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- Question
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
- Correct Answer
- Rs. 10.40
ExplanationS.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
True Discount problems
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- 1. 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 - 2. 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%.
- 3. 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. [ 2200 x 100 ] 100 + (10 x 1) = Rs. 2000. ∴ Gain = Rs. (2000 - 1950) = Rs. 50.
- 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 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. [ 10028 x 100 ] 100 + ❨ 12 x 9 ❩ 12 = Rs. 9200. - 6. 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. [ ❨ 100 x 702 ❩ + ❨ 100 x 702 ❩ 100 + (8 x 1) ] 100 + 8 x ½ = Rs. (675 + 650) = Rs. 1325. - 7. 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%. 2440 x 1 3 - 8. 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:
Let P.W. be Rs. x.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.
- 9. 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% 612 x 3 4 - 10. 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)
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