Q 1-The banker's discount on a certain amount due 2 years hence is 11/10 of the true discount. What is the rate percent?

A - 1%

B - 5%

C - 10%

D - 12%

```Answer - B

Explanation

"Let TD = Rs. 1 Then BD = (11/10)×1= Rs. 11/10
T = 2 R = ?
F = BD × TD/(BD - TD)
=((11/10)×1)/((11/10)−1)
=(11/10)/(1/10) = Rs. 11
BD =FTR/100
⇒11/10=11×2×R/100
⇒110=22R
⇒R=110/22=5%
"```

Q 2-The present worth of a certain bill due sometime hence is Rs. 800 and the true discount is Rs. 36. The banker's discount is:

A - Rs. 37

B - Rs. 37.62

C - Rs. 34.38

D - Rs. 38.98

```Answer - B

Explanation

"
B.G. = (T.D.)^2/P.W.
= Rs.(36 x 36)/800
= Rs. 1.62 B.D.
= (T.D. + B.G.)
= Rs. (36 + 1.62)
= Rs. 37.62
"```

Q 3-The B.G. on a certain sum 4 years hence at 5% is Rs. 200. What is the present worth?

A - Rs. 4500

B - Rs. 6000

C - Rs. 5000

D - Rs. 4000

```Answer - C

Explanation

"T = 4 years R = 5%
Banker's Gain, BG = Rs.200
TD = (BG ×100)/TR
=(200×100)/(4×5) = Rs. 1000
TD = √PW × BG 1000=√PW ×200 1000000
=PW ×200 PW =1000000/200
= Rs. 5000
"```

Q 4-The present worth of a certain bill due sometime hence is Rs. 400 and the true discount is Rs. 20. What is the banker's discount?

A - Rs. 19

B - Rs. 22

C - Rs. 20

D - Rs. 21

```Answer - D

Explanation

"BG = (TD)^2/PW=((20)^2)/400
= Rs. 1 BG = BD - TD
=> 1 = BD - 20
=> BD = 1 + 20
= Rs. 21
"```

Q 5-The true discount on a certain sum due 6 months hence at 15% is Rs. 240. What is the banker's discount on the same sum for the same time at the same rate?

A - Rs. 258

B - Rs. 278

C - Rs. 228

D - None of these

```Answer - A

Explanation

"TD = Rs. 240
T = 6 months = 1/2 year
R = 15% TD = (BG ×100)/TR
⇒240=BG×100(1/2×15)
BG =(240×15)/(100×2) =(120×15)/100
=Rs. 18
BG = BD - TD => 18
= BD - 240
=> BD = 18 + 240
= Rs. 258
"```

Q 6-A bill for Rs. 6000 is drawn on July 14 at 5 months. It is discounted on 5th October at 10%. Find the banker's gain.

A - 2.36

B - 2.4

C - 2.45

D - 2.5

```Answer - A

Explanation

"Face value of the bill = Rs. 6000.
Date on which the bill was drawn = July 14 at 5 months.
Nominally due date = December 14.
Legally due date = December 17.
Date on which the bill was discounted = October 5.
Unexpired time : Oct. Nov. Dec.
26        + 30        + 17 = 73 days =1/ 5Years
B.D. = S.I. on Rs. 6000 for 1/5 year
= Rs. (6000 x 10 x1/5 x1/100)= Rs. 120.
T.D. = Rs.[(6000 x 10 x1/5)/(100+(10*1/5))]
=Rs.(12000/102)=Rs. 117.64.
B.G. = (B.D.) - (T.D.) = Rs. (120 - 117.64) = Rs. 2.36."```

Q 7-What rate percent does a man get for his money when in discounting a bill due 10 months hence, he deducts 10% of the amount of the bill?

A - 10/3%

B - 20/3%

C - 50/3%

D - 40/3%

```Answer - D

Explanation

"Let amount of the bill = Rs.100
Money deducted =Rs.10
Money received by the holder of the bill = Rs.100-10 = Rs.90
SI on Rs.90 for 10 months = Rs.10
Rate =[(100*10)/(90*10/12)% = 40/3%"```

Q 8-The banker's gain of a certain sum due 2 years hence at 10% per annum is Rs. 24. What is the present worth?

A - Rs. 600

B - Rs. 500

C - Rs. 400

D - Rs. 300

```Answer - A

Explanation

"T = 2 years R = 10%
TD = (BG ×100)/TR=(24×100)/(2×10)
=12×10=Rs. 120
TD = (PW × TR)/100
⇒120=(PW ×2×10)/100
⇒1200=PW ×2 PW =1200/2
= Rs. 600
"```

Q 9-A banker paid Rs.5767.20 for a bill of Rs.5840, drawn of Apr 4 at 6 months. If the rate of interest was 7%, what was the day on which the bill was discounted?

