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Bankers Discount - Aptitude MCQ Questions and Solutions with Explanations

Bankers Discount MCQ Questions and answers with easy and logical explanations.Arithmetic Ability provides you all type of quantitative and competitive aptitude mcq questions on Bankers Discount with easy and logical explanations. Bankers Discount MCQ is important for exams like Banking exams,IBPS,SCC,CAT,XAT,MAT etc.

1
The banker's discount on a bill due 4 months hence at 15% is Rs. 420. The true discount is:
Discuss
Answer & Solution
Answer: Option A
Solution:
$$\eqalign{ & T.D. = \frac{{B.D. \times 100}}{{100 + \left( {R \times T} \right)}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\left[ {\frac{{420 \times 100}}{{100 + \left( {15 \times \frac{1}{3}} \right)}}} \right] \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left( {\frac{{420 \times 100}}{{105}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,400 \cr} $$
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:
Discuss
Answer & Solution
Answer: Option B
Solution:
$$\eqalign{ & {\text{S}}{\text{.I}}{\text{.}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{1600 = T}}{\text{.D}}{\text{.}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{1680}}{\text{.}} \cr & \therefore {\text{Rs}}{\text{.}}\,{\text{1600}}\,{\text{is}}\,{\text{the}}\,{\text{P}}{\text{.W}}{\text{.}}\,{\text{of}}\,{\text{Rs}}{\text{.}}\,{\text{1680,}}\,{\text{i}}{\text{.e}}{\text{.,}} \cr & {\text{Rs}}{\text{.}}\,{\text{80}}\,{\text{is}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{1600}}\,{\text{at}}\,{\text{15}}\% . \cr & \therefore {\text{Time}} = \left( {\frac{{100 \times 80}}{{1600 \times 15}}} \right){\text{year}} \cr & = \frac{1}{3}{\text{year}} = 4\,{\text{months}}{\text{.}} \cr} $$
3
The banker's gain of a certain sum due 2 years hence at 10% per annum is Rs. 24. The present worth is:
Discuss
Answer & Solution
Answer: Option C
Solution:
$$\eqalign{ & T.D. = {\frac{{B.G. \times 100}}{{Rate \times Time}}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left( {\frac{{24 \times 100}}{{10 \times 2}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,120 \cr & \therefore P.W. = \frac{{100 \times T.D.}}{{Rate \times Time}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left( {\frac{{100 \times 120}}{{10 \times 2}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,600 \cr} $$
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:
Discuss
Answer & Solution
Answer: Option C
Solution:
$$\eqalign{ & {\text{B}}{\text{.D}}{\text{.}}\,{\text{for}}\frac{3}{2}{\text{years}} = Rs.\,558 \cr & {\text{B}}{\text{.D}}{\text{.}}\,{\text{for 2}}\,{\text{years}} \cr & = Rs.\left( {558 \times \frac{2}{3} \times 2} \right) \cr & = Rs.\,744 \cr & {\text{T}}{\text{.D}}{\text{.}}\,{\text{for}}\,{\text{2}}\,{\text{years}} = Rs.\,600 \cr & \therefore {\text{Sum}} = \frac{{B.D. \times T.D.}}{{B.D. - T.D.}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left( {\frac{{744 \times 600}}{{144}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,3100 \cr & {\text{Thus,}}\,{\text{Rs}}{\text{.}}\,{\text{744}}\,{\text{is}}\,{\text{S}}{\text{.I}}{\text{.}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{3100}}\,{\text{for}}\,{\text{2}}\,{\text{years}}{\text{.}} \cr & \therefore {\text{Rate}} = \left( {\frac{{100 \times 744}}{{3100 \times 2}}} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 12\% \cr} $$
