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 "in-terest 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 Dis-count ' 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 Dis-count' 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) 100

(ii) Banker's Gain (BG) = Simple interest on True Dis-T . D x R x T

count(TD)= 1 Q ( )

= Banker's Discount (B.D) - True Discount (TD.) (iif) True Discount (TD.) = Bill Amount (A) - Present

Worth (PW) = Simple Interest on Present Worth (PW)

P W x R x T 100

Rule 1 To find the Banker's Discount when Bill Amount (A), Time (T) and Rate (R) are given.

A x R x T Banker's Discount =

100

Illustrative Example E K 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 Banker's Discount = . . .

100x12 = Rs 51

Exercise 1. 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

2. 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

3. 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

716 PRACTICE BOOK ON QUICKER MATHS

SI on Rs 1800 for 8 months = Rs 60

Rate = 100x60

1800x % = 5%

1860x5x-

2. a

Banker's Discount =

3.c

100 -2- = R S 62

Rule 2 To find the Banker's Gain (BG) when Bill Amount (A), rime (T) and Rate (R) are given.

A ( R T ) 2 (I) Banker's Gain = 1 f t f t / l f t n , D T N or,

(TD) ' 100(100 + RT) PW '

where TD = True Discount, PW = Present Worth

A x R x T (11) True Discount (TD) = 100 +RT

Illustrative Example 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

2550x 6x

Banker's Gain = 100 100+ 6x

2550x4 100x102

= Rel .

Note: Banker's Gain = BD - TD [ie i f you calculate TD, you can find the Banker's Gain by subtracting TD from BD.

Exercise 1. 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

2. 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

3. The true disocunt on a bill of Rs 540 is Rs 90. The banker's discount is: a)Rs60 b)Rsl50 c)Rsl08 d )Rs l l0

4. 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

5. 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

Answers 1. d; Hint: Present Worth = Rs 1860 - Rs 60 = Rs 1800

\

BG = (TD) Z 60x60

Present Worth 1800 = Rs2

2. a 3. c; Hint: Present Worth = 540 - 90 = Rs 450

90x90 Banker's Gain = = Rs 18

450 .-. Banker's discount = 90 + 18 = Rs 108 [See Note].

4. c; Hint: BG = (TD) 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.

required answer = 8 1 0 0 x 5 x - x 5 x l

4 4

100 100 + 5x Rs 1.25.

Rule 3 To find the face value (or bill amount) when Banker's Dis-count (BD) and Time (T) are given.

I O O X B D Face value (A) =

R x T Illustrative Example 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

Face value = 100x60

Rs3000 4x-

12

Exercise 1. 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

2. I f 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

3. I f the B.D on a bill at 6% per annum is Rs 63, find the face value of 3 months bill. a)Rs415

i Banker's Discount 717

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

100 = TD 1 +

RT Too

Illustrative Example Ex: I f 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

12x100 = Rs 20.60.

Exercise 1. I f 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

2. 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 3. I f the TD on a certain sum due 1 years hence at 8% is

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

Answers 1. c

2. c; Hint: 37.08 = TD 1 , A A .-. TD

3. c 100

3708 103

= Rs36

Rule 5 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 TD x R x T

100 ~ 100

Illustrative Example Ex: I f 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 250x4x5

Banker's Gain = = Rs 50.

Exercise 1. Find the banker's discount on a bill due 3 years hence at

5% being given that the banker's gain is Rs 90. a)Rs550 b)Rs650 c)Rs690 d)Rs600

2. The banker's gain on a bill due 1 year 4 months hence at

7^-% per annum simple interest is Rs 16. Find the sum.

a)Rsl760 b)Rsl560 c)Rsl660 d)Rsl860 3. The banker's gain on a bill due 1 year hence at 5% is Re

1. The true discount is:

a)Rsl5 b)Rs20 c)Rs25 d)Rs5

Answers 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 =Rsl76

176x100 Sum = 4 15 x 3 2

= Rsl760 [See Rule 3]

3.b; Hint: TD = BGxlOO

R x T

1x100 5x1 = Rs20.

