True Discount problems
- 1. If the true discount on s sum due 2 years hence at 14% per annum be Rs. 168, the sum due is:
Options- A. Rs. 768
- B. Rs. 968
- C. Rs. 1960
- D. Rs. 2400 Discuss
Correct Answer: Rs. 768
Explanation:
| P.W. = | 100 x T.D. | = | 100 x 168 | = 600. |
| R x T | 14 x 2 |
∴ Sum = (P.W. + T.D.) = Rs. (600 + 168) = Rs. 768.
- 2. The interest on Rs. 750 for 2 years is the same as the true discount on Rs. 960 due 2 years hence. If the rate of interest is the same in both cases, it is:
Options- A. 12%
- B. 14%
- C. 15%
- D.
16 2 % 3
Discuss
Correct Answer: 14%
Explanation:
S.I. on Rs. 750 = T.D. on Rs. 960.
This means P.W. of Rs. 960 due 2 years hence is Rs. 750.
∴ T.D. = Rs. (960 - 750) = Rs. 210.
Thus, S.I. on R.s 750 for 2 years is Rs. 210.
| ∴ Rate = | ❨ | 100 x 210 | ❩% | = 14% |
| 750 x 2 |
- 3. A trader owes a merchant Rs. 10,028 due 1 year hence. The trader wants to settle the account after 3 months. If the rate of interest 12% per annum, how much cash should he pay?
Options- A. Rs. 9025.20
- B. Rs. 9200
- C. Rs. 9600
- D. Rs. 9560 Discuss
Correct Answer: Rs. 9200
Explanation:
| Required money | = P.W. of Rs. 10028 due 9 months hence | |||||||||||
|
||||||||||||
| = Rs. 9200. |
- 4. If Rs. 10 be allowed as true discount on a bill of Rs. 110 due at the end of a certain time, then the discount allowed on the same sum due at the end of double the time is:
Options- A. Rs. 20
- B. Rs. 21.81
- C. Rs. 22
- D. Rs. 18.33 Discuss
Correct Answer: Rs. 18.33
Explanation:
S.I. on Rs. (110 - 10) for a certain time = Rs. 10.
S.I. on Rs. 100 for double the time = Rs. 20.
T.D. on Rs. 120 = Rs. (120 - 100) = Rs. 20.
| T.D. on Rs. 110 = Rs. | ❨ | 20 | x 110 | ❩ | = Rs. 18.33 |
| 120 |
- 5. A man buys a watch for Rs. 1950 in cash and sells it for Rs. 2200 at a credit of 1 year. If the rate of interest is 10% per annum, the man:
Options- A. gains Rs. 55
- B. gains Rs. 50
- C. loses Rs. 30
- D. gains Rs. 30 Discuss
Correct Answer: gains Rs. 50
Explanation:
| S.P. | = P.W. of Rs. 2200 due 1 year hence | |||||
|
||||||
| = Rs. 2000. |
∴ Gain = Rs. (2000 - 1950) = Rs. 50.
- 6. A man purchased a cow for Rs. 3000 and sold it the same day for Rs. 3600, allowing the buyer a credit of 2 years. If the rate of interest be 10% per annum, then the man has a gain of:
Options- A. 0%
- B. 5%
- C. 7.5%
- D. 10% Discuss
Correct Answer: 0%
Explanation:
C.P. = Rs. 3000.
| S.P. = Rs. | [ | 3600 x 100 | ] | = Rs. 3000. |
| 100 + (10 x 2) |
Gain = 0%.
- 7. The true discount on Rs. 1760 due after a certain time at 12% per annum is Rs. 160. The time after which it is due is:
Options- A. 6 months
- B. 8 months
- C. 9 months
- D. 10 months Discuss
Correct Answer: 10 months
Explanation:
P.W. = Rs. (1760 -160) = Rs. 1600.
∴ S.I. on Rs. 1600 at 12% is Rs. 160.
| ∴ Time = | ❨ | 100 x 160 | ❩ | = | 5 | years = | ❨ | 5 | x 12 | ❩months = 10 months. |
| 1600 x 12 | 6 | 6 |
- 8. Rs. 20 is the true discount on Rs. 260 due after a certain time. What will be the true discount on the same sum due after half of the former time, the rate of interest being the same?
Options- A. Rs. 10
- B. Rs. 10.40
- C. Rs. 15.20
- D. Rs. 13 Discuss
Correct Answer: Rs. 10.40
Explanation:
S.I. on Rs. (260 - 20) for a given time = Rs. 20.
S.I. on Rs. 240 for half the time = Rs. 10.
T.D. on Rs. 250 = Rs. 10.
| ∴ T.D. on Rs. 260 = Rs. | ❨ | 10 | x 260 | ❩ | = Rs. 10.40 |
| 250 |
- 9. The present worth of Rs. 1404 due in two equal half-yearly installments at 8% per annum simple interest is:
Options- A. Rs. 1325
- B. Rs. 1300
- C. Rs. 1350
- D. Rs. 1500 Discuss
Correct Answer: Rs. 1325
Explanation:
| Required sum | = P.W. of Rs. 702 due 6 months + P.W. of Rs. 702 due 1 year hence | |||||||||||||
|
||||||||||||||
| = Rs. (675 + 650) | ||||||||||||||
| = Rs. 1325. |
- 10. The true discount on Rs. 2562 due 4 months hence is Rs. 122. The rate percent is:
Options- A. 12%
- B.
13 1 % 3 - C. 15%
- D. 14% Discuss
Correct Answer: 15%
Explanation:
P.W. = Rs. (2562 - 122) = Rs. 2440.
∴ S.I. on Rs. 2440 for 4 months is Rs. 122.
| ∴ Rate = | [ | 100 x 122 | ]% | = 15%. |
|
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