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Home > Practice > Arithmetic Aptitude > Banker's Discount > Miscellaneous

11. The present worth of a sum due sometime hence is Rs. 576 and the banker's gain is Rs. 16. The true discount is:

A. Rs. 36

B. Rs. 72

C. Rs. 48

D. Rs. 96

Discuss

Solution:

\begin{aligned} T . D . = \sqrt{P . W . \times B . G .} \\ = \sqrt{576 \times 16} \\ = 96 \end{aligned}

12. The true discount on a bill of Rs. 540 is Rs. 90. The banker's discount is:

A. Rs. 60

B. Rs. 108

C. Rs. 110

D. Rs. 112

Discuss

Solution:

\begin{aligned} P .W . = R s . (540 - 90) \\ = R s . 450 \\ ∴ S .I . on R s . 450 = R s . 90 \\ S .I . on R s . 540 \\ = R s . (\frac{90}{450} \times 540) \\ = R s . 108 \\ ∴ B .D . = R s . 108 \end{aligned}

13. 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%

Discuss

Solution:

\begin{aligned} Let T .D . be Re . 1 \\ Then, B .D . = R s . \frac{11}{10} \\ = R s . 1.10 \\ ∴ Sum = R s . (\frac{1.10 \times 1}{1.10 - 1}) \\ = R s . (\frac{110}{10}) \\ = R s . 11 \\ ∴ S .I . on Rs . 11 for 2 years is Rs . 1 .10 \\ ∴ Rate = (\frac{100 \times 1.10}{11 \times 2}) % \\ = 5 % \end{aligned}

14. 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

Discuss

Solution:

\begin{aligned} B . G . = S . I . o n T . D . \\ = Rs . (120 \times 15 \times \frac{1}{2} \times \frac{1}{100}) \\ = Rs . 9 \\ B . D . - T . D . = R s . 9 \\ B . D . = Rs . (120 + 9) \\ = Rs . 129 \end{aligned}

15. 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

Discuss

Solution:

\begin{aligned} T . D . = \sqrt{P . W .} \times B . G . \\ ∴ B . G . = \frac{{(T . D .)}^{2}}{P . W .} \\ = Rs . \frac{110 \times 110}{1100} \\ = Rs . 11 \\ ∴ B . D . = T . D . + B . G . \\ = Rs . 110 + 11 \\ = Rs . 121 \end{aligned}

16. The bankers discount on Rs. 1800 at 12% per annum is equal to the true discount on Rs 1872 for the same time at the same rate. Find the time.

A. 4 months

B. 5 months

C. 6 months

D. 3 months

Discuss

Solution:

S.I. on Rs. 1800 = T.D. on Rs. 1872
P.W. of Rs. 1872 is Rs. 1800
Rs. 72 is S.I. on Rs. 1800 at 12%

\begin{aligned} Time = \frac{100 \times 72}{12 \times 1800} \\ = \frac{1}{3} years \\ = 4 months \end{aligned}

17. The true discount on a bill of Rs. 2160 is Rs. 360. What is the banker's discount?

A. Rs. 432

B. Rs. 422

C. Rs. 412

D. Rs. 442

Discuss

Solution:

F = Rs. 2160
TD = Rs. 360
PW = F - TD = 2160 - 360 = Rs. 1800
True Discount is the Simple Interest on the present value for unexpired time
⇒ Simple Interest on Rs. 1800 for unexpired time = Rs. 360
Banker's Discount is the Simple Interest on the face value of the bill for unexpired time
= Simple Interest on Rs. 2160 for unexpired time

\begin{aligned} = \frac{360}{1800} \times 2160 \\ = \frac{1}{5} \times 2160 \\ = Rs . 432 \end{aligned}

18. The bankers discount and true discount on a sum of money due 8 months hence are Rs.120 & Rs.110 resp. Find the sum.

A. 1457

B. 1320

C. 1140

D. 1260

Discuss

Solution:

\begin{aligned} Sum = \frac{B . D . \times T . D .}{B . D . - T . D .} \\ = \frac{120 \times 110}{120 - 110} \\ = 1320 \end{aligned}

19. The banker's discount on Rs. 1650 due a certain time hence is Rs. 165. Find the true discount and the banker's gain

A. 15

B. 20

C. 18

D. 13

Discuss

Solution:

\begin{aligned} Sum = \frac{B . D . \times T . D .}{B . D . - T . D .} \\ = \frac{B . D . \times T . D .}{B . G .} \\ \frac{T . D .}{B . G .} = \frac{Sum}{B . D .} \\ = \frac{1650}{165} \\ = 10 \end{aligned}

Thus, if B.G. is Rs. 1, T.D. = Rs. 10
If B.D. is Rs. 11, T.D. = Rs. 10
If B.D. is Rs. 165,

\begin{aligned} T . D . = Rs . \frac{10}{11} \times 165 \\ = Rs . 150 \end{aligned}

And, B.G. = Rs. (165 - 150) = Rs. 15

20. 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

Discuss

Solution:

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

\begin{aligned} = Rs . (6000 \times 10 \times \frac{1}{5} \times \frac{1}{100}) \\ = Rs . 120 \\ T .D . = Rs . [\frac{6000 \times 10 \times \frac{1}{5}}{100 + (10 \times \frac{1}{5})}] \\ = Rs . \frac{12000}{102} \\ = Rs . 117.64 \end{aligned}

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

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