Practice MCQ Questions and Answer on Bankers Discount

1.

The banker's discount on a bill due 6 months hence at 6% is Rs. 18.54. What is the true discount?

• (A) Rs. 24
• (B) Rs. 12
• (C) Rs. 36
• (D) Rs. 18

Show Answer

 $$\eqalign{ & T = 6{\text{ months}} = \frac{1}{2}{\text{year}} \cr & R = 6\% \cr & TD = \frac{{BD \times 100}}{{100 + TR}} \cr & \,\,\,\,\,\,\,\,\,\,\, = \frac{{18.54 \times 100}}{{100 + \left( {\frac{1}{2} \times 6} \right)}} \cr & \,\,\,\,\,\,\,\,\,\,\, = \frac{{18.54 \times 100}}{{103}} \cr & \,\,\,\,\,\,\,\,\,\,\, = \frac{{1854}}{{103}} \cr & \,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,18 \cr} $$

2.

Find the banker’s gain, if the present worth of a certain amount is Rs.2400 and the true discount is Rs.120.

• (A) 5
• (B) 7
• (C) 6
• (D) 8

Show Answer

 $$\eqalign{ & {\text{Banker's}}\,{\text{Gain}} \cr & = \frac{{{{\left( {T.D.} \right)}^2}}}{{P.W.}} \cr & = \frac{{{{\left( {120} \right)}^2}}}{{2400}} \cr & = \frac{{14400}}{{2400}} \cr & = {\text{Rs}}{\text{.}}\,6 \cr} $$

3.

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

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

4.

The present worth of a certain sum due sometime hence is Rs. 3400 and the true discount is Rs. 340. The banker's gain is:

• (A) Rs. 21
• (B) Rs. 17
• (C) Rs. 18
• (D) Rs. 34

Show Answer

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

5.

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

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

6.

If the banker’s discount on a certain amount of money is Rs. 80 and the true discount on the same amount for the same time duration is Rs. 64, then the amount due is:

• (A) 310
• (B) 320
• (C) 330
• (D) 340

Show Answer

 $$\eqalign{ & {\text{Amount}}\,{\text{Due}} \cr & = \frac{{B.D. \times T.D.}}{{B.D. - T.D.}} \cr & = \frac{{80 \times 64}}{{80 - 64}} \cr & = {\text{Rs}}{\text{.}}\,320 \cr} $$

7.

The banker's discount on a bill due 4 months hence at 15% is Rs. 420. The true discount is:

• (A) Rs. 400
• (B) Rs. 360
• (C) Rs. 480
• (D) Rs. 320

Show Answer

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

8.

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

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

9.

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:

• (A) 3 months
• (B) 4 months
• (C) 6 months
• (D) 8 months

Show Answer

 $$\eqalign{ & {\text{S}}{\text{.I}}{\text{.}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{1600 = T}}{\text{.D}}{\text{.}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{1680}}{\text{.}} \cr & \therefore {\text{Rs}}{\text{.}}\,{\text{1600}}\,{\text{is}}\,{\text{the}}\,{\text{P}}{\text{.W}}{\text{.}}\,{\text{of}}\,{\text{Rs}}{\text{.}}\,{\text{1680,}}\,{\text{i}}{\text{.e}}{\text{.,}} \cr & {\text{Rs}}{\text{.}}\,{\text{80}}\,{\text{is}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{1600}}\,{\text{at}}\,{\text{15}}\% . \cr & \therefore {\text{Time}} = \left( {\frac{{100 \times 80}}{{1600 \times 15}}} \right){\text{year}} \cr & = \frac{1}{3}{\text{year}} = 4\,{\text{months}}{\text{.}} \cr} $$

10.

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

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