Rule 6 To find the Banker's Discount when True Discount and the Face Value are given. Banker's Discount

Bill Amount or Face Value x True Discount A x T D ~~ Bill Amount or Face Value-True Discount A - T D

Illustrative Example Ex: I f the true discount on a bill for Rs 480 is Rs 80. Find

the bankers' discount. Soln: Applying the above formula, we have

480x80 480x80 Banker's Discount1 480-80 400

= Rs96

Exercise 1. 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

2. I f 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

3. I f the true discount on a bill for Rs 670 is Rs 70. Find the bankers' discount. a)Rs88 b)Rs76 c)Rs78 d)Rs80

718 PRACTICE BOOK ON QUICKER MATHS

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:

H.NJ Present worth = Banker's Gain x

R T

Illustrative Example E K 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

3. 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

4. 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

Present Worth = 4 0 x 100x100

20x20 = 25 x40 = Rsl000. l . a ; H i n t : T D = V P W X B G

Exercise 1. 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

2. 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

3. 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

Answers 100x100

1. a; Hint: Present Worth = 8 x = R s goo 10x10

2 .d 3. a

Rule 8 To find True Discount when present worth and Banker's Gain are given.

True Discount'= ^ P W x B G

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. 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 )Rs l l ,Rs l21 b)Rs21,Rsl31 c) Rs 12, Rs 122 d) None of these

2. The banker's discount on Rs 1650 due a certain time

or, BG = (TP)

PW

110x110

1100 = Rs 11

.-. BD = BG + TD = Rs ( l l + 110) = Rsl21.

B D x T D B D x T D 2. a; Hint: Sum =

TD BG

B D - T D

Sum 1650

BG

10 1 BD 165

i.e., i f BG is Re 1, TD = Rs 10 or BD = Rs 11 .-. I f BD is Rs 11, TD = Rs 10

If BD is Rs 165,TD = Rs 10

1 1 xl65 Rs 150

Also BG = Rs (165- 150) = Rsl5.

3. c; Hint: 160= Vl600xBG

160x160 B G = - 7 6 ^ = R s 1 6 .-. Banker's Discount = 160 + 16 = Rs 176.

[ v BD=TD+BG].

4. c;Hint :TD= ^ (PWxBG) = (576x1) =Rs24.

Rule 9 To find the sum or Bill Amount when the banker's discount and the true discount are given.

Ban ker's Discount x True Discount Bill Amount (A) = B a n k e r . s Discount - True Discount

Banker's Discount x True Discount Banker's Gain

Illustrative Example Ex: The bankers discount and the true discount on a cer-

tain sum is Rs 50 and Rs 40. Find the sum.

Banker's Discount 719

Soln: Applying the above formula, we have

50x40 S u m = I o ^ o - = R s 2 0 -

Exercise 1. The banker's discount and the true discount on a sum of

money due 8 months hence are Rs 52 and Rs 50, respec-tively. Find the sum and the rate per cent. a) Rs 1300,6% b) Rs 1200,5% c) Rs 1500,8% d) None of these

2. The banker's discount on a certain sum of money is Rs 36 and the discount on the same sum for the same time and at the same rate is Rs 30. Find the sum. a)Rsl50 b)Rsl90 c)Rsl65 d)Rsl80

3. The banker's discount on a bill due 1 year 8 months hence is Rs 50 and the true discount on the same sum at the same rate per cent is Rs 45. The rate per cent is:

a) 6%

Answers

b) e | % c) 6 - % 2

BDxTD (52x50 1. a; Hint: Sum = gQ_-j-[)

44

; Rsl300

Since BD is SI on sum due, so SI on Rs 1300 for 8 months is Rs 52. Consequently,

/ ^

100x52 Rate =

1300x: % = 6%

2.d

3. c; Hint: Sunv BDxTD 50x45

B D - T D Now, Rs 50 is SI on Rs 450 for (5/3) years.

Rs450

Rate^ 100x50

450 x -= 6 - %

3

Rule 10 Theorem: The banker's discount on Rs x at R% is equal to the true discount on Rsy for the same time and at the same

lOOf y-rate. Then the time is given by ^ 1 ; years.

Illustrative Example Ex: The banker's discount on Rs 1000 at 5% is equal to

the true discount on Rs 1050 for the same time and at

the same rate. Find the time. Soln: Applying the above theorem, we have

100(1050-1000)

Time=j^m=lyear lOOf y - x ^

Note: I f time is given, R can be calculated by j I I

per cent.