5
The banker's gain on a sum due 3 years hence at 12% per annum is Rs. 270. The banker's discount is:
Discuss
Answer & Solution
Answer: Option C
Solution:
$$\eqalign{ & T.D. = {\frac{{B.G. \times 100}}{{R \times T}}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left( {\frac{{270 \times 100}}{{12 \times 3}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,750 \cr & \therefore B.D. = Rs.\left( {750 + 270} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,1020 \cr} $$
6
The banker's discount of a certain sum of money is Rs. 72 and the true discount on the same sum for the same time is Rs. 60. The sum due is:
Discuss
Answer & Solution
Answer: Option A
Solution:
$$\eqalign{ & \frac{{B.D. \times T.D.}}{{B.D. - T.D.}} \cr & = Rs.\,\left( {\frac{{72 \times 60}}{{72 - 60}}} \right) \cr & = Rs.\,\left( {\frac{{72 \times 60}}{{12}}} \right) \cr & = Rs.\,360 \cr} $$
7
The certain worth of a certain sum due sometime hence is Rs. 1600 and the true discount is Rs. 160. The banker's gain is:
Discuss
Answer & Solution
Answer: Option C
Solution:
$$\eqalign{ & B.G. = \frac{{{{\left( {T.D.} \right)}^2}}}{{P.W.}} \cr & = Rs.\,\left( {\frac{{160 \times 160}}{{1600}}} \right) \cr & = Rs.\,16 \cr} $$
8
The present worth of a certain bill due sometime hence is Rs. 800 and the true discount is Rs. 36. The banker's discount is:
Discuss
Answer & Solution
Answer: Option B
Solution:
$$\eqalign{ & B.G. = \frac{{{{\left( {T.D.} \right)}^2}}}{{P.W.}} \cr & = Rs.\,\left( {\frac{{36 \times 36}}{{800}}} \right) \cr & = Rs.\,1.62 \cr & \therefore B.D. = \left( {T.D. + B.G.} \right) \cr & = Rs.\,\left( {36 + 1.62} \right) \cr & = Rs.\,37.62 \cr} $$
9
The banker's gain on a bill due 1 year hence at 12% per annum is Rs. 6. The true discount is:
Discuss
Answer & Solution
Answer: Option D
Solution:
$$\eqalign{ & T.D. = \frac{{B.G. \times 100}}{{R \times T}} \cr & = Rs.\,\left( {\frac{{6 \times 100}}{{12 \times 1}}} \right) \cr & = Rs.\,50 \cr} $$
10
The banker's gain on a certain sum due $$1\frac{1}{2}$$ years hence is $$\frac{3}{{25}}$$ of the banker's discount. The rate percent is:
Discuss
Answer & Solution
Answer: Option B
Solution:
$$\eqalign{ & {\text{Let,}}\,{\text{B}}{\text{.D}}{\text{.}} = \operatorname{Rs} .\,{\kern 1pt} 1 \cr & {\text{Then,}}{\kern 1pt} \,{\text{B}}{\text{.G}}{\text{.}} = \operatorname{Re} .\,{\kern 1pt} \frac{3}{{25}} \cr & \therefore {\text{T}}{\text{.D}}{\text{. = }}\left( {{\text{B}}{\text{.D}}{\text{. - B}}{\text{.G}}{\text{.}}} \right) \cr & = \operatorname{Rs} .\,{\kern 1pt} \left( {1 - \frac{3}{{25}}} \right) \cr & = \operatorname{Rs} .{\kern 1pt} \,\frac{{22}}{{25}} \cr & {\text{Sum}} = {\frac{{1 \times {\frac{{22}}{{25}}} }}{{1 - {\frac{{22}}{{25}}} }}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}{\kern 1pt} \,\frac{{22}}{3} \cr & {\text{S}}{\text{.I}}{\text{.}}{\kern 1pt} \,{\text{on}}{\kern 1pt} {\text{Rs}}{\text{.}}\,{\kern 1pt} \frac{{22}}{3}{\kern 1pt} {\text{for}}\,{\kern 1pt} 1\frac{1}{2}\,{\text{years}}\,{\kern 1pt} {\text{is}}\,\operatorname{Rs} .\,{\kern 1pt} 1 \cr & \therefore {\text{Rate}} = \left( {\frac{{100 \times 1}}{{\frac{{22}}{3} \times \frac{3}{2}}}} \right)\% {\kern 1pt} \cr & {\kern 1pt} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 9\frac{1}{9}\% \cr} $$