Practice MCQ Questions and Answer on Bankers Discount

11.

The banker's gain on a bill due 1 year hence at 12% per annum is Rs. 6. The true discount is:

• (A) Rs. 72
• (B) Rs. 36
• (C) Rs. 54
• (D) Rs. 50

Show Answer

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

12.

The present worth of a sum due sometimes hence is Rs.5760 and the baker's gain is Rs.10. What is the true discount?

• (A) Rs. 480
• (B) Rs. 420
• (C) Rs. 120
• (D) Rs. 240

Show Answer

 $$\eqalign{ & TD = \sqrt {PW \times BG} \cr & \,\,\,\,\,\,\,\,\,\, = \sqrt {5760 \times 10} \cr & \,\,\,\,\,\,\,\,\,\, = \sqrt {57600} \cr & \,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}240 \cr} $$

13.

The banker's gain on a sum due 3 years hence at 12% per annum is Rs. 360. The banker's discount is:

• (A) Rs. 1360
• (B) Rs. 1000
• (C) Rs. 360
• (D) Rs. 640

Show Answer

 BG = Rs. 360 T = 3 years R = 12% $$\eqalign{ & TD = \frac{{BG \times 100}}{{TR}} \cr & \,\,\,\,\,\,\,\,\,\,\, = \frac{{360 \times 100}}{{3 \times 12}} \cr & \,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{. }}1000 \cr} $$ BG = BD - TD ⇒ BD = BG + TD = 360 + 1000 = Rs. 1360

14.

The banker’s gain on a bill due 2 years hence at 10% per annum is Rs.10. What is the true discount?

• (A) Rs. 20
• (B) Rs. 30
• (C) Rs. 40
• (D) Rs. 50

Show Answer

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

15.

A bill for Rs. 6000 is drawn on July 14 at 5 months. It is discounted on 5th October at 10%. Find the banker's discount, true discount, banker's gain and the money that the holder of the bill receives.

• (A) 4390
• (B) 6580
• (C) 5880
• (D) 5350

Show Answer

 Face value of the bill = Rs. 6000 Date on which the bill was drawn = July 14 at 5 months Nominally due date = December 14 Legally due date = December 17 Date on which the bill was discounted = October 5 Unexpired time : Oct.   Nov.   Dec. 26   +   30   +   17 = 73 days = $$\frac{1}{5}$$ Years B.D. = S.I. on Rs. 6000 for $$\frac{1}{5}$$ year $$\eqalign{ & = {\text{Rs}}{\text{.}}\,\left( {6000 \times 10 \times \frac{1}{5} \times \frac{1}{{100}}} \right) \cr & = {\text{Rs}}{\text{.}}\,120 \cr & {\text{T}}{\text{.D}}{\text{.}} = {\text{Rs}}{\text{.}}\,\left[ {\frac{{6000 \times 10 \times \frac{1}{5}}}{{100 + \left( {10 \times \frac{1}{5}} \right)}}} \right] \cr & = {\text{Rs}}{\text{.}}\,\frac{{12000}}{{102}} \cr & = {\text{Rs}}{\text{.}}\,117.64 \cr} $$ B.G. = B.D. - T.D. = Rs. 120 - 117.64 = Rs. 2.36 Money received by the holder of the bill = Rs. 6000 - 120 = Rs. 5880

16.

What is the present worth of a bill of Rs. 1764 due 2 years hence at 5% compound interest is

• (A) Rs. 1600
• (B) Rs. 1200
• (C) Rs. 1800
• (D) Rs. 1400

Show Answer

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

17.

The banker's gain of a certain sum due 2 years hence at 10% per annum is Rs. 24. The present worth is:

• (A) Rs. 480
• (B) Rs. 520
• (C) Rs. 600
• (D) Rs. 960

Show Answer

 $$\eqalign{ & T.D. = {\frac{{B.G. \times 100}}{{Rate \times Time}}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left( {\frac{{24 \times 100}}{{10 \times 2}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,120 \cr & \therefore P.W. = \frac{{100 \times T.D.}}{{Rate \times Time}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left( {\frac{{100 \times 120}}{{10 \times 2}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,600 \cr} $$

18.

What is the difference between the banker's discount and the true discount on Rs. 8100 for 3 months at 5%

• (A) Rs. 2
• (B) Rs. 1.25
• (C) Rs. 2.25
• (D) Rs. 0.5

Show Answer

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

19.

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.

• (A) 120
• (B) 121
• (C) 130
• (D) 151

Show Answer

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

20.

The true discount on a bill for Rs. 2520 due 6 months hence at 10% per annum is

• (A) Rs. 180
• (B) Rs. 140
• (C) Rs. 80
• (D) Rs. 120

Show Answer

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