Practice MCQ Questions and Answer on Bankers Discount

Solution:

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

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:

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

Solution:

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

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:

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

Solution:

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

Solution:

 $$\eqalign{ & {\text{Sum}} = \frac{{B.D. \times T.D.}}{{B.D. - T.D.}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,\frac{{120 \times 110}}{{120 - 110}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,1320 \cr} $$ Since B.D. is S.I. on sum due, so S.I. on Rs. 1320 for 8 months is Rs. 120. $$\eqalign{ & {\text{Rate}} = \frac{{100 \times 120}}{{1320 \times \frac{2}{3}}}\,\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{150}}{{11}}\,\% \cr} $$

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:

 $$\eqalign{ & F = \frac{{BD \times TD}}{{(BD - TD)}} \cr & \,\,\,\,\,\,\, = \frac{{36 \times 30}}{{(36 - 30)}} \cr & \,\,\,\,\,\,\, = \frac{{36 \times 30}}{6} \cr & \,\,\,\,\,\,\, = 36 \times 5 \cr & \,\,\,\,\,\,\, = {\text{ Rs}}{\text{. }}180 \cr} $$