Exercise 1. The banker's disocunt 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. a) 3 months b) 4 months c) 6 months d) None of these

2. The banker's discount on Rs 1600 at 6% is the same as the true discount on Rs 1624 for the same time and at the same rate. Then, the time is: a) 3 months b) 4 months c) 6 months d) 8 months

3. The banker's discount on Rs 800 at 15% is equal to the true discount on Rs 950 for the same time and at the same rate. Find the time.

. 1 a) 1 years

c) I- years

, 1 b) 1 years

d) None of these

Answers 1. b 2. a; Hint: SI on Rs 1600 = TD on Rs 1624

.-. Rs 1600isPWofRs 1624 i.e., Rs 24 is the SI on Rs 1600 at 6%

(100x24") _ 1 T i m e = l l 6 0 0 x 6 j ~ 4 y.

Illustrative Example Ex: I f the banker's gain on a certain sum due 4 years hence

is of the banker's discount on it for the same time

720 PRACTICE BOOK ON QUICKER MATHS

and at the same rate, find the rate per cent. Soln: Applying the above theorem, we have

Required rate per cent

100 4 59-9

25x9 9 1 ^ = ~ = 4-percent

Note: When in place of time, rate (R) is given then the time (T) can be calculated by

100 R y - x years.

Exercise

1. The banker's gain on a certain sum due 2 years hence

is r r of the banker's discount on it for the same time

and at the same rate. Find the rate per cent, a) 5% b)4% c)8% d)6%

2. If the banker's gain on a certain sum due 5 years hence is 1 of the banker's discount on it for the same time and at the same rate, find the rate per cent.

a) 4% b)5% c)6%

If the banker's gain on a certain sum due 3 years hence is

d) 5-o/ 0 2

of the banker's discount on it for the same time and J I

at the same rate, find the rate per cent. a) 5% b)6% c)8% d)9%

Answers

1. d; Hint: Rate per cent =

2. b 3.c

100x2 23-3 = 6%

Rule 12 Theorem: If the banker's discount on a certain sum due 'T'

x

years hence is ~ of the true discount on it for the same

time and at the same rate, then the rate per cent is given by 100

y

Note: Here.v>y.

Illustrative Example Ex: The banker's discount on a certain sum due 5 years

11 hence is of the true discount on it for the same

time and at the same rate. Find the rate per cent. Soln: Applying the above theorem, we have the

,100(11 ^ 1 required rate per cent = L Q 1 I = 20 X - 2 /O

Note: When in place of time (T), rate (R) is given, then the time (T) can be calculated by

T = 100 7T

* - i years.

Exercise 1. The banker's discount on a certain sum due 2 years hence

11 is of the true discount on it for the same time and at

the same rate. Find the rate per cent. a) 2% b)3% c)4% d)5%

2. The banker's discount on a certain sum due 3 years hence

31 is of the true discount on it for the same time and at

the same rate. Find the rate per cent. a) 6% b)7% c)8% d) None of these

3. The banker's discount on a certain sum due 4 years hence

21 is of the true discount on it for the same time and at

the same rate. Find the rate per cent.

a) l i %

Answers l . d

b) 2 - %

2.c

c ) l - % d) None of these

3.a

Rule 13 Theorem: If the rate per cent and timefor a bill are numeri-cally equal and also the true discount is 'n' times the banker's gain, then the rate per cent or time is given by

4 Illustrative Example Ex: I f the rate per cent and time for a bill are numerically

equal and also the true discount is 25 times the banker's gain, find the rate per cent. Applying the above theorem, we have

T Soln:

Rate per cent = 10, 25

: 2 per cent.

Note: I f time and rate are not equal, use the following result to calculate R and T.

RT Too

Banker's Discount 721

the

esuh

Exercise 1. I f the rate per cent and time for a bill are numerically

equal and also the true discount is 4 times the banker's gain, find the rate per cent. a) 5% b)4% c)6% d)3%

2. I f the rate per cent and time for a bill are numerically equal and also the true discount is 16 times the banker's gain, find the rate per cent.

a) 2 - % b)5% 2

c)6% d)4%

3. I f the rate per cent and time for a bill are numerically equal and also the true discount is 9 times the banker's gain, find the rate per cent.

a) 2%

Answers l .a

1 b)3% c ) 3 j % d) None of these

2.a 3.c

Rule 14 To find the true discount if the banker's discount and bill amount are given.

