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Banker's Discount
Introduction
As discussed in the chapter of "True Discount", i f
the borrower returns the loan before the due date, he has to
pay slightly less money than the amount due. This less money
is the benefit given to the borrower for earlier repayment and
is known as True Discount. In fact true discount is the "interest calculated on the Present Worth of the Due Amount
for due periodfrom right new ".
But, suppose the debtor (who has taken the loan) is
not able to clear the loan before it is due, but the creditor
(who has given the loan) requires money, he has no right to
ask the debtor to pay back before the bill is due. The only
way the creditor can raise money is to go to a bank and
encash the bill. During encashment of the bill, the bank will
charge a simple interest on the amount mentioned in the bill
for the unexpired time.
Now look at some important terms that are frequently
used in this chapter.
1. Face value:
The amount mentioned in the bill is called face value.
2. Banker's Discount: (B.D.)
It is the simple interest on the amount mentioned in
the bill (or face value) for the period from the date on which
the bill was encashed and the legally due date.
"Banker's Discount is slightly more than True Discount '
3. Banker's Gain (B.G.):
The difference between Banker's Discount (B.D) and
True Discount (TD) is known as Banker's Gain.
Note: 1. Banker's Discount, True Discount and Banker's Gain
are on the unexpired (unutilised) time of the bill and
face value (or actual amount) of the bill.
2. In Arithmetic 'Discount' always means 'True Discount' unless Banker's Discount is expressly meant.
Banker's Discount is generally denoted by BD.
Important Results
(i)
Banker's Discount (BD) = Simple interest on bill for
its unexpired time
Bill amount (A) x Rate (R) x Unexpired Time (T)
(ii)
100
Banker's Gain (BG) = Simple interest on True DisT.DxRxT
count(TD)=
(iif)
1 Q ( )
= Banker's Discount (B.D) - True Discount (TD.)
True Discount ( T D . ) = Bill Amount (A) - Present
Worth (PW)
= Simple Interest on Present Worth (PW)
PWxRxT
100
Rule 1
To find the Banker's Discount when Bill Amount (A), Time
(T) and Rate (R) are given.
AxRxT
Banker's Discount =
100
Illustrative Example
EK
Find the banker's discount on a bill of Rs 2550 due 4
months hence and 6% per annum.
Soln: Applying the above formula, we have
2550x6x4
= Rs 51
Banker's Discount =
...
100x12
Exercise
1.
2.
3.
The true discount on a bill of Rs 1860 due after 8 months
is Rs 60. Find the banker's discount.
a)Rs62
b)Rs52
c)Rs60
d) None of these
Find the banker's discount on a bill of Rs 12750 due 2
months hence and 3% per annum.
a) Rs 63.75 b)Rs61.75 c)Rs 64.75 d)Rs 63.25
The true discount on a bill of Rs 3720 due after 4 months
is Rs 120. Find the banker's discount.
a)Rsl22
b)Rsl34
c) 124
d) None of these
Answers
1. a; Hint: Amount = Rs 1860; True Discount * Rs 60
• Present Worth = Rs 1860 - Rs 60 - Rs 1800

PRACTICE BOOK ON QUICKER MATHS
716
Answers
SI on Rs 1800 for 8 months = Rs 60
1. d; Hint: Present Worth = Rs 1860 - Rs 60 = Rs 1800
\
100x60
(TD)
% = 5%
Rate =
BG =
1800x
60x60
Z
Present Worth
1800
= Rs2
2. a
3. c; Hint: Present Worth = 540 - 90 = Rs 450
Banker's Discount =
1860x5x-2- = R 62
100
Banker's Gain =
S
.-. Banker's discount = 90 + 18 = Rs 108 [See Note].
3.c
2. a
(TD)
Rule 2
A(RT)
(TD)'
,
or,
100(100 + RT)
PW '
2
1 f t f t / l f t n
36x36
= Rsl.62.
PW
^ 800
.-. BD = TD + BG = Rs36 + Rsl.62 = Rs37.62
5. b; Hint: Difference between the banker's discount and the
true discount = Banker's gain.
4. c; Hint: BG =
To find the Banker's Gain (BG) when Bill Amount (A), rime
(T) and Rate (R) are given.
(I) Banker's Gain =
90x90
—
= Rs 18
450
D T N
where TD = True Discount, PW = Present Worth
8100x5x-x5xl
4
4
required answer =
AxRxT
(11) True Discount (TD) =
100 + R T
Illustrative Example
Rule 3
Ex:
Find the banker's gain on a bill of Rs 2550 due 4 months
hence at 6% per annum.
Soln: Applying the above formula, we have
To find theface value (or bill amount) when Banker's Discount (BD) and Time (T) are given.
Face value (A) =
2550x 6x
Banker's Gain =
100 100+
Rs 1.25.
