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

31. A bill is discounted at 10% per annum. If banker's discount is allowed, at what rate percent should the proceeds be invested so that nothing will be lost?

A. $10 \frac{1}{9} %$

B. $11 \frac{1}{9} %$

C. $11 %$

D. $10 \frac{2}{9} %$

Discuss

Solution:

Let the amount = Rs. 100
Then BD = Rs.10 (∵ banker's discount, BD is the simple Interest on the face value of the bill for unexpired time and bill is discounted at 10% per annum)
Proceeds = Rs. 100 - Rs. 10 = Rs. 90
Hence we should get Rs. 10 as the interest of Rs. 90 for 1 year so that nothing will be lost

\begin{aligned} \Rightarrow 10 = \frac{90 \times 1 \times R}{100} \\ \Rightarrow R = \frac{10 \times 100}{90} \\ = \frac{100}{9} \\ = 11 \frac{1}{9} % \end{aligned}

32. 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

Discuss

Solution:

F = Rs. 498
TD = Rs. 18
PW = F - TD = 498 - 18 = Rs. 480
R = 5%

\begin{aligned} T D = \frac{P W \times T R}{100} \\ \Rightarrow 18 = \frac{480 \times T \times 5}{100} \\ \Rightarrow 18 = 24 \times T \\ \Rightarrow T = \frac{18}{24} = \frac{3}{4} years \\ = \frac{12 \times 3}{4} months \\ =  9 months \end{aligned}

33. The banker's discount of a certain sum of money is Rs. 36 and the true discount on the same sum for the same time is Rs. 30. What is the sum due?

A. Rs. 180

B. Rs. 120

C. Rs. 220

D. Rs. 200

Discuss

Solution:

\begin{aligned} F = \frac{B D \times T D}{(B D - T D)} \\ = \frac{36 \times 30}{(36 - 30)} \\ = \frac{36 \times 30}{6} \\ = 36 \times 5 \\ = Rs . 180 \end{aligned}

34. 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

Discuss

Solution:

BG = Rs. 360
T = 3 years
R = 12%

\begin{aligned} T D = \frac{B G \times 100}{T R} \\ = \frac{360 \times 100}{3 \times 12} \\ = Rs . 1000 \end{aligned}

BG = BD - TD
⇒ BD = BG + TD = 360 + 1000 = Rs. 1360

35. The Banker Gain on a certain sum 4 years hence at 5% is Rs. 200. What is the present worth?

A. Rs. 4500

B. Rs. 6000

C. Rs. 5000

D. Rs. 4000

Discuss

Solution:

T = 4 years
R = 5%
Banker's Gain, BG = Rs. 200

\begin{aligned} T D = \frac{B G \times 100}{T R} \\ = \frac{200 \times 100}{4 \times 5} \\ = Rs . 1000 \\ T D = \sqrt{P W \times B G} \\ 1000 = \sqrt{P W \times 200} \\ 1000000 = P W \times 200 \\ P W = \frac{1000000}{200} \\ = Rs . 5000 \end{aligned}

36. The banker's discount on a sum of money for 3 years is Rs. 1116. The true discount on the same sum for 4 years is Rs. 1200. What is the rate per cent?

A. 8%

B. 12%

C. 10%

D. 6%

Discuss

Solution:

\begin{aligned} B D for 3 years = Rs . 1116 \\ B D for 4 years = \frac{1116}{3} \times 4 \\ = Rs . 1488 \\ T D for 4 years = Rs . 1200 \\ F = \frac{B D \times T D}{B D - T D} \\ = \frac{1488 \times 1200}{1488 - 1200} \\ = \frac{1488 \times 1200}{288} \\ = \frac{124 \times 1200}{24} \\ = \frac{124 \times 100}{2} \\ = 62 \times 100 \\ = Rs . 6200 \end{aligned}

⇒ Rs. 1488 is the simple interest on Rs. 6200 for 4 years

\begin{aligned} \Rightarrow 1488 = \frac{6200 \times 4 \times R}{100} \\ \Rightarrow R = \frac{1488 \times 100}{6200 \times 4} \\ = \frac{372 \times 100}{6200} \\ = \frac{372}{62} \\ = 6 % \end{aligned}

37. 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

Discuss

Solution:

\begin{aligned} T D = \sqrt{P W \times B G} \\ = \sqrt{5760 \times 10} \\ = \sqrt{57600} \\ = Rs . 240 \end{aligned}

38. 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

Discuss

Solution:

\begin{aligned} T = 6 months = \frac{1}{2} year \\ R = 6 % \\ T D = \frac{B D \times 100}{100 + T R} \\ = \frac{18.54 \times 100}{100 + (\frac{1}{2} \times 6)} \\ = \frac{18.54 \times 100}{103} \\ = \frac{1854}{103} \\ = Rs . 18 \end{aligned}

39. The banker's discount and the true discount on a sum of money due 8 months hence are Rs. 120 and Rs. 110 respectively. Find the rate percent.

A. $\frac{120}{11} %$

B. $\frac{130}{11} %$

C. $\frac{140}{11} %$

D. $\frac{150}{11} %$

Discuss

Solution:

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

Since B.D. is S.I. on sum due, so S.I. on Rs. 1320 for 8 months is Rs. 120.

\begin{aligned} Rate = \frac{100 \times 120}{1320 \times \frac{2}{3}} % \\ = \frac{150}{11} % \end{aligned}

40. The present worth of a certain bill due sometime hence is Rs. 400 and the true discount is Rs. 20. What is the banker's discount?

A. Rs. 19

B. Rs. 22

C. Rs. 20

D. Rs. 21

Discuss

Solution:

\begin{aligned} B G = \frac{{(T D)}^{2}}{P W} = \frac{20^{2}}{400} = Rs . 1 \\ B G = B D - T D \\ \Rightarrow 1 = B D - 20 \\ \Rightarrow B D = 1 + 21 \\ = Rs . 21 \end{aligned}

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