Bill Amount x Banker's Discount True Discount = Bill Amount + Banker's Discount

Illustrative Example Ex: I f the B.D on a bill for Rs 540 is Rs 108. Find the true

discount. Soln: Applying the above theorem, we have

540x108

T D = = R s 9 a Exercise 1. I f the B.D on a bill for Rs 650 is Rs 150. Find the true

discount. a)Rsl20 b)Rs 129.8 c)Rs 121.8 d)Rs 120.8

2. I f the B.D on a bill for Rs 540 is Rs 180. Find the true discount. a)Rsl30 b)Rsl35 c)Rsl25 d) None of these

3. I f the B.D on a bill for Rs 350 is Rs 50. Find the true discount.

a) Rs 43.75 b)Rs45 c)Rs 39.75 d) None of these

Answers l .c 2.b 3.a

Rule 15 To find the amount of bill or bill amount or face value when Banker's Discount and Banker's gain are given. Bill Amount (A)

Ban ker's Discount x (Ban ker' J Discount - Ban ker's Gain)

Ban ker's Gain

B D x ( B D - B G ) BG ,

Illustrative Example Ex: The banker's discount and banker's gain are Rs 125

and Rs 5 respectively. Find the amount of the bill. Soln: Applying the above formula, we have

125x(125-5) Bill amount = 125 x 24 = Rs 3000.

Exercise 1. The banker's discount and banker's gain are Rs 120 and

Rs 5 respectively. Find the amount of the bill. a)Rs2760 b)Rs2560 c)Rs2670 d) None of these

2. The banker's discount and banker's gain are Rs 144 and Rs 12 respectively. Find the amount of the bill. a)Rsl854 b)Rsl485 c)Rsl584 d)Noneofthese

3. The banker's discount and banker's gain are Rs 49 and Rs 7 respectively. Find the amount of the bill. a)Rs294 b)Rs284 c)Rs249 d)Rs274

Answers l .a 2.c 3.a

Miscellaneous Exercise 1. What rate per cent does a man get for his money when in

discounting a bill due 10 months hence, he deducts 4% of the amount of the bill? a) 5% b)6% c)8% d)4%

2. A bill was drawn on March 8, at 7 months date and was discounted on May 18, at 5%. I f the banker's gain is Rs 3, find (i) the true discount

a)Rsl60 b)Rsl52 c)Rsl53 d)Rsl50 (ii) the banker's discount and

a)Rsl53 b)Rs 151 c)Rsl55 d)Rsl63 (iii) the sum of the bill.

a) Rs 7650 b) Rs 7550 c) Rs7850 d) None ofthese

3. The holder of a bill for Rs 17850 nominally due on 21st May, 1991 received Rs 357 less than the amount of the bi l l by having it discounted at 5%. When was it disocunted? a) Dec 29,1990 b) Dec 30,1989 c) Dec 19,1990 d) None of these

4. A bill for Rs 5656 is drawn on July, 14 at 5 months. It is discounted on Oct 5th at 5%. (i) banker's discount

a) Rs 56.56 b)Rs56 c)Rs 56.50 d) None of these (ii) true discount

a)Rs50 b)Rs 54.56 c) Rs 56 d) None of these (iii) banker's gain and

a)Rs6.56 b)Rsl.44 c)Rs0.56 d)None ofthese (iv) Money received by the holder of the bill,

a) Rs 5599.56 b)Rs 5599.44

722 PRACTICE BOOK ON QUICKER MATHS

c) Rs 5599 d) None of these A banker paid Rs 5767.50 for a bill of Rs 5840, drawn on April 4, at 6 months. On what day was the bill discounted, the rate of interest being 7%? a) 3rd Aug b) 4th Aug c) 3rd Sep d) 3rd Jul

The banker's discount on a sum of money for \ years

is Rs 60 and the true discount on the same sum for 2 years is Rs 75. The rate per cent is:

a) 5% b) 6% ,2

c) 6 - 0 / 0 1

d) 3-o/ 0 3 -

A bill is discounted at 5% per annum. I f banker's dis-count be allowed, at what rate per cent must the pro-ceeds be invested, so that nothing may be lost?

a) 5% b)4Yi% b)5]|% d) 10%

8. The interest on a certain sum of money is Rs 67.20 and the discount on the same sum of money for the same time and at the same rate is Rs 60. What is the sum? a)Rs560 b)Rs480 c)Rs590 d)Rs860

Answers l .a; Hint: Let the amount of bill be Rs 100.

