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

41. 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

Discuss

Solution:

\begin{aligned} F = Rs . 2520 \\ T = 6 months = \frac{1}{2} years \\ R = 10 % \\ T D = \frac{F T R}{100 + (T R)} \\ = \frac{2520 \times \frac{1}{2} \times 10}{100 + (\frac{1}{2} \times 10)} \\ = \frac{1260 \times 10}{100 + 5} \\ = \frac{12600}{105} \\ = \frac{2520}{21} \\ = Rs . 120 \end{aligned}

42. The true discount on a certain sum due 6 months hence at 15% is Rs. 240. What is the banker's discount on the same sum for the same time at the same rate?

A. Rs. 258

B. Rs. 278

C. Rs. 228

D. None of these

Discuss

Solution:

\begin{aligned} T D = Rs . 240 \\ T = 6 months = \frac{1}{2} year \\ R = 15 % \\ T D = \frac{B G \times 100}{T R} \\ \Rightarrow 240 = \frac{B G \times 100}{(\frac{1}{2} \times 15)} \\ B G = \frac{240 \times 15}{100 \times 2} \\ = \frac{120 \times 15}{100} \\ = Rs . 18 \\ B G = B D - T D \\ \Rightarrow 18 = B D - 240 \\ \Rightarrow B D = 18 + 240 \\ = Rs . 258 \end{aligned}

43. 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

Discuss

Solution:

\begin{aligned} B G = \frac{{(T D)}^{2}}{P W} \\ = \frac{{(340)}^{2}}{3400} \\ = \frac{340 \times 340}{3400} \\ = \frac{340}{10} \\ = Rs . 34 \end{aligned}

44. The banker's discount on a sum of money for $1 \frac{1}{2}$ years is Rs. 120. The true discount on the same sum for 2 years is Rs. 150. What is the rate per cent?

A. $3 \frac{1}{3} %$

B. $4 \frac{1}{3} %$

C. $3 \frac{2}{3} %$

D. $4 \frac{2}{3} %$

Discuss

Solution:

\begin{aligned} B D for 1 \frac{1}{2} years = Rs . 120 \\ B D for 2 years = 120 \times \frac{2}{3} \times 2 \\ = Rs . 160 \\ T D for 2 year = R s . 150 \\ F = \frac{B D \times T D}{(B D - T D)} \\ = \frac{160 \times 150}{160 - 150} \\ = \frac{160 \times 150}{10} \\ = Rs . 2400 \end{aligned}

⇒ Rs.160 is the simple interest on Rs. 2400 for 2 years

\begin{aligned} \Rightarrow 160 = \frac{2400 \times 2 \times R}{100} \\ \Rightarrow R = \frac{160 \times 100}{2400 \times 2} \\ = \frac{160}{48} \\ = \frac{20}{6} \\ = \frac{10}{3} \\ = 3 \frac{1}{3} % \end{aligned}

45. The present worth of a certain bill due sometime hence is Rs. 1296 and the true discount is Rs. 72. What is the banker's discount?

A. Rs. 76

B. Rs. 72

C. Rs. 74

D. Rs. 4

Discuss

Solution:

\begin{aligned} B G = \frac{{(T D)}^{2}}{P W} \\ = \frac{72^{2}}{1296} \\ = \frac{72 \times 72}{1296} \\ = \frac{12 \times 12}{36} \\ = \frac{12}{3} \\ = Rs . 4 \\ B G = B D - T D \\ \Rightarrow 4 = B D - 72 \\ \Rightarrow B D = 72 + 4 \\ = Rs . 76 \end{aligned}

46. The banker's gain on a sum due 6 years hence at 12% per annum is Rs. 540. What is the banker's discount?

A. 1240

B. 1120

C. 1190

D. 1290

Discuss

Solution:

\begin{aligned} T D = \frac{B G \times 100}{T R} \\ = \frac{540 \times 100}{6 \times 12} \\ = \frac{90 \times 100}{12} \\ = \frac{15 \times 100}{2} \\ = Rs . 750 \\ B G = B D - T D \\ \Rightarrow 540 = B D - 750 \\ \Rightarrow B D = 540 + 750 \\ = 1290 \end{aligned}

47. 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

Discuss

Solution:

Since the compound interest is taken here,

\begin{aligned} P W {(1 + \frac{5}{100})}^{2} = 1764 \\ P W {(1 + \frac{1}{20})}^{2} = 1764 \\ P W {(\frac{21}{20})}^{2} = 1764 \\ P W \times \frac{441}{400} = 1764 \\ \Rightarrow P W = \frac{1764 \times 400}{441} \\ = 4 \times 400 \\ = Rs . 1600 \end{aligned}

48. 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 + 20 \\ = Rs . 21 \end{aligned}

49. A bill for Rs. 3000 is drawn on 14^th July at 5 months. It is discounted on 5^th October at 10%. What is the Banker's Discount?

A. Rs. 60

B. Rs. 82

C. Rs. 90

D. Rs. 120

Discuss

Solution:

F = Rs. 3000
R = 10%
Date on which the bill is drawn = 14^th July at 5 months
Nominally Due Date = 14^th December
Legally Due Date = 14^th December + 3 days = 17^th December
Date on which the bill is discounted = 5^th October
Unexpired Time
= [6^th to 31^th of October] + [30 Days in November] + [1^th to 17^th of December]
= 26 + 30 + 17
= 73 Days

\begin{aligned} = \frac{73}{365} year \\ = \frac{1}{5} year \end{aligned}

Banker's Discount = Simple Interest on the face value of the bill for unexpired time =

\frac{FTR}{100}

\begin{aligned} = \frac{3000 \times \frac{1}{5} \times 10}{100} \\ = 30 \times \frac{1}{5} \times 10 \\ = Rs . 60 \end{aligned}

50. 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

Discuss

Solution:

\begin{aligned} F = Rs . 8100 \\ R = 5 % \\ T = 3 months = \frac{1}{4} years \\ B D = \frac{F T R}{100} \\ = \frac{8100 \times \frac{1}{4} \times 5}{100} \\ = \frac{2025}{20} \\ = \frac{405}{4} \\ = Rs . 101.25 \\ T D = \frac{F T R}{100 + (T R)} \\ = \frac{8100 \times \frac{1}{4} \times 5}{100 + (\frac{1}{4} \times 5)} \\ = \frac{2025 \times 5}{100 + (\frac{5}{4})} \\ = \frac{2025 \times 5 \times 4}{400 + 5} \\ = \frac{2025 \times 5 \times 4}{405} \\ = \frac{405 \times 5 \times 4}{81} \\ = \frac{45 \times 5 \times 4}{9} \\ = 5 \times 5 \times 4 \\ = Rs . 100 \\ B D - T D = 101.25 - 100 \\ = Rs . 1.25 \end{aligned}

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