Practice MCQ Questions and Answer on Bankers Discount

Solution:

 $$\eqalign{ & T.D. = \frac{{B.G. \times 100}}{{R \times T}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{10 \times 100}}{{10 \times 2}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,50 \cr} $$

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:

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

Solution:

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

Solution:

 $$\eqalign{ & TD = \frac{{BG \times 100}}{{TR}} \cr & \,\,\,\,\,\,\,\,\,\,\, = \frac{{20 \times 100}}{{10}} \cr & \,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,200 \cr} $$

Solution:

 $$\eqalign{ & {\text{Sum}} = \frac{{B.D. \times T.D.}}{{B.D. - T.D.}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{120 \times 110}}{{120 - 110}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = 1320 \cr} $$

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

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:

 $$\eqalign{ & F = {\text{Rs}}{\text{.}}\,8100 \cr & R = 5\% \cr & T = 3\,{\text{months}} = \frac{1}{4}\,{\text{years}} \cr & BD = \frac{{FTR}}{{100}} \cr & \,\,\,\,\,\,\,\,\,\,\,\, = \frac{{8100 \times \frac{1}{4} \times 5}}{{100}} \cr & \,\,\,\,\,\,\,\,\,\,\,\, = \frac{{2025}}{{20}} \cr & \,\,\,\,\,\,\,\,\,\,\,\, = \frac{{405}}{4} \cr & \,\,\,\,\,\,\,\,\,\,\,\, = {\text{ Rs}}{\text{.}}\,101.25 \cr & TD = \frac{{FTR}}{{100 + (TR)}} \cr & \,\,\,\,\,\,\,\,\,\,\, = \frac{{8100 \times \frac{1}{4} \times 5}}{{100 + \left( {\frac{1}{4} \times 5} \right)}} \cr & \,\,\,\,\,\,\,\,\,\,\, = \frac{{2025 \times 5}}{{100 + \left( {\frac{5}{4}} \right)}} \cr & \,\,\,\,\,\,\,\,\,\,\, = \frac{{2025 \times 5 \times 4}}{{400 + 5}} \cr & \,\,\,\,\,\,\,\,\,\,\, = \frac{{2025 \times 5 \times 4}}{{405}} \cr & \,\,\,\,\,\,\,\,\,\,\, = \frac{{405 \times 5 \times 4}}{{81}} \cr & \,\,\,\,\,\,\,\,\,\,\, = \frac{{45 \times 5 \times 4}}{9} \cr & \,\,\,\,\,\,\,\,\,\,\, = 5 \times 5 \times 4 \cr & \,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,100 \cr & BD - TD = \,101.25 - 100 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,1.25 \cr} $$

Solution:

 F = Rs. 3000 R = 10% Date on which the bill is drawn = 14th July at 5 months Nominally Due Date = 14th December Legally Due Date = 14th December + 3 days = 17th December Date on which the bill is discounted = 5th October Unexpired Time = [6th to 31th of October] + [30 Days in November] + [1th to 17th of December] = 26 + 30 + 17 = 73 Days $$\eqalign{ & = \frac{{73}}{{365}}\,{\text{year}} \cr & {\text{ = }}\frac{1}{5}\,{\text{year}} \cr} $$ Banker's Discount = Simple Interest on the face value of the bill for unexpired time = $$\frac{{{\text{FTR}}}}{{100}}$$ $$\eqalign{ & = \frac{{3000 \times \frac{1}{5} \times 10}}{{100}} \cr & = 30 \times \frac{1}{5} \times 10 \cr & = {\text{Rs}}{\text{.}}\,60 \cr} $$