# Banker's Discount Questions

FACTS  AND  FORMULAE  FOR  BANKER'S  DISCOUNT  QUESTIONS

Banker's Discount :

Suppose a merchant 'A' buys goods worth, say Rs. 10,000 from another merchant 'B' at a credit of say 5 months.Then, B prepares a bill, called the bill of exchange. A signs this bill and allows B to withdraw the amount from his bank account after exactly 5 months.

The date exactly after 5 months is called nominally due date. Three days (known as grace days) are added to it to get a date, known as legally due date.

Suppose B wants to have the money before the legally due date. Then he can have the money from the banker or a broker, who deducts S.I on the face value (i.e., Rs. 10,000 in this case) for the period from the date on which the bill was discounted (i.e , paid by the banker) and the legally due date. This amount is known as Banker's Discount (B.D) Thus, B.D is the S.I on the face value for the period from the date on which the bill was discounted and the legally due date.

Banker's Gain (B.G) = (B.D) - (T.D) for the unexpired time.

Note : When the date of the bill is not given, grace days are not to be added.

IMPORTANT FORMULAE

1. B.D = S.I on bill for unexpired time

2. B.G = (B.D) - (T.D) = S.I  on $T.D=\frac{{\left(T.D\right)}^{2}}{P.W}$

3. $T.D=\sqrt{P.W×B.G}$

4. $B.D=\left(\frac{Amount×Rate×Time}{100}\right)$

5. $T.D=\left[\frac{Amount×Rate×Time}{100+\left(Rate×Time\right)}\right]$

6. $Amount=\frac{B.D×T.D}{B.D-T.D}$

7. $T.D=\frac{B.G×100}{Rate×Time}$

Q:

The banker's gain on a bill due 1 year hence at 12% per annum is Rs. 6. The true discount

is:

 A) 62 B) 58 C) 47 D) 50

Answer & Explanation Answer: D) 50

Explanation:

T.D. =(B.G. x 100)/ (R x T)= Rs. (6 x 100)/( 12 x 1) = Rs. 50.

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9 26298
Q:

The banker's gain on a sum due 3 years hence at 12% per annum is Rs. 270. The banker's

discount is:

 A) 1315 B) 1150 C) 1020 D) 980

Answer & Explanation Answer: C) 1020

Explanation:

T.D. =(B.G*100)/(R*T)=Rs(270*100)/(12*3) = Rs. 750.

B.D. = Rs.(750 + 270) = Rs. 1020.

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3 20181
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 yearR = 6%
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2 19877
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

=(360/1800)* 2160

= (1/5) * 2160

=Rs. 432

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3 18703
Q:

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

 A) 108 B) 115 C) 100 D) 120

Answer & Explanation Answer: A) 108

Explanation:

P.W. = Rs. (540 - 90) = Rs. 450.

S.I. on Rs. 450 = Rs. 90.

S.I. on Rs. 540 = Rs.( 90 /450)x 540 = Rs. 108.

B.D. = Rs. 108.

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8 16389
Q:

The bankers gain of a certain sum due 2 years hence at 10% per annum is Rs 24 .The percent worth is

 A) 400 B) 800 C) 500 D) 600

Answer & Explanation Answer: D) 600

Explanation:

T.D = (B.G * 100) / (Rate * Time)

(24*100) / (10 * 2)

= 120.

P.W = (100 *T.D) / (Rate * Time)

= (100 * 120) /(10 * 2)

= 600

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17 14999
Q:

The banker's discount on a certain sum due 2 years hence is11/10of the true discount.

The rate percent is:

 A) 10% B) 7% C) 8% D) 5%

Answer & Explanation Answer: D) 5%

Explanation:

Let T.D. be Re. 1.

Then, B.D. = Rs.11/10= Rs. 1.10.

Sum = Rs. (1.10*1)/(1.10-1) = Rs. (110/10)= Rs. 11.

S.I. on Rs. 11 for 2 years is Rs. 1.10

Rate = [(100 x 1.10)/(11 x 2 )]% = 5%.

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7 14919
Q:

The banker's discount of a certain sum of money is Rs. 72 and the true discount on the

same sum for the same time is Rs. 60. The sum due is:

 A) 290 B) 480 C) 360 D) 420

Answer & Explanation Answer: C) 360

Explanation:

Sum =(B.D. x T.D.)/(B.D. - T.D.)

= Rs. (72 x 60) / (72 - 60)

= Rs. (72 x 60) /12

= Rs. 360.

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