Banker's Discount problems
- 1. The present worth of a bill due sometime, hence is ? 2200 and true discount on the bill is ? 220. Find the banker's discount and banker's gain?
Options- A. BG = ? 22 and BD = ? 242
- B. BG = ? 242 and BD = ? 22
- C. BG = ? 11 and BD = ? 121
- D. BG = ? 31 and BD = ? 343 Discuss
Correct Answer: BG = ? 22 and BD = ? 242
Explanation:
Given that, PW = ? 2200, TD = ? 220
According to the formula,
BG = (TD)2/PW = (220 x 220)/2200 = ? 22
BD = (TD + BG) = ?(220 + 22) = ? 242
- 2. The present worth of a sum due sometime hence is ? 576 And banker's gain is ? 9. Find the true and discount?
Options- A. ? 8
- B. ? 70
- C. ? 95
- D. ? 72 Discuss
Correct Answer: ? 72
Explanation:
Given that PW = ? 576 , BG = ? 9 and TD = ?
TD = PW x BG
= 576 x 9
= 24 x 3
= ? 72
- 3. If rate of interest and time on a certain bill are numerically equal and true discount is 81 times of banker's gain, find the rate of interest?
Options- A. 29/13 %
- B. 12/9 %
- C. 17/9 %
- D. 11/9 % Discuss
Correct Answer: 11/9 %
Explanation:
Given that, n = 81
According to the formula.
R = 10?1/n%
= 10?1/81%
= 10 x (1/9) % = 11/9 %
- 4. The true discount on a certain sum due 1 yr hence at 30% per annum, is ? 240. What is the banker' discount on the same sum for the same time and at the same rate?
Options- A. ? 400
- B. ? 212
- C. ? 312
- D. ? 445 Discuss
Correct Answer: ? 312
Explanation:
We know that
BG = SI on TD = (240 x 30 x 1 x 1)/100
= ? 72
BG = BD - TD
? BD = BG + TD
= 72 + 240
= ? 312
- 5. What rate per cent does Shantanu get for his money in discounting a bill due 30 months hence he deducts 30% of the amount of the bill?
Options- A. 172/7%
- B. 173/7%
- C. 175/7%
- D. 171/7% Discuss
Correct Answer: 171/7%
Explanation:
Let the amount of the bill = ? 100.
Money deducted = ? 30
Money received by the holder of the bill = ? (100 - 30) = ? 70
SI on ? 70 for 30 months = ? 30
? Rate = [100 x 30] / [70 x (30/12)]% per annum
= (10 x 3 x 12) / 21 %
= (10 x 12) / 7 %
= 120/7 %
= 171/7 %
- 6. The banker's gain on a certain sum due 2 1/ 2 years hence is (3/23)
of the banker's discount. The rate per cent is?
Options- A. 5%
- B. 6%
- C. 214/23%
- D. 623% Discuss
Correct Answer: 6%
Explanation:
Let B.D. be Re. 1. Then B.G. = Re. (3/23)
? T.D.= Re. (1 - 3/23) = Re. (20/23)
Sum = Rs. [(1 x 20/23 / (1 - 20/23)] = Rs. 20/3
? S.I. on Rs. 20/3 for 21/2 years is Re. 1
? Rate = (100 x 1 / 20/3 x 5/2)% = 6%
- 7. The banker's discount on Rs. 1650 due a certain time hence is Rs. 165. Find the true discount and the banker's gain?
Options- A. Rs. 150, Rs. 15
- B. Rs. 160, Rs. 5
- C. Rs. 145, Rs. 20
- D. None of these Discuss
Correct Answer: Rs. 150, Rs. 15
Explanation:
Sum = (B.D. x T.D.) / (B.D. - T.D.) = (B.D. x T.D.) / B.G.
? T.D. / B.G. = Sum / B.D. = 1650/165 = 10/1
i.e., if B.G. is Re. 1, T.D. = Rs. 10 or B.D. = Rs. 11
? if B.D. is Rs. 11, T.D. = Rs. 10
If B.D. is Rs. 165, T.D. = Rs. (10/11) x 165 = Rs. 150
Also, BG = Rs. (165 - 150) = Rs. 15
- 8. The banker's discount on a sum of money for 1 1/ 2 years is Rs. 60 and
the true discount on the same sum for 2 years is Rs. 75. The rate per cent is?
Options- A. 5%
- B. 6%
- C. 62/3%
- D. 31/3% Discuss
Correct Answer: 31/3%
Explanation:
B.D. for (3/2) years = Rs. 60
B.D. for 2 years = Rs. (60 x 2/3 x 2) = Rs. 80
Now, B.D. = Rs. 80; T.D. = Rs. 75
and Time = 2 years
? Sum = Rs. (80 x 75 / 5) = Rs. 1200
? Rs. 80 is S.I. on Rs. 1200 for 2 years.
So, rate = (100 x 80/1200 x 2)% = 31/3%B.D. for (3 / 2) years = Rs. 60
B.D. for 2 years = Rs. (60 x 2 / 3 x 2) = Rs. 80
Now, B.D. = Rs. 80; T.D. = Rs. 75 and Time = 2 years
? Sum = Rs. (80 x 75 / 5) = Rs. 1200
? Rs. 80 is S.I. on Rs. 1200 for 2 years.
So, rate = (100 x 80 / 1200 x 2)% = 31/3%
- 9. Find the difference between the banker's discount and the true discount on Rs. 8100 for 3 months at 5%?
Options- A. Rs. 0.125
- B. Rs. 1.25
- C. Rs. 12.5
- D. None of these Discuss
Correct Answer: Rs. 1.25
Explanation:
Difference between banker's discount and the true discount = Banker's gain.
? B.G. = (B.D.) - (T.D.)
B.D. = FTR / 100
= [8100 x (1/4) x 5] / 100
= 101.25
T.D. = FTR / (100 + TR)
= [8100 x (1/4) x 5] / (100 + 5/4)
= 100
? B.G. = 101.25 - 100
= Rs. 1.25
- 10. The interest on a certain sum of money is Rs. 67.20 and the discount on the same of money for the same time and at the same rate is Rs. 60. What is sum?
Options- A. Rs. 560
- B. Rs. 480
- C. Rs. 590
- D. Rs. 860 Discuss
Correct Answer: Rs. 560
Explanation:
Interest on Sum - True discount
= Interest on true Discount.
Proof Sum = P.W. + T.D.
? Interest on Sum = Interest on P.W. + Interest on T.D.
= T.D. + Interest on T.D.
Interest on Sum - T.D. = Interest on T.D. or Banker's gain = Int. on T.D.
Rs. 67.20 - Rs. 60 = Interest on Rs. 60
? Rs. 71/5 = Interest on Rs. 60
? Re.1 = Interest on Rs. 60/71/5
? Rs. 671/5 = Interest on Rs. 60 / 71/5 x 671/5
? The required sum = Rs. 60/71/5 x 671/5 = Rs. 560
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