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=T.D2P.W

 

 

 

3. T.D=P.W×B.G

 

 

4. B.D=Amount×Rate×Time100

 

5. T.D=Amount×Rate×Time100+Rate×Time

 

6. Amount=B.D×T.DB.D-T.D

 

7. T.D=B.G×100Rate×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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17 14110
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 12118
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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7 15090
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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7 18046
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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6 6556
Q:

A bill for Rs. 6000 is drawn on July 14 at 5 months. It is discounted on 5th October at 10%. Find the banker's discount, true discount, banker's gain and the money that the holder of the bill receives.

A) 4390 B) 6580
C) 5880 D) 5350
 
Answer & Explanation Answer: C) 5880

Explanation:

Face value of the bill = Rs. 6000.

Date on which the bill was drawn = July 14 at 5 months. Nominally due date =                  December 14.

Legally due date = December 17.

Date on which the bill was discounted = October 5.

Unexpired time  : Oct.               Nov.                Dec.

                                 26  +               30  +              17     = 73 days  =1/ 5Years

 

 B.D. = S.I. on Rs. 6000 for 1/5 year

= Rs.   (6000 x 10 x1/5 x1/100)= Rs. 120.

T.D. = Rs.[(6000 x 10 x1/5)/(100+(10*1/5))]

            =Rs.(12000/102)=Rs. 117.64.

B.G. = (B.D.) - (T.D.) = Rs. (120 - 117.64) = Rs. 2.36.

Money received by the holder of the bill = Rs. (6000 - 120) = Rs. 5880.

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5 7426
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%

 

TD=PW×TR100

 

18=480×T×5100

 

=> T = 3/4 years = 9 months

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4 5251
Q:

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?

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
 
Answer & Explanation Answer: C) Sum = Rs.400 and Time = 2.5 years

Explanation:

BD = Rs.100

TD = Rs.80

R = 10%

 

F=BD×TDBD-TD=100×80100-80=Rs.400 

 

BD = Simple interest on the face value of the bill for unexpired time= FTR/100

 

100=400×T×10100

=> T = 2.5 years

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4 5953