A - 3rd March

B - 3rd September

C - 3rd October

D - 3rd August

```Answer - D

Explanation

"F = Rs.5840 R = 7%
BD = 5840 - 5767.20 = Rs.72.8
BD = FTR/100
⇒72.8=(5840×T×7)/100
⇒ T=(72.8×100)/(7×5840) =(10.4×100)/5840=1040/5840
=104/584=13/73 years=(13×365)/73
Days =65 Days
⇒ Unexpired Time = 65 Days
Given that Date of Draw of the bill = 4th April at 6 months
=> Nominally Due Date = 4th October
=> Legally Due Date = (4th October + 3 days)
= 7th October
Hence, The date on which the bill was discounted = (7th October - 65 days)
= (7th October - 7 days in October - 30 days in September - 28 days in August)
= 3rd August
"```

Q 10-The banker's gain of a certain sum due 3 years hence at 10% per annum is Rs. 36. What is the present worth ?

A - Rs. 400

B - Rs. 300

C - Rs. 500

D - Rs. 350

```Answer - A

Explanation

"T = 3 years R = 10%
TD = (BG ×100)/TR
=(36×100)/(3×10)=12×10
=Rs. 120 TD = (PW × TR)/100
⇒120=(PW ×3×10)/100
⇒1200=PW ×3 PW =1200/3
= Rs. 400
"```

Q 11-If the true discount on a certain sum due 6 months hence at 15% is Rs. 120, what is the banker's discount on the same sum for the same time and at the same rate?

A - 123

B - 129

C - 131

D - 137

```Answer - B

Explanation

"B.G. = S.I. on T.D. = Rs.(120 x 15 x 1/2 x 1/100) = Rs. 9.
(B.D.) - (T.D.) = Rs. 9.
B.D. = Rs. (120 + 9) = Rs. 129."```

Q 12-The bankers discount and the true discount of a sum at 10% per annum simple interest for the same time are Rs.100 and Rs.80 respectively. What is the sum and the time?

A - Sum = Rs.400 and Time = 5 years

B - Sum = Rs.200 and Time = 2.5 years

C - Sum = Rs.400 and Time = 2.5 years

D - Sum = Rs.200 and Time = 5 years

```Answer - C

Explanation

"BD = Rs.100
TD = Rs.80 R = 10%
F = (BD × TD)/(BD- TD) =100×80/(100-80)
=(100×80)/20=Rs.400
BD = Simple Interest on the face value of the bill for unexpired time = FTR/100
⇒ 100=(400×T×10)/100
⇒100=4×T×10 ⇒10=4×T⇒T=104=2.5 years
"```

Q 13-The present worth of a sum due sometimes hence is Rs.5760 and the baker's gain is Rs.10. What is the true discount?

A - Rs. 480

B - Rs. 420

C - Rs. 120

D - Rs. 240

```Answer - D

Explanation

TD = √PW × BG=√5760×10=√57600 = Rs. 240```

Q 14-The banker's gain on a bill due 1 year hence at 12% per annum is Rs. 6. The true discount is:

A - Rs. 72

B - Rs. 36

C - Rs. 54

D - Rs. 50

```Answer - D

Explanation

"T.D. =(B.G. x 100)/R x T= Rs.6 x 100)/12 x 1 = Rs. 50.
"```

Q 15-A man sells Rs.5000, 12 % stock at 156 and uinvests the proceeds parity in 8 % stock at 90 and 9 % stock at 108. He hereby increases his income by Rs. 70. How much of the proceeds were invested in each stock?

A - 3600(8%),4200(9%)

B - 4000(8%),4200(9%)

C - 3600(8%),4000(9%)

D - 4000(8%),4000(9%)

```Answer - A

Explanation

"S.P of Rs. 5000 stock = Rs. [(156/100)*5000] = Rs. 7800.
Income from this stock = Rs. [(12/100)*5000] = Rs. 600.
Let investment in * % stock be x and that in 9 % stock = (7800-x).
[x*(8/90)] + (7800-x) * (9/108) = (600+7)
4x/45) + [(7800-x)/12] = 670 Ã¯Æ’Â³ 16x + 117000-15x = (670*180)
x = 3600
Money invested in 8 % stock at 90 = Rs. 3600.
Money invested in 9 % at 108 = Rs. (7800-3600) = Rs. 4200."```