Practice MCQ Questions and Answer on Bankers Discount

31.

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

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

32.

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?

• (A) 50
• (B) 129
• (C) 100
• (D) 150

Show Answer

 $$\eqalign{ & B.G. = S.I.\,on\,T.D. \cr & = {\text{Rs}}{\text{.}}\,\left( {120 \times 15 \times \frac{1}{2} \times \frac{1}{{100}}} \right) \cr & = {\text{Rs}}{\text{.}}\,9 \cr & B.D. - T.D. = Rs.\,9 \cr & B.D. = {\text{Rs}}{\text{.}}\,\left( {120 + 9} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,129 \cr} $$

33.

If the discount on Rs. 498 at 5% simple interest is Rs.18, when is the sum due?

• (A) 8 months
• (B) 11 months
• (C) 10 months
• (D) 9 months

Show Answer

 F = Rs. 498 TD = Rs. 18 PW = F - TD = 498 - 18 = Rs. 480 R = 5% $$\eqalign{ & TD = \frac{{PW \times TR}}{{100}} \cr & \Rightarrow 18 = \frac{{480 \times T \times 5}}{{100}} \cr & \Rightarrow 18 = 24 \times T{\text{ }} \cr & \Rightarrow {\text{ }}T{\text{ }} = \frac{{18}}{{24}} = \frac{3}{4}{\text{ years}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{12 \times 3}}{4}{\text{ months}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = 9 months}} \cr} $$

34.

The banker's discount on a certain sum due 2 years hence is $$\frac{{11}}{{10}}$$ of the true discount. The rate percent is:

• (A) 11%
• (B) 10%
• (C) 5%
• (D) 5.5%

Show Answer

 $$\eqalign{ & {\text{Let}}\,{\text{T}}{\text{.D}}{\text{.}}\,{\text{be}}\,{\text{Re}}{\text{.}}\,{\text{1}}{\text{}} \cr & {\text{Then,}}\,{\text{B}}{\text{.D}}. = Rs.\,\frac{{11}}{{10}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,1.10 \cr & \therefore {\text{Sum}} = Rs.\,\left( {\frac{{1.10 \times 1}}{{1.10 - 1}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left( {\frac{{110}}{{10}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,11 \cr & \therefore {\text{S}}{\text{.I}}{\text{.}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{11}}\,{\text{for}}\,{\text{2}}\,{\text{years}}\,{\text{is}}\,{\text{Rs}}{\text{.}}\,{\text{1}}{\text{.10}} \cr & \therefore {\text{Rate}} = \left( {\frac{{100 \times 1.10}}{{11 \times 2}}} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 5\% \, \cr} $$

35.

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

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

36.

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

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

37.

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

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

38.

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

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

39.

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:

• (A) 10%
• (B) 13%
• (C) 12%
• (D) 15%

Show Answer

 $$\eqalign{ & {\text{B}}{\text{.D}}{\text{.}}\,{\text{for}}\frac{3}{2}{\text{years}} = Rs.\,558 \cr & {\text{B}}{\text{.D}}{\text{.}}\,{\text{for 2}}\,{\text{years}} \cr & = Rs.\left( {558 \times \frac{2}{3} \times 2} \right) \cr & = Rs.\,744 \cr & {\text{T}}{\text{.D}}{\text{.}}\,{\text{for}}\,{\text{2}}\,{\text{years}} = Rs.\,600 \cr & \therefore {\text{Sum}} = \frac{{B.D. \times T.D.}}{{B.D. - T.D.}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,\left( {\frac{{744 \times 600}}{{144}}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = Rs.\,3100 \cr & {\text{Thus,}}\,{\text{Rs}}{\text{.}}\,{\text{744}}\,{\text{is}}\,{\text{S}}{\text{.I}}{\text{.}}\,{\text{on}}\,{\text{Rs}}{\text{.}}\,{\text{3100}}\,{\text{for}}\,{\text{2}}\,{\text{years}}{\text{.}} \cr & \therefore {\text{Rate}} = \left( {\frac{{100 \times 744}}{{3100 \times 2}}} \right)\% \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 12\% \cr} $$

40.

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