Answer: Option D. -> Rs. 120
$$\eqalign{
& F = {\text{Rs}}{\text{.}}\,2520 \cr
& T = 6\,{\text{months}} = \frac{1}{2}\,{\text{years}} \cr
& R = 10\% \cr
& TD = \frac{{FTR}}{{100 + \left( {TR} \right)}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\, = \frac{{2520 \times \frac{1}{2} \times 10}}{{100 + \left( {\frac{1}{2} \times 10} \right)}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\, = \frac{{1260 \times 10}}{{100 + 5}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\, = \frac{{12600}}{{105}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\, = \frac{{2520}}{{21}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,120 \cr} $$

Answer: Option A. -> Rs. 76
$$\eqalign{
& BG = \frac{{{{(TD)}^2}}}{{PW}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\, = \frac{{{{72}^2}}}{{1296}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\, = \frac{{72 \times 72}}{{1296}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\, = \frac{{12 \times 12}}{{36}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\, = \frac{{12}}{3} \cr
& \,\,\,\,\,\,\,\,\,\,\,\, = {\text{ Rs}}{\text{. }}4 \cr
& BG = BD - TD \cr
& \Rightarrow 4 = BD - 72 \cr
& \Rightarrow BD = 72 + 4 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,76 \cr} $$

Answer: Option A. -> Rs. 258
$$\eqalign{
& TD = {\text{Rs}}{\text{.}}\,240 \cr
& T = 6\,{\text{months}}\, = \frac{1}{2}\,{\text{year}} \cr
& R = 15\% \cr
& TD = \frac{{BG \times 100}}{{TR}} \cr
& \Rightarrow 240 = \frac{{BG \times 100}}{{\left( {\frac{1}{2} \times 15} \right)}} \cr
& BG = \frac{{240 \times 15}}{{100 \times 2}} \cr
& \,\,\,\,\,\,\,\,\,\,\, = \frac{{120 \times 15}}{{100}} \cr
& \,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,18 \cr
& BG = BD - TD \cr
& \Rightarrow 18 = BD - 240 \cr
& \Rightarrow BD = 18 + 240 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,258 \cr} $$

Answer: Option A. -> $$3\frac{1}{3}\,\% $$
$$\eqalign{
& BD{\text{ for }}1\frac{1}{2}{\text{ years}} = {\text{Rs}}{\text{.}}\,\,120 \cr
& BD{\text{ for }}2{\text{ years}} = 120 \times \frac{2}{3} \times 2 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,160 \cr
& TD\,{\text{for}}\,2\,{\text{year}} = Rs.\,150 \cr
& F = \frac{{BD \times TD}}{{\left( {BD - TD} \right)}} \cr
& \,\,\,\,\,\,\,\, = \frac{{160 \times 150}}{{160 - 150}} \cr
& \,\,\,\,\,\,\,\, = \frac{{160 \times 150}}{{10}} \cr
& \,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,2400 \cr} $$
⇒ Rs.160 is the simple interest on Rs. 2400 for 2 years
$$\eqalign{
& \Rightarrow 160 = \frac{{2400 \times 2 \times R}}{{100}} \cr
& \Rightarrow R = \frac{{160 \times 100}}{{2400 \times 2}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{160}}{{48}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{20}}{6} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{10}}{3} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = 3\frac{1}{3}\,\% \cr} $$

Answer: Option D. -> Rs. 34
$$\eqalign{
& BG = \frac{{{{(TD)}^2}}}{{PW}} \cr
& \,\,\,\,\,\,\,\,\,\,\, = \frac{{{{(340)}^2}}}{{3400}} \cr
& \,\,\,\,\,\,\,\,\,\,\, = \frac{{340 \times 340}}{{3400}} \cr
& \,\,\,\,\,\,\,\,\,\,\, = \frac{{340}}{{10}} \cr
& \,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,34 \cr} $$

Answer: Option A. -> Rs. 360
$$\eqalign{
& \frac{{B.D. \times T.D.}}{{B.D. - T.D.}} \cr
& = Rs.\,\left( {\frac{{72 \times 60}}{{72 - 60}}} \right) \cr
& = Rs.\,\left( {\frac{{72 \times 60}}{{12}}} \right) \cr
& = Rs.\,360 \cr} $$

Answer: Option D. -> Rs. 50
$$\eqalign{
& T.D. = \frac{{B.G. \times 100}}{{R \times T}} \cr
& = Rs.\,\left( {\frac{{6 \times 100}}{{12 \times 1}}} \right) \cr
& = Rs.\,50 \cr} $$

Answer: Option C. -> Rs. 16
$$\eqalign{
& B.G. = \frac{{{{\left( {T.D.} \right)}^2}}}{{P.W.}} \cr
& = Rs.\,\left( {\frac{{160 \times 160}}{{1600}}} \right) \cr
& = Rs.\,16 \cr} $$

Answer: Option B. -> Rs. 37.62
$$\eqalign{
& B.G. = \frac{{{{\left( {T.D.} \right)}^2}}}{{P.W.}} \cr
& = Rs.\,\left( {\frac{{36 \times 36}}{{800}}} \right) \cr
& = Rs.\,1.62 \cr
& \therefore B.D. = \left( {T.D. + B.G.} \right) \cr
& = Rs.\,\left( {36 + 1.62} \right) \cr
& = Rs.\,37.62 \cr} $$

Answer: Option B. -> $$9\frac{1}{{9}}$$ %
$$\eqalign{
& {\text{Let,}}\,{\text{B}}{\text{.D}}{\text{.}} = \operatorname{Rs} .\,{\kern 1pt} 1 \cr
& {\text{Then,}}{\kern 1pt} \,{\text{B}}{\text{.G}}{\text{.}} = \operatorname{Re} .\,{\kern 1pt} \frac{3}{{25}} \cr
& \therefore {\text{T}}{\text{.D}}{\text{. = }}\left( {{\text{B}}{\text{.D}}{\text{. - B}}{\text{.G}}{\text{.}}} \right) \cr
& = \operatorname{Rs} .\,{\kern 1pt} \left( {1 - \frac{3}{{25}}} \right) \cr
& = \operatorname{Rs} .{\kern 1pt} \,\frac{{22}}{{25}} \cr
& {\text{Sum}} = {\frac{{1 \times {\frac{{22}}{{25}}} }}{{1 - {\frac{{22}}{{25}}} }}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}{\kern 1pt} \,\frac{{22}}{3} \cr
& {\text{S}}{\text{.I}}{\text{.}}{\kern 1pt} \,{\text{on}}{\kern 1pt} {\text{Rs}}{\text{.}}\,{\kern 1pt} \frac{{22}}{3}{\kern 1pt} {\text{for}}\,{\kern 1pt} 1\frac{1}{2}\,{\text{years}}\,{\kern 1pt} {\text{is}}\,\operatorname{Rs} .\,{\kern 1pt} 1 \cr
& \therefore {\text{Rate}} = \left( {\frac{{100 \times 1}}{{\frac{{22}}{3} \times \frac{3}{2}}}} \right)\% {\kern 1pt} \cr
& {\kern 1pt} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 9\frac{1}{9}\% \cr} $$