Banker's Discount  Important Formulas, Questions and Study Material
Introduction on Banker's Discount
Suppose a merchant A purchases goods worth of say Rs.5000 from another merchant B at a credit of a certain period say 4 months. Then B draws up a draft i.e.., prepares a special type of a bill called "Hundi" or Bill of exchange. On the receipt of the goods A gives an agreement dually signed on the bill stating that he has accepted the bill and money can be withdrawn from his bank account after 4 months of the date of the bill. On this bill there is an order from A to his bank asking to pay Rs.5000 to B after 4 months. Moreover 3 more days (known as grace days) are added to the date (called nominally due date) of expiry of 4 months, and on the date so obtained (called the legally due date) the bill can be presented to the bank by B to collect Rs.5000 from A ‘s account . Suppose the bill is drawn on 5th January at 4 months, then the nominally due date is 5th May and the legally due date is 8th May. The amount given on the draft or bill is called the face value which is Rs.5000 in this case.
Now, Suppose that B needs the money of this bill earlier than 8th May say on 3rd March. In such a case, B can sell the bill to a banker or a broker who pays him the money against the bill but somewhat less than the face value, Now the natural questions is, as how much cash the banker should pay to B on 3rd March to 8th May, he gains nothing. So in order to make some profit, the banker deducts from the face value. The simple interest on the face value for the unexpired time i.e…, from 3rd March to 8th May. This deduction is known as Banker’s Discount (B.D.) or commercial discount.
Thus B.D. is the S.I. on face value for the period from the date on which the bill was discounted and the legally due date. The money paid by the banker to the bill holder is called the discountable value.
Also, the difference between the banker’s discount and the true discount for the unexpired time is called the Banker’s Gain (B.G.). Thus, Banker’s Gain
B.G. = (B.D.)  (T.D.)
Remark When date of the bill is not given, grace days are not to be added.
Banker's Discount Important formulas
B.D.=S.I. on bill for unexpired time.
Banker’s Gain=(B.D.)(T.D.)
B.G.=S.I. on T.D.
T.D.=
B.G.=
B.D.=
T.D.=
Amount=
T.D.=
Banker's Discount Important Examples
Question 1. The true discount on a bill Rs.1860 due after 8 months is Rs.60. Find the rate, the banker’s discount and the banker’s gain.
Solution : Amount = Rs.1860, T.D.
= RS.60
P.W. = Rs.(186060)
= Rs. 1800
S.I. on Rs. 1800 for 8 months
= Rs.60
Rate= %
= 5%
B.G.=
=Rs. = Rs. 2
B.D.= (T.D.) + (B.G.)
= Rs.(60+2)
= Rs.62.
Question 2. The present worth of a bill due sometime hence is Rs. 1100 and the true discount on the bill is Rs. 110. Find the banker’s discount and the extra gain the banker would make in the transaction.
Solution : T.D.=
Or B.G.=
= Rs.
= Rs.11
B.D.= B.G. + T.D.
= Rs.(11+110)
= Rs.121
Question 3. The banker’s discount and the true discount on a sum of money due 8 months hence are Rs. 52 and Rs. 50, respectively. Find the sum and the rate per cent.
Solution : Sum =
= Rs.
= Rs.1300
Since B.D. is S.I. on sum due. So S.I. on Rs. 1300 for 8 months is Rs. 52, Consequently.
Rate= %=6%
Question 4. The banker’s discount on Rs. 1800 at 5% is equal to the true discount on Rs. 1830 for the same time and at the same rate, Find the time.
Solution : S.I. on Rs. 1800
= T.D.on Rs. 1830
P.W. of Rs. 1830 is Rs. 1800
i.e.., Rs. 30 is S.I. on Rs. 1800 at 5%
Time= years
= years=4 months
Question 5. If the true discount on a certain sum due 6 months hence at 6% is Rs. 36, what is the banker’s discount on the same sum for the same time and at the same rate ?
Solution : B.G.= S.I. on T.D.
= Rs.
= Rs.1.08
(B.D.)–(T.D.)=Rs. 1.08
Or B.D.=(T.D.)+Rs.1.08
= Rs.(36+1.08)
= Rs.37.08
Banker's Discount Important Questions
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Question 1 of 13
1. Question
1 pointsThe banker's gain on a sum due 3 years hence at 12% per annum is Rs.270.The banker's discount is:
Correct
T.D.= = Rs.750
B.D.= Rs.(750+270) = Rs.1020
Incorrect
T.D.= = Rs.750
B.D.= Rs.(750+270) = Rs.1020

Question 2 of 13
2. Question
1 pointsThe banker's discount on Rs.1600 at 15% per annum is the same as ture discount on Rs.1680 for the same time and at the same rate. The time is :
Correct
S.I. on Rs.1600=T.D.on Rs.1680.
Rs.1600 is the P.W of Rs 1680,i.e Rs 80 is S.I. on Rs 1600 at 15%
Time = year = year = 4 months.
Incorrect
S.I. on Rs.1600=T.D.on Rs.1680.
Rs.1600 is the P.W of Rs 1680,i.e Rs 80 is S.I. on Rs 1600 at 15%
Time = year = year = 4 months.