100 100 + 5x
6x
2550x4
100x102
IOOXBD
RxT
Illustrative Example
= Rel.
Ex:
I f the B . D on a bill at 4% per annum is Rs 60, find the
face value of 6 months bill.
Soln: Applying the above formula, we have
Note: Banker's Gain = BD - TD [ie if you calculate TD, you
can find the Banker's Gain by subtracting TD from
BD.
100x60
Face value =
4x-
Rs3000
12
Exercise
1.
2.
3.
4.
5.
The true discount on a bill of Rs 1860 due after 8 months
is Rs 60. Find the banker's gain.
a)Rsl.5
b)Rs2.5
c)Rs4
d)Rs2
Find the banker's gain on a bill of Rs 6900 due 3 years
hence at 5% per annum simple interest.
a)Rsl35
b)Rsl25
_c)Rsl85
d)Rsl45
The true disocunt on a bill of Rs 540 is Rs 90. The banker's
discount is:
a)Rs60
b)Rsl50
c)Rsl08
d)Rsll0
The present worth of a certain bill due sometime hence
is Rs 800 and the true discount is Rs 36. Then, the banker's
discount is:
a)Rs37
b)Rs 34.38 c)Rs 37:62 d)Rs 38.98
Find the difference between the banker's discount and
the true discount on Rs 8100 for 3 months at 5%.
a)Rs0.125 b)Rsl.25
c)Rs!2.5 d) None of these
Exercise
1.
2.
3.
I f the B.D on a bill at 8% per annum is Rs 120, find the
face value of 1 year bill.
a) Rs 3000
b) Rs 750
c)Rsl500
d)Rs2250
If the B.D on a bill at 5% per annum is Rs 135, find the
face value of 9 months bill.
a)Rs3600
b)Rs3650
c)Rs2750
d)Rs3250
If the B.D on a bill at 6% per annum is Rs 63, find the face
value of 3 months bill.
a)Rs415<)
b)Rs4200
c)Rs4250
d) None of these
Answers
!.c
2.'a
3.b

i Banker's Discount
717
5% being given that the banker's gain is Rs 90.
a)Rs550
b)Rs650
c)Rs690
d)Rs600
The banker's gain on a bill due 1 year 4 months hence at
Rule 4
To find the Banker's Discount if True Discount, Rate and
Time are given.
Banker's Discount
True Discount 1 +
Rate x Time
= TD 1 +
2.
7^-% per annum simple interest is Rs 16. Find the sum.
RT
Illustrative Example
a)Rsl760
b)Rsl560
c)Rsl660
d)Rsl860
The banker's gain on a bill due 1 year hence at 5% is Re
1. The true discount is:
Ex:
a)Rsl5
Too
100
If the TD on a certain sum due 9 months hence at 4%
is Rs 20. What is the BD on the same sum for the same
time and at the same rate?
Soln: Applying the above formula, we have
BD=20 1 +
4x9
= Rs 20.60.
12x100
Exercise
1.
2.
3.
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?
a) Rs 37.80 b)Rs 27.08 c)Rs 37.08 d) None of these
The banker's discount on a bill due 6 months hence at
6% is Rs 37.08. Find the true discount.
a)Rs38
b)Rs32
c)Rs36
d)Noneofthese
,1
If the TD on a certain sum due 1 — years hence at 8% is
3.
d)Rs5
90x100
1. c; Hint: True Discount = ——2—
Rs 600
3x5
.-. Banker's Discount = True Discount + Banker's Gain
= Rs600 + Rs90 = Rs690
16x100
2. a; Hint: TD = j p= = Rs 160
—x —
3 2
=
BD = Rsl60 + Rs 16 = R s l 7 6
Sum =
176x100
= Rsl760
4 15
—x —
3 2
3.b; Hint: TD =
BGxlOO
1x100
RxT
5x1
[See Rule 3]
= Rs20.
Rule 6
To find the Banker's Discount when True Discount and the
Face Value are given.
Banker's Discount
Answers
1. c
,
100
1
A A
3708
.-. TD
103
AxTD
~~ Bill Amount or Face Value-True Discount
A-TD
Illustrative Example
Rule 5
Ex:
To find Banker's Gain (BG) when True Discount (TD), Rate
(R) and Time (T) are given.
Banker's Gain (BG)
True Discount x Rate x Time
100
Bill Amount or Face Value x True Discount
= Rs36
3. c
If the true discount on a bill for Rs 480 is Rs 80. Find
the bankers' discount.
Soln: Applying the above formula, we have
TD x R x T
~
Banker's Discount
100
Illustrative Example
Exercise
Ex:
1.
If the TD on a certain sum due 4 years hence at 4% is
Rs 250. What is the Banker's gain (BG) on the same
sum for the same time and at the same rate?
