Bankers Discount(Quantitative Aptitude > Discount ) Questions and Answers

Question 1. The banker's discount on a bill due 4 months hence at 15% is Rs. 420. The true discount is:
  1.    Rs. 400
  2.    Rs. 360
  3.    Rs. 480
  4.    Rs. 320
Explanation:-
Answer: Option A. -> Rs. 400
$$\eqalign{
& T.D. = \frac{{B.D. \times 100}}{{100 + \left( {R \times T} \right)}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\left[ {\frac{{420 \times 100}}{{100 + \left( {15 \times \frac{1}{3}} \right)}}} \right] \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left( {\frac{{420 \times 100}}{{105}}} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,400 \cr} $$
Question 2. The banker's discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is:
  1.    3 months
  2.    4 months
  3.    6 months
  4.    8 months
Explanation:-
Answer: Option B. -> 4 months
$$\eqalign{
& {\text{S}}{\text{.I}}{\text{.}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{1600 = T}}{\text{.D}}{\text{.}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{1680}}{\text{.}} \cr
& \therefore {\text{Rs}}{\text{.}}\,{\text{1600}}\,{\text{is}}\,{\text{the}}\,{\text{P}}{\text{.W}}{\text{.}}\,{\text{of}}\,{\text{Rs}}{\text{.}}\,{\text{1680,}}\,{\text{i}}{\text{.e}}{\text{.,}} \cr
& {\text{Rs}}{\text{.}}\,{\text{80}}\,{\text{is}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{1600}}\,{\text{at}}\,{\text{15}}\% . \cr
& \therefore {\text{Time}} = \left( {\frac{{100 \times 80}}{{1600 \times 15}}} \right){\text{year}} \cr
& = \frac{1}{3}{\text{year}} = 4\,{\text{months}}{\text{.}} \cr} $$
Question 3. The banker's gain of a certain sum due 2 years hence at 10% per annum is Rs. 24. The present worth is:
  1.    Rs. 480
  2.    Rs. 520
  3.    Rs. 600
  4.    Rs. 960
Explanation:-
Answer: Option C. -> Rs. 600
$$\eqalign{
& T.D. = {\frac{{B.G. \times 100}}{{Rate \times Time}}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left( {\frac{{24 \times 100}}{{10 \times 2}}} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,120 \cr
& \therefore P.W. = \frac{{100 \times T.D.}}{{Rate \times Time}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left( {\frac{{100 \times 120}}{{10 \times 2}}} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,600 \cr} $$
Question 4. The banker's discount on a sum of money for $$1\frac{1}{2}$$ years is Rs. 558 and the true discount on the same sum for 2 years is Rs. 600. The rate percent is:
  1.    10%
  2.    13%
  3.    12%
  4.    15%
Explanation:-
Answer: Option C. -> 12%
$$\eqalign{
& {\text{B}}{\text{.D}}{\text{.}}\,{\text{for}}\frac{3}{2}{\text{years}} = Rs.\,558 \cr
& {\text{B}}{\text{.D}}{\text{.}}\,{\text{for 2}}\,{\text{years}} \cr
& = Rs.\left( {558 \times \frac{2}{3} \times 2} \right) \cr
& = Rs.\,744 \cr
& {\text{T}}{\text{.D}}{\text{.}}\,{\text{for}}\,{\text{2}}\,{\text{years}} = Rs.\,600 \cr
& \therefore {\text{Sum}} = \frac{{B.D. \times T.D.}}{{B.D. - T.D.}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left( {\frac{{744 \times 600}}{{144}}} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,3100 \cr
& {\text{Thus,}}\,{\text{Rs}}{\text{.}}\,{\text{744}}\,{\text{is}}\,{\text{S}}{\text{.I}}{\text{.}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{3100}}\,{\text{for}}\,{\text{2}}\,{\text{years}}{\text{.}} \cr
& \therefore {\text{Rate}} = \left( {\frac{{100 \times 744}}{{3100 \times 2}}} \right)\% \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 12\% \cr} $$
Question 5. The banker's gain on a sum due 3 years hence at 12% per annum is Rs. 270. The banker's discount is:
  1.    Rs. 960
  2.    Rs. 840
  3.    Rs. 1020
  4.    Rs. 760
Explanation:-
Answer: Option C. -> Rs. 1020
$$\eqalign{