Money deducted = Rs 4 Money received by holder of the bill

= Rs(100-4) = Rs96 SI on Rs 96 for 10 months = Rs 4

Rate : 100x4x6

96x5 = 5%.

2. Hint: Date on which the bill was drawn = March 8th at 7 months.

Nominally due date = Oct 8th. Legally due date Oct, 11th. Date on which the bill was discounted = May, 18th. Time for Which the bill has yet to run May June July Aug Sep Oct

13 + 30+ 31 + 31 + 30+ 1 1 = 146 days = - years.

Now (i) d; Banker's gain = SI on TD

i.e., Rs 3 is SI on TD for years at 5%

100x3 2 = 5

(ii)a;BD = TD + SI on TD

. TD = Rs 5 x =Rsl50 5

Rs 150 + SI on Rs 150 for ~ years at 5%

. . . 2 5 ;Rsl50 + Rs 1 5 0 x y x ^ =Rsl53.

(iii) a; Sum ! B D x T D 153x150

= Rs7650. B D - T D 153-150

3. a; Hint: Clearly, SI on Rs 17850 at 5% is Rs 357.

(100x357 T i m e = 17850^5 146 days.

So, the bill is 146 days prior to 24th may, the legally due date. May April March Feb Jan Dec 24+ 30+ 31 + 28+ 31 + 2 = 146 days.

So, the bill was discounted on Dec 29,1990. 4. Hint: (i) a; Face value of the bill = Rs 5656

Date on which the bill was drawn = July, 14th at 5 months. Nominally due date = December, 14 th Legally due date = December, 17th. Date on which the bill was discounted = October, 5th Period for which the bill has yet to run Oct Nov Dec

1 26 + 30 + 17 = 73 days or year

.-. BD = SI on Rs 5656 fpr - years at 5%

= Rs ^5656x1x5^

100x5 = Rs 56.56

( i i )c ;TD = Rs '

5656x5x 5

100+ 5x Rs56

(iii) c; BG = BD - TD = 56 paise (iv) b; Money received by the holder of the bill

= Rs (5656 - 56.56) = Rs 5599.44. 5. a; Hint: BD = Rs (5840 - 5767.20) = Rs 72.80

.-. Rs 72.80 is SI on Rs 5840 at 7%

100x72.80 13 So, unexpired time = _ ,_ = years = 65 days.

7x5840 73 Now, date of draw of bill = April, 4 at 6 months. Nominally due date = October, 4 Legally due date = October, 7 So, we must go back 65 days from October, 7 Oct Sept Aug = 7 + 30 + 28 i.e., The bill was discounted on 3rd August.

6. d; Hint: BD for (3/2) years = Rs 60

f 6 0 x 2 ,1 BDfor2years = Rs I x 2 =Rs80

Banker's Discount 723

Now, BD = Rs 80 : TD = Rs 75 and Time = 2 years.

( 80x75"! .-. Sum = R s l ; j = R s l 2 0 0

.-. Rs 80 is SI on Rs 1200 for 2 years.

1 0 0 x 8 0 \

3 So, rate : % = 3-o/ 0

,1200x2,

7. c; Hint: Let the sum be Rs 100. Then, BD = Rs 5. Proceeds = Rs (100 - 5) = Rs 95 .-. Rs 5 must be the interest on Rs 95 for 1 year.

e 100x5" So, rate = 95x1 =V / o-

8. a; Hint: Interest on Sum - True Discount = Interest on True Discount [ The difference between the simple interest and the true discount on a sum of money is equal to the simple interest on the true discount for the given time at the given rate per cent.

Proof: Sum = PW + TD .. Interest on sum = Int on PW + Int on TD = TD + Int onTD Interest on sum - TD = Int on TD or, Banker's gain = IntonTDj In the given question, we have Rs 67.20 - Rs 60 = Int on Rs 60

Rs 7 1

Re 1 = Int on Rs

Int on Rs 60

60 1

Rs 6 7 - =IntonRs r x 6 7 -5 1 5

5

.-. the required sum = Rs ~- x 67 = Rs 560. 7 5

5