Soln: Applying the above theorem, we have
2.
250x4x5
Banker's Gain = — —
= Rs 50.
3.
Exercise
1.
c)Rs25
Answers
Rs 25. What is the BD on the same sum for the same time
and at the same rate?
a) Rs 27.50 b)Rs 28.50 c)Rs28
d)Rs 27.25
2. c; Hint: 37.08 = TD
b)Rs20
Find the banker's discount on a bill due 3 years hence at
1
480x80
480x80
480-80
400
= Rs96
I f the true discount on a bill for Rs 560 is Rs 60. Find the
bankers' discount.
a)Rs67.2
b)Rs68
c)Rs68.5
d)Rs67.5
If the true discount on a bill for Rs 450 is Rs 50. Find the
bankers' discount.
a) Rs 66.25 b)Rs 56.25 c)Rs 56.50 d) None of these
If the true discount on a bill for Rs 670 is Rs 70. Find the
bankers' discount.
a)Rs88
b)Rs76
c)Rs78
d)Rs80

PRACTICE BOOK ON QUICKER MATHS
718
Answers
I.a
2.b
3.c
Rule 7
To find present worth, when Banker's Gain (BG), Time (T)
and Rate (R) are given:
3.
H.NJ
Present worth = Banker's Gain x
RT
Illustrative Example
4.
EK
The banker's gain on a bill due 4 years hence at 5% is
Rs 40. Find the present worth of the bill.
Soln: Applying the above formula, we have
hence is Rs 165. Find the true discount and the banker's
gain.
a)Rsl50,Rsl5
b)Rsl60,Rs5
c)Rsl45,Rs20
d) None of these
The present worth of a certain bill due some time hence
is Rs 1600 and the true discount on the bill is Rs 160.
Find the banker's discount and the extra gain the banker
would make in the transaction.
a)Rsl76,Rsl8
b)Rsl86,Rsl6
c)Rsl76,Rsl6
d) None of these
The present worth of a sum due sometimes hence is Rs
576 and the banker's gain is Re 1. The true discount is:
a)Rsl6
b)Rsl8
c)Rs24
d)Rs32
Answers
100x100
Present Worth =
4
0
x
20x20
= 25 x40 = Rsl000.
l.a;Hint:TD= V P W X B G
110x110
(TP)
or, BG =
= Rs 11
PW
1100
.-. BD = BG + TD = R s ( l l + 110) = Rsl21.
Exercise
1.
2.
3.
The banker's gain on a bill due 2 years hence at 5% is Rs
8, find the present worth of the bill.
a)Rs800
b)Rs650
c)Rs750
d)Rs850
The banker's gain on a bill due 2 years hence at 6% is Rs
36. Find the present worth of the bill.
a)Rs2400
b)Rs2550
c)Rs2440
d)Rs2500
The banker's gain on a bill due 3 years hence at 5% is Rs
45. Find the present worth of the bill.
a)Rs2000
b)Rs2200
c)Rs2250 d) None of these
BDxTD
2. a; Hint: Sum = B D - T D
TD
Sum
BDxTD
BG
1650
10
BG
1
BD
165
i.e., if BG is Re 1, TD = Rs 10 or BD = Rs 11
.-. If BD is Rs 11, TD = Rs 10
Answers
10
If BD is Rs 165,TD = Rs
„ 100x100
1. a; Hint: Present Worth = 8 x — — = R s goo
10x10
3. a
2.d
xl65
11
Rs 150
Also BG = Rs (165- 150) = Rsl5.
3. c; Hint: 160= V l 6 0 0 x B G
Rule 8
160x160
To find True Discount when present worth and Banker's
Gain are given.
••
True Discount'= ^ P W x B G
.-. Banker's Discount = 160 + 16 = Rs 176.
[ v BD=TD+BG].
Illustrative Example
Ex:
The present worth and the banker's gain on a bill is
Rs 160000 and Rs 25 respectively. Find the discount
of the bill.
Soln: Applying the above formula, we have
True Discount = Vl60000x25 =400x5 = Rs2000.
Exercise
1.
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.
a)Rsll,Rsl21
b)Rs21,Rsl31
c) Rs 12, Rs 122
d) None of these
The banker's discount on Rs 1650 due a certain time
B
G
=
- 7 6 ^
=
R
s
1
6
4. c;Hint:TD= ^ ( P W x B G ) = ^(576x1) =Rs24.
Rule 9
Tofind the sum or Bill Amount when the banker's discount
and the true discount are given.
Bill Amount (A) =
Ban ker's Discount x True Discount
. Discount - True Discount
B
a
nk e r
s
Banker's Discount x True Discount
Banker's Gain
Illustrative Example
Ex:
The bankers discount and the true discount on a certain sum is Rs 50 and Rs 40. Find the sum.

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