Bankers Discount - Aptitude MCQ Questions and Solutions with Explanations

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

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

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

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

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

$$\eqalign{ & TD = \frac{{BG{\text{ }} \times 100}}{{TR}} \cr & \,\,\,\,\,\,\,\,\,\,\, = \frac{{540 \times 100}}{{6 \times 12}} \cr & \,\,\,\,\,\,\,\,\,\,\, = \frac{{90 \times 100}}{{12}} \cr & \,\,\,\,\,\,\,\,\,\,\, = \frac{{15 \times 100}}{2} \cr & \,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,750 \cr & BG = BD - TD \cr & \Rightarrow 540 = BD - 750 \cr & \Rightarrow BD = 540 + 750 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 1290 \cr} $$

Since the compound interest is taken here,
$$\eqalign{ & PW{\text{ }}{\left( {1 + \frac{5}{{100}}} \right)^2} = 1764 \cr & PW\,{\left( {1 + \frac{1}{{20}}} \right)^2} = 1764 \cr & PW\,{\left( {\frac{{21}}{{20}}} \right)^2} = 1764 \cr & PW \times \frac{{441}}{{400}} = 1764 \cr & \Rightarrow PW = \frac{{1764 \times 400}}{{441}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 4 \times 400 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,1600 \cr} $$

$$\eqalign{ & BG = \frac{{{{(TD)}^2}}}{{PW}} \cr & \,\,\,\,\,\,\,\,\,\,\,\, = \frac{{{{20}^2}}}{{400}} \cr & \,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,1 \cr & BG = BD - TD \cr & \Rightarrow 1 = BD - 20 \cr & \Rightarrow BD = 1 + 20 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,21 \cr} $$

F = Rs. 3000
R = 10%
Date on which the bill is drawn = 14^th July at 5 months
Nominally Due Date = 14^th December
Legally Due Date = 14^th December + 3 days = 17^th December
Date on which the bill is discounted = 5^th October
Unexpired Time
= [6^th to 31^th of October] + [30 Days in November] + [1^th to 17^th 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 = $$\frac{{{\text{FTR}}}}{{100}}$$
$$\eqalign{ & = \frac{{3000 \times \frac{1}{5} \times 10}}{{100}} \cr & = 30 \times \frac{1}{5} \times 10 \cr & = {\text{Rs}}{\text{.}}\,60 \cr} $$

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