True Discount problems
- 1. The present worth of a bill due 7 months hence is Rs. 1200 and if the bill were due at the end of 2 1/ 2 years, its present worth would be Rs. 1016. Find the rate percent and the sum of the bill?
Options- A. 10%, Rs. 1270
- B. 8%, Rs. 1720
- C. 16%, Rs. 1570
- D. 18%, Rs. 1560 Discuss
Correct Answer: 10%, Rs. 1270
Explanation:
? 1200/1016 = (100 + R x 5/2) / (100 + R x 7/12)
? 1200 x (100 + R x 7/12) = 1016 x (100 + R x 5/2)
? 3680 x R = 36800
? R = 10%
? Sum due = 1200 + S.I. on Rs. 1200 for 7 months at 10%. = Rs. 1270
- 2. If the true discount on Rs. 161 due 2 1/ years hence be Rs. 21. At what rate per cent is the interest calculated?
Options- A. 6%
- B. 4%
- C. 8%
- D. 12% Discuss
Correct Answer: 6%
Explanation:
Required rate percent = (100 x 21) / {(161 - 21) x 21/2} = 6%
- 3. 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 given time = Rs. 10
S.I. on Rs. 100 for double the time = 20
Sum = Rs. (100 + 20) = Rs. 120
T.D. on Rs. 110 = Rs. (20 /120) x 110 = Rs. 18.33
- 4. Goods were bought for Rs. 600 and sold the same day for Rs. 650.25 at a credit of 9 month and still there was a gain of 2%. The rate percent is?
Options- A. 61/3%
- B. 81/3%
- C. 8%
- D. 743/61% Discuss
Correct Answer: 81/3%
Explanation:
S.P. = (102% of Rs. 600) = Rs. (102/100) x 600 = Rs. 612
? P.W. of Rs. 650.25 due 9 months later is Rs. 612.
? Rs. 38.25 is S.I. on Rs. 612 for 9 months
? Rate = (100 x 38.25) / (612 x 3/4)% = 81/3%
- 5. The true discount on Rs. 1860 due 3 years hence is Rs. 40. Find the rate per cent?
Options- A. 10%
- B. 12%
- C. 5%
- D. 15% Discuss
Correct Answer: 10%
Explanation:
R = (100 x T.D.) / (P.W. x T) = (100 x T.D.) / [(A - T.D.) x T]
= (100 x 60) / (1800 x 3) [ since P.W. = A - T.D.]
= 10%
? The rate per cent is 10% per annum
- 6. The interest on Rs. 750 for 2 years is equal to the true discount on Rs. 810 for the same time and at the same rate. The rate percent is?
Options- A. 41/3%
- B. 51/6%
- C. 4%
- D. 5% Discuss
Correct Answer: 4%
Explanation:
Since T.D. is S.I. on Rs. P.W.,
we have Rs. (810 - 750) or Rs. 60 as S.I. on Rs. 750 for 2 years
? Rate = (100 x 60) / (750 x 2) = 4%
- 7. A trader owes a merchant Rs. 901 due 1 year's hence. However, the trader wants to settle the account after 3 months. How much cash should he pay, If rate of interest is 8% per annum?
Options- A. Rs. 870
- B. Rs. 850
- C. Rs. 828.92
- D. Rs. 846.94 Discuss
Correct Answer: Rs. 850
Explanation:
P.W. of Rs. 901 due 9 months hence at 8%
= Rs { (100 x 901) / (100 + (8 x 3 / 4))} = Rs. (100 x 901) / 106
= Rs. 850
- 8. I want to sell my scooter. There are two offers, One at cash payment of Rs. 8100 and another at a credit of Rs. 8250 to be paid after 6 months. If money being worth 6 1/ 4% per annum simple interest, which is the better offer?
Options- A. Rs. 8100 in cash
- B. Rs. 8250 due 6 months hence
- C. Both are equally good
- D. Ca't be said Discuss
Correct Answer: Rs. 8100 in cash
Explanation:
P.W. of Rs. 8285 due 6 months hence = Rs. { (100 x 8250) / {100 + (25 / 4 x 1 / 2)} } = Rs. 8000
? Rs. 8100 in cash is a better offer.
- 9. A has to pay Rs. 220 to B after 1 year. B asks A to pay Rs. 110 in cash and defer the payment of Rs. 110 for 2 years. A agrees to it. Counting the rate of interest at 10% per annum in this new mode of payment?
Options- A. There is no gain or loss to ant one
- B. A gains Rs. 7.34
- C. A loses Rs. 7.34
- D. A loses Rs. 1.66 Discuss
Correct Answer: A loses Rs. 1.66
Explanation:
A has to pay the P.W. of Rs. 220 due 1 year hence, which is
= Rs. [ (100 x 220) / {100 + (10 x 1)} ] = Rs. 200
A, actually pays = Rs. [110 + P.W. of Rs. 110 due 2 years hence]
= Rs. [ 110 + (100 x 110) / {100 + (10 x 2)} ]
= Rs. [110 + 91.66] = Rs. [201.66]
? A loses = Rs. [200 - 201.66] = Rs. 1.66
- 10. 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. 240 for a given time = Rs. 20
S.I. on Rs. 240 for half the time = Rs. 10
? Rs. 10 is T.D. on Rs. 250
So, T.D. on Rs. 260 = Rs. (10 / 250) x 260 = Rs. 10.40
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