 \cr
& \therefore {\text{B}}{\text{.D}}. = Rs.\,108 \cr} $$

Answer: Option C. -> 5%
$$\eqalign{
& {\text{Let}}\,{\text{T}}{\text{.D}}{\text{.}}\,{\text{be}}\,{\text{Re}}{\text{.}}\,{\text{1}}{\text{}} \cr
& {\text{Then,}}\,{\text{B}}{\text{.D}}. = Rs.\,\frac{{11}}{{10}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,1.10 \cr
& \therefore {\text{Sum}} = Rs.\,\left( {\frac{{1.10 \times 1}}{{1.10 - 1}}} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left( {\frac{{110}}{{10}}} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,11 \cr
& \therefore {\text{S}}{\text{.I}}{\text{.}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{11}}\,{\text{for}}\,{\text{2}}\,{\text{years}}\,{\text{is}}\,{\text{Rs}}{\text{.}}\,{\text{1}}{\text{.10}} \cr
& \therefore {\text{Rate}} = \left( {\frac{{100 \times 1.10}}{{11 \times 2}}} \right)\% \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 5\% \, \cr} $$

Answer: Option B. -> 129
$$\eqalign{
& B.G. = S.I.\,on\,T.D. \cr
& = {\text{Rs}}{\text{.}}\,\left( {120 \times 15 \times \frac{1}{2} \times \frac{1}{{100}}} \right) \cr
& = {\text{Rs}}{\text{.}}\,9 \cr
& B.D. - T.D. = Rs.\,9 \cr
& B.D. = {\text{Rs}}{\text{.}}\,\left( {120 + 9} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,129 \cr} $$

Answer: Option B. -> 121
$$\eqalign{
& T.D. = \sqrt {P.W.} \times B.G. \cr
& \therefore B.G. = \frac{{{{\left( {T.D.} \right)}^2}}}{{P.W.}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,\frac{{110 \times 110}}{{1100}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,11 \cr
& \therefore B.D. = T.D. + B.G. \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,110 + 11 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,121 \cr} $$