The bankers discount and the true discount of a su | Banker's Discount Questions & Answers

Q:

Two consecutive discounts x% and y% is equivalent to the discount

A) (x-y+xy100)%	B) (x+y+xy100)%
C) (x-y-xy100)%	D) (x+y-xy100)%

Answer & Explanation Answer: D) (x+y-xy100)%

Explanation:

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Q:

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

Answer & Explanation Answer: D) 9 months

Explanation:

F = Rs. 498

TD = Rs. 18

PW = F - TD = 498 - 18 = Rs. 480

R = 5%

$T D = \frac{P W \times T R}{100}$

$\Rightarrow 18 = \frac{480 \times T \times 5}{100}$

=> T = 3/4 years = 9 months

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Q:

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

Answer & Explanation Answer: B) Rs. 1.25

Explanation:

F = Rs. 8100

R = 5%

T = 3 months = 1/4 years

$B D = \frac{F T R}{100} = \frac{8100 \times \frac{1}{4} \times 5}{100} = R s . 101.25$

$T D = \frac{F T R}{100 + T R} = \frac{8100 \times \frac{1}{4} \times 5}{100 + (\frac{1}{4} \times 5)} = R s . 100$

Therefore BD - TD = 101.25-100 = Rs.1.25

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Q:

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

Answer & Explanation Answer: D) Rs. 18

Explanation:

T= 6 months = 1/2 year

R = 6%

 $T D = \frac{B D \times 100}{100 + T R} = \frac{18.54 \times 100}{100 + (\frac{1}{2} \times 6)} = R s . 18$

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Q:

The B.D. and T.D. on a certain sum is Rs.200 and Rs.100 respectively. Find out the sum.

A) Rs. 400	B) Rs. 300
C) Rs. 100	D) Rs. 200

Answer & Explanation Answer: D) Rs. 200

Explanation:

$F = \frac{B D \times T D}{B D - T D} = \frac{200 \times 100}{200 - 100} = \frac{200 \times 100}{100} = R s . 200$

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Q:

The B.G. 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

Answer & Explanation Answer: C) Rs. 5000

Explanation:

T = 4 years

R = 5%

Banker's Gain, BG = Rs.200

$T D = \frac{B G \times 100}{T R} = \frac{200 \times 100}{4 \times 5} = R s . 1000$

$T D = \sqrt{P W \times B G}$

$\Rightarrow 1000 = \sqrt{P W \times 200}$

=>PW = Rs.5000

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Q:

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

Answer & Explanation Answer: A) Rs. 1600

Explanation:

Since the compound interest is taken here,

$P W {(1 + \frac{5}{100})}^{2} = 1764$

=> PW = 1600

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Q:

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

Answer & Explanation Answer: A) Rs. 432

Explanation:

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

A) Sum = Rs.400 and Time = 5 years	B) Sum = Rs.200 and Time = 2.5 years
C) Sum = Rs.400 and Time = 2.5 years	D) Sum = Rs.200 and Time = 5 years

The bankers discount and the true discount of a sum at 10% per annum simple interest for the same time are Rs.100 and Rs.80 respectively. What is the sum and the time?

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