Q 1-The true discount on a bill for Rs. 2520 due 6 months hence at 10% per annum is

A - Rs. 180

B - Rs. 140

C - Rs. 80

D - Rs. 120

Answer - D

Explanation

"F= Rs. 2520 T=6 months = 1/2 year R = 10%
TD = FTR/[100+(TR)] =[2520×1/2×10]/100+((1/2)×10)
=>(1260×10)/(100+5)
=>12600/105 =>2520/21
=Rs. 120
"

Q 2-The present worth of a sum due sometime hence is Rs. 576 and the banker's gain is Rs. 16. The true discount is:

A - Rs. 36

B - Rs. 72

C - Rs. 48

D - Rs. 96

Answer - D

Explanation

T.D. = P.W. x B.G. = 576 x 16 = 96.

Q 3-What is the present worth of a bill of Rs.1764 due 2 years hence at 5% compound interest is

A - Rs. 1600

B - Rs. 1200

C - Rs. 1800

D - Rs. 1400

Answer - A

Explanation

"Since the compound interest is taken here,
PW (1+5/100)^2 =1764
PW (1+1/20)^2=1764
PW (21/20)^2=1764
PW ×441/400=1764
⇒PW =(1764×400)/441
=4×400
=Rs. 1600
"

Q 4-The banker's discount of a certain sum of money is Rs. 36 and the true discount on the same sum for the same time is Rs. 30. What is the sum due?

A - Rs. 180

B - Rs. 120

C - Rs. 220

D - Rs. 200

Answer - A

Explanation

F = BD × TD/(BD -TD)=36×30/(36-30)=(36×30)/6=36×5 = Rs. 180 

Q 5-The banker's discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. What is the time?

A - 3 months

B - 4 months

C - 5 months

D - 6 months

Answer - B

Explanation

"Bankers Discount,
BD = Simple Interest on the face value of the bill for unexpired time.
True Discount,
TD = Simple Interest on the present value for unexpired time.
Simple Interest on Rs. 1600 = True Discount on Rs.1680
=> Rs. 1600 is the Present Worth (PW) of Rs. 1680
=> Rs. 80 is the Simple Interest of Rs.1600 at 15%
⇒80=(1600×T×15)/100
⇒80=16×T×15 ⇒5=T×15
⇒1=T×3=>
T = 1/3 year=12/3 months
=4 months
"

Q 6-What is the difference between the banker's discount and the true discount on Rs.8100 for 3 months at 5%

A - Rs. 2

B - Rs. 1.25

C - Rs. 2.25

D - Rs. 0.5

Answer - B

Explanation

"F = Rs. 8100
R = 5%
T = 3 months = 14 years
BD = FTR/100
=(8100×14×5)/100=2025/20=405/4= Rs. 101.25
and TD = FTR/100+(TR) =(8100×14×5)/(100+((1/4)×5))
=(2025×5)/(100+(5/4)
=(2025×5×4)/(400+5)
=(2025×5×4)/405
=(405×5×4)/81
= (45×5×4)/9 =5×5×4
= Rs. 100
=> BD - TD = Rs. 101.25 - Rs. 100
= Rs. 1.25
"

Q 7-What is the banker's discount if the true discount on a bill of Rs.540 is Rs.90 ?

A - Rs. 108

B - Rs. 120

C - Rs. 102

D - Rs. 106

Answer - A

Explanation

"Present Worth, PW = F - TD = 540 - 90 = Rs. 450

Simple Interest on the Present Worth = True Discount

Hence Simple Interest on 450 = 90 ------(Equation 1)

Simple Interest on the face value = Bankers Discount

=> Simple Interest on 540 = Bankers Discount

From Equation 1, Simple Interest on 450 = 90

Hence, Simple Interest on 540 = (90/450)×540=540/5 = Rs. 108"

Q 8-The banker's discount on a bill due 6 months hence at 6% is Rs. 18.54. What is the true discount?

A - Rs. 24

B - Rs. 12

C - Rs. 36

D - Rs. 18

Answer - D

Explanation

"T = 6 months = 12 year
T = 6 months = 12 year
R = 6% TD = (BD ×100)/(100+ TR) =18.54×100/100+((1/2)×6)
=18.54×100/103 =1854/103
=Rs. 18
"

Q 9-The true discount on a bill of Rs. 2160 is Rs. 360. What is the banker's discount?