& T.D. = {\frac{{B.G. \times 100}}{{R \times T}}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left( {\frac{{270 \times 100}}{{12 \times 3}}} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,750 \cr
& \therefore B.D. = Rs.\left( {750 + 270} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,1020 \cr} $$
Question 6. The present worth of a sum due sometime hence is Rs. 576 and the banker's gain is Rs. 16. The true discount is:
  1.    Rs. 36
  2.    Rs. 72
  3.    Rs. 48
  4.    Rs. 96
Explanation:-
Answer: Option D. -> Rs. 96
$$\eqalign{
& T.D. = \sqrt {P.W. \times B.G.} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = \sqrt {576 \times 16} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = 96 \cr} $$
Question 7. The true discount on a bill of Rs. 540 is Rs. 90. The banker's discount is:
  1.    Rs. 60
  2.    Rs. 108
  3.    Rs. 110
  4.    Rs. 112
Explanation:-
Answer: Option B. -> Rs. 108
$$\eqalign{
& {\text{P}}{\text{.W}}{\text{.}} = Rs.\,\left( {540 - 90} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,450 \cr
& \therefore {\text{S}}{\text{.I}}{\text{.}}\,{\text{on}}\,Rs.\,450 = Rs.\,90 \cr
& {\text{S}}{\text{.I}}{\text{.}}\,{\text{on}}\,Rs.\,540 \cr
& = Rs.\,\left( {\frac{{90}}{{450}} \times 540} \right) \cr
& = Rs.\,108 \cr
& \therefore {\text{B}}{\text{.D}}. = Rs.\,108 \cr} $$
Question 8. The banker's discount on a certain sum due 2 years hence is $$\frac{{11}}{{10}}$$ of the true discount. The rate percent is:
  1.    11%
  2.    10%
  3.    5%
  4.    5.5%
Explanation:-
Answer: Option C. -> 5%
$$\eqalign{
& {\text{Let}}\,{\text{T}}{\text{.D}}{\text{.}}\,{\text{be}}\,{\text{Re}}{\text{.}}\,{\text{1}}{\text{}} \cr
& {\text{Then,}}\,{\text{B}}{\text{.D}}. = Rs.\,\frac{{11}}{{10}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,1.10 \cr
& \therefore {\text{Sum}} = Rs.\,\left( {\frac{{1.10 \times 1}}{{1.10 - 1}}} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left( {\frac{{110}}{{10}}} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,11 \cr
& \therefore {\text{S}}{\text{.I}}{\text{.}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{11}}\,{\text{for}}\,{\text{2}}\,{\text{years}}\,{\text{is}}\,{\text{Rs}}{\text{.}}\,{\text{1}}{\text{.10}} \cr
& \therefore {\text{Rate}} = \left( {\frac{{100 \times 1.10}}{{11 \times 2}}} \right)\% \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 5\% \, \cr} $$
Question 9. If the true discount on a certain sum due 6 months hence at 15% is Rs. 120, what is the banker's discount on the same sum for the same time and at the same rate?
  1.    50
  2.    129
  3.    100
  4.    150
Explanation:-
Answer: Option B. -> 129
$$\eqalign{
& B.G. = S.I.\,on\,T.D. \cr
& = {\text{Rs}}{\text{.}}\,\left( {120 \times 15 \times \frac{1}{2} \times \frac{1}{{100}}} \right) \cr
& = {\text{Rs}}{\text{.}}\,9 \cr
& B.D. - T.D. = Rs.\,9 \cr
& B.D. = {\text{Rs}}{\text{.}}\,\left( {120 + 9} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,129 \cr} $$
Question 10. The present worth of a bill due sometime hence is Rs. 1100 and the true discount on the bill is Rs. 110. Find the banker’s discount and the banker’s gain.
  1.    120
  2.    121
  3.    130
  4.    151
Explanation:-
Answer: Option B. -> 121
$$\eqalign{
& T.D. = \sqrt {P.W.} \times B.G. \cr
& \therefore B.G. = \frac{{{{\left( {T.D.} \right)}^2}}}{{P.W.}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,\frac{{110 \times 110}}{{1100}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,11 \cr
& \therefore B.D. = T.D. + B.G. \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,110 + 11 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,121 \cr} $$
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