# 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 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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13 8440
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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3 7585
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 6370
Q:

The banker's 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) 7 months B) 6 months C) 3 months D) 4 months

Answer & Explanation Answer: D) 4 months

Explanation:

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%.

Time =[(100 x 72)/ (12x1800)]year

=1/3year = 4 months.

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3 6069
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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3 5710
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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0 5540
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 5217
Q:

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

Answer & Explanation Answer: A) 15

Explanation:

Sum = [(B.D.xT.D.)/ (B.D.-T.D.)]

= [(B.D.xT.D.)/B.G.]

T.D./B.G.  = Sum/ B.D.

=1650/165

=10

Thus, if B.G. is Re 1, T.D. = Rs. 10.

If B.D.is Rs. ll, T.D.=Rs. 10.

If B.D. is Rs. 165, T.D. = Rs. [(10/11)xl65]

=Rs.150

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

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