True Discount problems
- 1. A owes B, Rs. 1120 payable 2 years hence and B owes A, Rs. 1081.50 payable 6 months hence. If they decide to settle their accounts forthwith by payment of ready money and the rate of interest be 6% per annum, then who should pay and how much?
Options- A. A Rs. 50
- B. B Rs. 50
- C. A Rs. 70
- D. B Rs. 70 Discuss
Correct Answer: B Rs. 50
Explanation:
P.W. of Rs. 1120 due 2 years hence at 6%
= Rs. [{100 x 1120} / {100 + (6 x 2)}] = Rs. 1000
P.W. of Rs. 1081.50 due 6 months hence at 6%
= Rs. [ {100 x 1081.50} / {100 + (6 x 1/2)} ]
= Rs [ (100 x 1081.50) / 103 ] = Rs. 1050
So, A owes B, Rs. 1000 cash and B owes A Rs. 1050 cash.
? B must pay Rs. 50 to A.
- 2. A man purchased a cow for Rs. 300 and sold it the same day for Rs. 360, allowing the buyer at the credit of 2 years. If the rate of interest be 7 1/ 2% per annum, then the man has a gain of?
Options- A. 41/2%
- B. 53/7%
- C. 6%
- D. 5% Discuss
Correct Answer: 5%
Explanation:
P.W. of Rs. 360 due 2 years hence at 71/7% per annum
= Rs. { {100 x 360} / {100 + (50/7 x 2)}}
= Rs. { (100 x 360 x 7) / 800} = Rs. 315
? S.P. = Rs. 315
Hence, gain % = (15 x 100) / 300 = 5%
- 3. What sum will discharge a debt of Rs. 5300 due a year and a half hence at 4% per annum?
Options- A. Rs. 5000
- B. Rs. 4500
- C. Rs. 4200
- D. Rs. 5250 Discuss
Correct Answer: Rs. 5000
Explanation:
Required sum = (100 x 5300) / {(100 + (3/2) x 4)}
= (100 x 5300) / 106 = Rs. 5000
- 4. The true discount on Rs. 2575 due 4 months hence is Rs. 75. The rate percent is?
Options- A. 6%
- B. 8%
- C. 9%
- D. 5% Discuss
Correct Answer: 9%
Explanation:
P.W. = Rs. (2575 - 75) = Rs. 2500
? Rate = (100 x 75 x 3) / (2500 x 1)% = 9%
- 5. Find the present worth (PW) and the true discount reckoning 6% per annum simple interest of Rs. 176 due in 20 months time?
Options- A. Rs. 160, Rs. 16
- B. Rs. 130, Rs. 46
- C. Rs. 150, Rs. 26
- D. None of these Discuss
Correct Answer: Rs. 160, Rs. 16
Explanation:
P.W. = (100 x 176) / (100 + (6 x 20)/12) = Rs. 160
T.D. = Amount - present worth
= Rs. 176 - Rs. 160 = Rs. 16
- 6. The true discount on Rs. 1860 due after a certain time at 5% is Rs. 60. The time after which it is due is?
Options- A. 6 months
- B. 8 months
- C. 9 months
- D. 10 months Discuss
Correct Answer: 8 months
Explanation:
P.W. = (Sum due) - (T.D.)
= Rs. (1860 - 60) = Rs. 1800
Thus, Rs. 60 is S.I. on Rs. 1800 at 5% per annum
? Time = (100 x 60) / (1800 x 5) years
= 2 / 3 years = 8 months
- 7. The true discount on a bill a due 8 months hence at 12% per annum is Rs. 240. Find the amount of the bill and its present worth?
Options- A. Rs. 3000, Rs . 3240
- B. Rs. 2000, Rs . 2240
- C. Rs. 2100, Rs . 2340
- D. None of these Discuss
Correct Answer: Rs. 3000, Rs . 3240
Explanation:
P.W. = (100 x T.D.) / (R x T) = (100 x 240) / (12 x 8/12) = Rs. 3000
? P.W. is Rs. 3000
? A = Amount of bill = P.W. + T.D. = 3000 + 240 = 3240
- 8. The difference between the simple interest and the true discount on a certain sum for 6 months at 4% is Rs. 15. Find the sum?
Options- A. Rs. 32850
- B. Rs. 28250
- C. Rs. 38250
- D. Rs. 38350 Discuss
Correct Answer: Rs. 38250
Explanation:
? 15 = [A x (4 x 1/2)2] / [100(100 + 4 x 1/2)]
? 15 = (A x 4) / (100 x 102)
? A = 15 x 25 x 102
? A = Rs. 38, 250.
- 9. Find the difference between simple interest and true discount on Rs. 960 due 4 year hence at 5% per annum simple interest?
Options- A. Rs. 32
- B. Rs. 52
- C. Rs. 42
- D. None of these Discuss
Correct Answer: Rs. 32
Explanation:
S.I. - T.D. = [A x (R.T)2] / [100(100 + R.T.)]
= [960 x (4 x 5)2] / [100 x (100 + 4 x 5)]
= [(960 x 20 x 20) / (100 x 120)] = Rs. 32
- 10. What will be the present worth of ? 3720 due 3 yr hence at 8% per annum? Also, find the true discount.
Options- A. PW = ? 3000 and TD = ? 720
- B. PW =? 15000 and TD = ? 720
- C. PW = ? 3000 and TD = ? 320
- D. PW = ? 1000 and TD = ? 420 Discuss
Correct Answer: PW = ? 3000 and TD = ? 720
Explanation:
Let PW be N.
? 3720 - N = (N x 8 x 3) / 100 = 6N / 25
? 31N = 3720 x 25
? N = (3720 x 25) / 31 = ? 3000
TD = Amount - PW = 3720 - 3000 = ? 720
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