Question 3 of 13
3. Question
1 pointsThe banker's discount on a sum of money for years is Rs.558 and the true discount on the same sum for 2 years is Rs.600.The rate percent is :
Correct
B.D. for years.= Rs.558 B.D for 2 years = Rs.
T.D. for 2 years =Rs.600.
sum = = Rs = Rs.3100
Thus,Rs 744 is S.I on Rs 3100 for 2 years.
Rate = % = 12%
Incorrect
B.D. for years.= Rs.558 B.D for 2 years = Rs.
T.D. for 2 years =Rs.600.
sum = = Rs = Rs.3100
Thus,Rs 744 is S.I on Rs 3100 for 2 years.
Rate = % = 12%

Question 4 of 13
4. Question
1 pointsThe 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 :
Correct
sum = = Rs 360
Incorrect
sum = = Rs 360

Question 5 of 13
5. Question
1 pointsThe true discount on a bill or Rs 540 is Rs 90.The banker's discount is :
Correct
P.W = Rs.(54090) = Rs.450.
S.I on Rs 450 = Rs 90
S.I on Rs 540 = Rs = Rs 108.
B.D = Rs 108.
Incorrect
P.W = Rs.(54090) = Rs.450.
S.I on Rs 450 = Rs 90
S.I on Rs 540 = Rs = Rs 108.
B.D = Rs 108.

Question 6 of 13
6. Question
1 pointsThe present worth of a certain bill due sometime hence is Rs.800 and the true discount is Rs.36.The banker's discount is :
Correct
B.G = = Rs 1.62
B.D = (T.D + B.G)= Rs (36 + 1.62) = Rs 37.62
Incorrect
B.G = = Rs 1.62
B.D = (T.D + B.G)= Rs (36 + 1.62) = Rs 37.62

Question 7 of 13
7. Question
1 pointsThe banker's gain on a certain sum due years hence is of the banker's discount .The rate percent is :
Correct
Let, B.D = Rs 1
Then B.G = Rs
T.D = (B.D  B.G) = Rs
Sum = = Rs
S.I on Rs for ears is Rs 1
Rate = % = %
Incorrect
Let, B.D = Rs 1
Then B.G = Rs
T.D = (B.D  B.G) = Rs
Sum = = Rs
S.I on Rs for ears is Rs 1
Rate = % = %

Question 8 of 13
8. Question
1 pointsThe banker's discount on a certain sum due 2 years hence is of the true discount .The rate percent is :
Correct
Let T.D. be Rs.1 .Then,B.D.=Rs.= Rs.1.10
sum= = Rs. = Rs.11
S.I.on RS11 for 2 years is Rs1.10.
Rate = % = 5%
sum = Rs = Rs = Rs.11
S.I on Rs 11 for 2 years is Rs 1.10.
Rate = % = 5%
Incorrect
Let T.D. be Rs.1 .Then,B.D.=Rs.= Rs.1.10
sum= = Rs. = Rs.11
S.I.on RS11 for 2 years is Rs1.10.
Rate = % = 5%
sum = Rs = Rs = Rs.11
S.I on Rs 11 for 2 years is Rs 1.10.
Rate = % = 5%

Question 9 of 13
9. Question
1 pointsThe banker's gain on a bill due 1 year hence at 12% per annum is Rs.6. The hence discount is :
Correct
T.D.=
Incorrect
T.D.=

Question 10 of 13
10. Question
1 pointsThe banker's discount on a bill due 4 months hence at 15% is Rs.420.The true discount is :
Correct
T.D=
= Rs.
= Rs.
= Rs. 400
Incorrect
T.D=
= Rs.
= Rs.
= Rs. 400

Question 11 of 13
11. Question
1 pointsThe present worth of a sum due sometime hence is Rs.576 and the banker's gain is Rs.16.The true discount is :
Correct
T.D.=
Incorrect
T.D.=

Question 12 of 13
12. Question
1 pointsThe present worth of a certain sum due sometime hence is Rs.1600 and the true discount is Rs.160. The banker's gain is :
Correct
B.G.=
Incorrect
B.G.=

Question 13 of 13
13. Question
1 pointsThe banker's gain of a certain sum due 2 years hence at 10% per annum is Rs.24.The present worth is :
Correct
T.D=
P.W.=
Incorrect
T.D=
P.W.=
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