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. "