Practice MCQ Questions and Answer on Bankers Discount

Solution:

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

Solution:

 S.I. on Rs. 1800 = T.D. on Rs. 1872 P.W. of Rs. 1872 is Rs. 1800 Rs. 72 is S.I. on Rs. 1800 at 12% $$\eqalign{ & {\text{Time}} = \frac{{100 \times 72}}{{12 \times 1800}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{1}{3}\,{\text{years}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 4\,{\text{months}} \cr} $$

Solution:

 F = Rs. 498 TD = Rs. 18 PW = F - TD = 498 - 18 = Rs. 480 R = 5% $$\eqalign{ & TD = \frac{{PW \times TR}}{{100}} \cr & \Rightarrow 18 = \frac{{480 \times T \times 5}}{{100}} \cr & \Rightarrow 18 = 24 \times T{\text{ }} \cr & \Rightarrow {\text{ }}T{\text{ }} = \frac{{18}}{{24}} = \frac{3}{4}{\text{ years}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{12 \times 3}}{4}{\text{ months}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = 9 months}} \cr} $$

Solution:

 T = 4 years R = 5% Banker's Gain, BG = Rs. 200 $$\eqalign{ & TD = \frac{{BG \times 100}}{{TR}} \cr & \,\,\,\,\,\,\,\,\,\, = \frac{{200 \times 100}}{{4 \times 5}} \cr & \,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,1000 \cr & \cr & TD = \sqrt {PW \times BG} \cr & 1000 = \sqrt {PW \times 200} \cr & 1000000 = PW \times 200 \cr & PW = \frac{{1000000}}{{200}} \cr & \,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}5000 \cr} $$

Solution:

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

Solution:

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

Solution:

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

Solution:

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

Solution:

 $$\eqalign{ & BD\,{\text{for}}\,3\,{\text{years}} = {\text{Rs}}{\text{.}}\,1116 \cr & BD\,{\text{for}}\,4\,{\text{years}} = \frac{{1116}}{3} \times 4 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}1488 \cr & TD\,{\text{for}}\,4\,{\text{years}} = {\text{Rs}}{\text{.}}\,1200 \cr & F = \frac{{BD \times TD}}{{BD - TD}} \cr & \,\,\,\,\,\,\, = \frac{{1488 \times 1200}}{{1488 - 1200}} \cr & \,\,\,\,\,\,\, = \frac{{1488 \times 1200}}{{288}} \cr & \,\,\,\,\,\,\, = \frac{{124 \times 1200}}{{24}} \cr & \,\,\,\,\,\,\, = \frac{{124 \times 100}}{2} \cr & \,\,\,\,\,\,\, = 62 \times 100 \cr & \,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,6200 \cr} $$ ⇒ Rs. 1488 is the simple interest on Rs. 6200 for 4 years $$\eqalign{ & \Rightarrow 1488 = \frac{{6200 \times 4 \times R}}{{100}} \cr & \Rightarrow R = \frac{{1488 \times 100}}{{6200 \times 4}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{372 \times 100}}{{6200}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{372}}{{62}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 6\% \cr} $$

Solution:

 $$\eqalign{ & {\text{Sum}} = \frac{{B.D. \times T.D.}}{{B.D. - T.D.}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{B.D. \times T.D.}}{{B.G.}} \cr & \frac{{T.D.}}{{B.G.}} = \frac{{{\text{Sum}}}}{{B.D.}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{1650}}{{165}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = 10 \cr} $$ Thus, if B.G. is Rs. 1, T.D. = Rs. 10 If B.D. is Rs. 11, T.D. = Rs. 10 If B.D. is Rs. 165, $$\eqalign{ & T.D. = {\text{Rs}}{\text{.}}\,\frac{{10}}{{11}} \times 165 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,150 \cr} $$ And, B.G. = Rs. (165 - 150) = Rs. 15