Bankers Discount.pdf

https://telegram.me/Banking_Zone

https://telegram.me/pdf4exams

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

https://telegram.me/Banking_Zone

https://telegram.me/pdf4exams

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

https://telegram.me/Banking_Zone

https://telegram.me/pdf4exams

i Banker's Discount

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 +

717

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

https://telegram.me/Banking_Zone

https://telegram.me/pdf4exams

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.

https://telegram.me/Banking_Zone

https://telegram.me/pdf4exams

Banker's Discount

Soln: Applying the above formula, we have

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

50x40 S u m =

100(1050-1000)

Io^o-=Rs20°Time=

Exercise 1.

2.

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. a) Rs 1300,6% b) Rs 1200,5% c) Rs 1500,8% d) None of these 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 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:

b) e | %

a) 6%

—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 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 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.

2.

44

c) 6 - % 2

3.

Answers BDxTD 1. a; Hint: Sum = gQ_-j-[)

(52x50 ;

Rsl300

.1 a) 1— years

,1 b) 1— years

c) I- years

d) None of these

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

^

100x52

Answers

% = 6%

Rate =

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%

1300x: 2.d 3. c; Hint: Sunv

BDxTD

50x45

(100x24") _ 1 ••• l l 6 0 0 x 6 j ~ 4 y<*r= 3 months. Note: Try to solve by direct formula also.

Rs450

BD-TD

T i m e =

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

100x50 Rate^ 450 x -

719

fa

Rule 11

= 6-% 3

Theorem: If the banker's gain on a certain sum due 'T' x years hence is ~ of the banker's discount on itfor the same

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 yrate. Then the time is given by ^ 1 ;

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

years.

\_y-x

Note: Herex<>>.

Illustrative Example 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

Ex:

If the banker's gain on a certain sum due 4 years hence is — of the banker's discount on it for the same time

https://telegram.me/Banking_Zone

https://telegram.me/pdf4exams

PRACTICE BOOK ON QUICKER MATHS

720

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

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

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

100

2.

7T

*-i

years.

years.

y-x

Exercise

Exercise 1.

^ 1 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=

R

,100(11 LQ

1.

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

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

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

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

the same rate. Find the rate per cent. a) 2% b)3% c)4% d)5% The banker's discount on a certain sum due 3 years hence

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

2.

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

3.

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

d) 5 - o / 2 If the banker's gain on a certain sum due 3 years hence is

a) 4%

b)5%

c)6%

0

the same rate. Find the rate per cent.

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

a) l i %

J I

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

d)9%

the same rate. Find the rate per cent. a) 6% b)7% c)8% d) None of these The banker's discount on a certain sum due 4 years hence

2. b

3.a

2.c

Rule 13

100x2 1. d; Hint: Rate per cent =

d) None of these

c)l-%

Answers l.d

Answers

b) 2 - %

23-3

= 6%

3.c

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

Theorem: If the rate per cent and timefor a bill are numerically 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

x

Ex:

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

Rate per cent = 10,

Note: Here.v>y.

Illustrative Example Ex:

If 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. Soln: Applying the above theorem, we have

T

2 per cent. 25 Note: I f time and rate are not equal, use the following result to calculate R and T.

The banker's discount on a certain sum due 5 years

RT

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

Too

:

https://telegram.me/Banking_Zone Banker's Discount

https://telegram.me/pdf4exams

Exercise

Illustrative Example

1.

Ex:

2.

3.

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% 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% c)6% d)4% 2 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%

„1 c ) 3 j % d) None of these

b)3%

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) 125 x 24 = Rs 3000. Bill amount =

Exercise 1.

2.

3.

Answers l.a

2.a

3.c

To find the true discount if the banker's discount and bill amount are given. Bill Amount x Banker's Discount True Discount =

Answers

Bill Amount + Banker's Discount

If the B.D on a bill for Rs 540 is Rs 108. Find the true discount.

1.

2.

540x108

=Rs9a

Exercise 1.

2.

3.

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 If 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 I f the B.D on a bill for Rs 350 is Rs 50. Find the true discount. a) Rs 43.75

the

b)Rs45

l.c

2.b

3.a

Rule 15 esuh

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

BDx(BD-BG) BG

,

3.

c)Rs 39.75 d) None of these

Answers

- Ban ker's Gain)

3.a

Exercise

Soln: Applying the above theorem, we have

TD=

2.c

Miscellaneous

Illustrative Example Ex:

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 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 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

l.a

Rule 14

721

4.

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% 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 ) R s l 5 2 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 The holder of a bill for Rs 17850 nominally due on 21st May, 1991 received Rs 357 less than the amount of the bill 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 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

https://telegram.me/Banking_Zone

https://telegram.me/pdf4exams

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: „1 d) 3-o/ 3-• A bill is discounted at 5% per annum. I f banker's discount be allowed, at what rate per cent must the proceeds be invested, so that nothing may be lost? a) 5%

a) 5% 8.

c)

b) 6%

) Yi

b 4

,2

6-0/0

) ]|

%

b 5

%

0

d) 10%

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

... ;Rsl50 + Rs

(iii) a; Sum

!

1

5

0

x

2 y

x

5 ^ =Rsl53.

BDxTD

153x150

BD-TD

153-150

= Rs7650.

3. a; Hint: Clearly, SI on Rs 17850 at 5% is Rs 357. (100x357 T

i

m

e

=

146 days.

17850^5

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

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

.-. BD = SI on Rs 5656 fpr - years at 5% ^5656x1x5^ = Rs

= Rs 56.56

100x5

100x4x6 Rate 2.

:

96x5

= 5%.

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 =R s l 5 0 •. TD = Rs ±2 = 5 5

x

(ii)a;BD = TD + SI on TD Rs 150 + SI on Rs 150 for ~ years at 5%

( i i ) c ; T D = Rs '

5656x5x — 5 100+

Rs56

5x

(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% So, unexpired time =

100x72.80 13 • _ ,_ = — 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 BDfor2years = Rs

f60x2 — I —

,1 x

2

=Rs80

Banker's Discount https://telegram.me/Banking_Zone

https://telegram.me/pdf4exams

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. So, rate

100x80\ % = 3-o/ 3

:

0

Proof: Sum = PW + T D .. Interest on sum = Int on PW + Int on TD = TD + Int onTD Interest on sum - T D = Int on TD or, Banker's gain = IntonTDj In the given question, we have Rs 67.20 - Rs 60 = Int on Rs 60

,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.

Rs 7

1

Int on Rs 60

Re 1 = Int on Rs e

So, rate =

100x5" 95x1

=

60 1

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.

723

• Rs 6 7 - = I n t o n R s — x 6 7 5 1 5 5 r

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