True Discount problems
- 1. The true discount on a bill due 9 months hence at 16% per annum is Rs. 189. The amount of the bill is:
Options- A. Rs. 1386
- B. Rs. 1764
- C. Rs. 1575
- D. Rs. 2268 Discuss
Correct Answer: Rs. 1764
Explanation:
Then, S.I. on Rs. x at 16% for 9 months = Rs. 189.
| ∴ x x 16 x | 9 | x | 1 | = 189 or x = 1575. |
| 12 | 100 |
∴ P.W. = Rs. 1575.
∴ Sum due = P.W. + T.D. = Rs. (1575 + 189) = Rs. 1764.
- 2. Goods were bought for Rs. 600 and sold the same for Rs. 688.50 at a credit of 9 months and thus gaining 2% The rate of interest per annum is:
Options- A.
16 2 % 3 - B.
14 1 % 2 - C.
13 1 % 3 - D. 15% Discuss
Correct Answer:
| 16 | 2 | % |
| 3 |
Explanation:
| S.P. = 102% of Rs. 600 = | ❨ | 102 | x 600 | ❩ | = Rs. 612. |
| 100 |
Now, P.W. = Rs. 612 and sum = Rs. 688.50.
∴ T.D. = Rs. (688.50 - 612) = Rs. 76.50.
Thus, S.I. on Rs. 612 for 9 months is Rs. 76.50.
| ∴ Rate = | ❨ | 100 x 76.50 | ❩% | = 16⅔% |
|
- 3. The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 85 and Rs. 80 respectively. The sum is:
Options- A. Rs. 1800
- B. Rs. 1450
- C. Rs. 1360
- D. Rs. 6800 Discuss
Correct Answer: Rs. 1360
Explanation:
| Sum = | S.I. x T.D. | = | 85 x 80 | = Rs. 1360. |
| (S.I.) - (T.D.) | (85 - 80) |
- 4. The present worth of Rs. 2310 due 2½ years hence, the rate of interest being 15% per annum, is:
Options- A. Rs. 1750
- B. Rs. 1680
- C. Rs. 1840
- D. Rs. 1443.75 Discuss
Correct Answer: Rs. 1680
Explanation:
| P.W. = Rs. | [ | 100 x 2310 | ] | = Rs. 1680. | ||
|
- 5. A man wants to sell his scooter. There are two offers, one at Rs. 12,000 cash and the other a credit of Rs. 12,880 to be paid after 8 months, money being at 18% per annum. Which is the better offer?
Options- A. Rs. 12,000 in cash
- B. s. 12,880 at credit
- C. Both are equally good Discuss
Correct Answer: Rs. 12,000 in cash
Explanation:
| P.W. of Rs. 12,880 due 8 months hence |
|
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| = Rs. 11500. |
- 6. If the interest on Rs. 50 at 4 1/ 2 be equal to the discount on Rs. 59 for the same time and at the same rate when is the latter sum due?
Options- A. 2 years
- B. 4 years
- C. 6 years
- D. 3 years Discuss
Correct Answer: 4 years
Explanation:
? 9/2 = [(59 - 50) x 100] / 50 x T
? T = 4 years
- 7. The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 25 and Rs. 20 respectively. The sum is?
Options- A. Rs. 500
- B. Rs. 200
- C. Rs. 250
- D. Rs. 100 Discuss
Correct Answer: Rs. 100
Explanation:
Sum = [(S.I.) x (T.D.)] / [(S.I.) - (T.D.)] = Rs. (25 x 20) / (25 - 20)
= Rs. 100
- 8. The difference between the simple interest and the true discount on a certain sum of money foe 6 months at 6% is Rs. 27. Find the sum?
Options- A. Rs. 30900
- B. Rs. 39000
- C. Rs. 20900
- D. Rs. 30600 Discuss
Correct Answer: Rs. 30900
Explanation:
Req. amount = [27 x (100 + 6 x 1/2) x 100] / [(6 x 1/2)2]
= (2700 x 103) / 9 = Rs. 30900
- 9. A man buys a watch for Rs. 195 in cash and sells it for Rs. 220 at a credit of 1 year. If the rate of interest is 10%, the man?
Options- A. Gains Rs. 15
- B. Gains Rs. 3
- C. Gains Rs. 5
- D. Loses Rs. 5 Discuss
Correct Answer: Gains Rs. 5
Explanation:
P.W. of Rs. 220 due 1 year hence = Rs. (100 x 220) / (100 + 10)
= Rs. 200
hence, the man gains Rs. 5
- 10. What will be the true discount for the present worth of ? 600 for a period of 4 yr at 4% per annum rate of interest?
Options- A. ? 100
- B. ? 32
- C. ? 86
- D. ? 96 Discuss
Correct Answer: ? 96
Explanation:
Given that, T = 4 yr, R = 4%
PW = ? 600 and TD = ?
According to the formula, (1)
TD = (PW x R x T)/100
TD = (600 x 4 x 4)/100 = 6 x 4 x 4 = ? 96
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