A - Rs. 432

B - Rs. 422

C - Rs. 412

D - Rs. 442

Answer - A

Explanation

"F = Rs. 2160

TD = Rs. 360

PW = F - TD = 2160 - 360 = Rs. 1800

True Discount is the Simple Interest on the present value for unexpired time

=>Simple Interest on Rs. 1800 for unexpired time = Rs. 360

Banker's Discount is the Simple Interest on the face value of the bill for unexpired time

= Simple Interest on Rs. 2160 for unexpired time

=(360/1800)×2160=(1/5)×2160=Rs. 432"

Q 10-The banker's discount on a sum of money for 3 years is Rs. 1116. The true discount on the same sum for 4 years is Rs. 1200. What is the rate per cent?

A - 8%

B - 12%

C - 10%

D - 6%

Answer - D

Explanation

"BD for 3 years = Rs. 1116
BD for 4 years = 11163×4 = Rs. 1488
BD for 4 years = 11163×4 = Rs. 1488
TD for 4 years = Rs. 1200
F = BD × TD(BD - TD) =1488×1200/(1488-1200)
=(1488×1200)/288 =(124×1200)/24
=(124×100)/2 = 62×100 =Rs. 6200
=> Rs.1488 is the simple interest on Rs. 6200 for 4 years
⇒1488 = (6200×4×R)/100
⇒ R=(1488×100)/(6200×4)
=(372×100/6200)=372/62=6%
"

Q 11-A bill is discounted at 10% per annum. If banker's discount is allowed, at what rate percent should the proceeds be invested so that nothing will be lost?

A - 91/9%

B - 100/9%

C - 11

D - 92/9%

Answer - B

Explanation

"Let the amount = Rs.100
Then BD = Rs.10 (banker's discount, BD is the simple Interest
on the face value of the bill for unexpired time
and bill is discounted at 10% per annum)
Proceeds = Rs.100 - Rs.10 = Rs.90
Hence we should get Rs.10 as the interest of Rs.90 for 1 year
so that nothing will be lost ⇒(10=90×1×R)/100
⇒R=(10×100)/90
=100/9%
"

Q 12-The banker's discount and the true discount on a sum of money due 8 months hence are Rs. 120 and Rs. 110 respectively. Find the rate percent.

A - 120/11%

B - 130/11%

C - 140/11%

D - 150/11%

Answer - D

Explanation

"Sum =[( B.D.*T.D.)/(B.D.-T.D.)] = Rs.[(120x110)/(120-110)] = Rs. 1320.
Since B.D. is S.I. on sum due, so S.I. on Rs. 1320 for 8 months is Rs. 120.
Rate =[(100 x120)/( 1320 x 2/3)% = 150/11%."

Q 13-The banker's discount on a sum of money for 1 years is Rs. 558 and the true discount on the same sum for 2 years is Rs. 600. The rate percent is:

A - 10%

B - 13%

C - 12%

D - 15%

Answer - C

Explanation

"B.D. for 1 years = Rs. 558. B.D. for 2 years = Rs.558 x (2/3) x 2
= Rs. 744 T.D. for 2 years = Rs. 600.
Sum = B.D. x T.D.)/(B.D. - T.D)
= Rs.(744 x 600)/144 =Rs.3100.
Thus, Rs. 744 is S.I. on Rs. 3100 for 2 years.
Rate =(100 x 744)/(3100 x 2)% = 12%
"

Q 14-The banker's gain on a sum due 6 years hence at 12% per annum is Rs. 540. What is the banker's discount?

A - 1240

B - 1120

C - 1190

D - 1290

Answer - D

Explanation

"TD = (BG ×100)/TR =(540×100)/(6×12)
=(90×100)/12
=(15×100)/2
= Rs. 750
BG = BD - TD
=> 540 = BD - 750
=> BD = 540 + 750 = 1290
"

Q 15-The banker's gain on a sum due 3 years hence at 12% per annum is Rs. 270. The banker's discount is:

A - Rs. 960

B - Rs. 840

C - Rs. 1020

D - Rs. 760

Answer - C

Explanation

"T.D. =(B.G. x 100)/(R x T)
= Rs.270 x 100/12 x 3= Rs. 750.
B.D. = Rs.(750 + 270) = Rs. 1020.
"

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