True Discount problems
- 1. Find the sum due, if the true discount on a sum due 2 yr hence at 7% be ? 672.
Options- A. ? 5500
- B. ? 5425
- C. ? 5472
- D. ? 5300 Discuss
Correct Answer: ? 5472
Explanation:
Given that, R = 7%, T = 2 yr,
TD = ? 672 and Sum due (A) = ?
According to the formula, (3)
TD = (A x R x T) / (100 + R x T)
? 672 = (A x 7 x 2) / (100 + 7 x 2) = 14A/114
? A = (114 x 672)/14 = ? 5472
- 2. The true discount on a certain sum money due 4 yr hence is ? 75 and the simple interest on the same sum for the same time and at the same rate of interest is ? 225. Find the rate per cent.
Options- A. 25%
- B. 50%
- C. 31%
- D. 45% Discuss
Correct Answer: 50%
Explanation:
Given that, SI = ? 225, TD = ? 75,
T = 4 yr and R = ?
According to the formula,
SI - TD = (TD x R x T)/100
? 225 - 75 = (75 x R x 4)/100
? 150 = (75 x R x 4) /100
? 3R = 150
R = 50%
- 3. Vandana bought a watch for ? 600 and sold it the same day for ? 688.50 at a credit of 9 months and this way she gained 2%. Find the rate of interest per annum.
Options- A. 162/3%
- B. 152/3%
- C. 112/3%
- D. 52/3% Discuss
Correct Answer: 162/3%
Explanation:
SP = 102% of ? 600 = (102/100) x 600 = ? 612
Now, PW = ? 612 and sum = ? 688.50
? TD = 688.50 - 612 = ? 76.50
Thus, SI on ? 612 for 9 months is ? 76.50.
? Rate = (100 x 76.50) / (612 x 3/4)
= (100 x 76.50) / (153 x 3)
=162/3%
- 4. The present worth of Rs. 1404 due in two equal half yearly instalments?
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 + 8 x (1/2)} + Rs. {100 x 702} / {100 + 8 x 1}
? Total P.W. = Rs. (675 + 650)
= Rs. 1325
- 5. A owes B Rs. 456.75 payable 4 1/ 2 months hence and B owes A Rs. 455.51 payable 3 months hence. If they agree to settle their account by a ready money payment. What sum should be paid over and to whom reckoning the rate of true discount at 4 per cent per annum?
Options- A. Re.1`,A
- B. Rs. 2,B
- C. Rs. 2,A
- D. Re. 1, B Discuss
Correct Answer: Re.1`,A
Explanation:
Time = 41/2 months = 3/8 year,
Rate = 4 percent
? Amount of Rs. 100 = 203/2
? P.W. = Rs. 456.75 / (203/2) x 100 = Rs. 450
Again, time = 3 months = 1/4 year, rate = 4 percent
P.W. = Rs. 455.51 x 100 x 101 = Rs. 451
Hence the required sum to be paid to A = Rs. 451 - Rs. 450 = Re. 1
- 6. Kailash wants to sell his television.There are to two offers, one at ? 10000 cash and the other at a credit of ? 6440 to be paid after 8 months, money being at 18% per annum. Which one is better offer?
Options- A. ? 6440 at credit
- B. ? 6440 in cash
- C. ? 6440 at credit and ?10000 in cash both
- D. ? 10000 in cash Discuss
Correct Answer: ? 10000 in cash
Explanation:
PW of ? 6440 due 8 month hence
= (6440 x 100)/[100 + (18 x 8)/12] = (6440 x 100)/112 = ?5750
clearly, ? 10000 in cash is better offer.
- 7. Jagatram, a trader, owes a merchant. Mangalal ? 5014 due 1 yr hence. Jagatram wants to settle the account after 3 months. If the rate of interest is 12% per annum, how much cash should Jagatram pay?
Options- A. ? 9200
- B. ? 5600`
- C. ? 4600
- D. ? 6600 Discuss
Correct Answer: ? 4600
Explanation:
Required cash = PW of ? 5014 due 9 month hence
= {95014 x 1000} /{100 + 12 x (9/12)}
= (5014 x 100)/(100 + 9)
= (5014 x 100)/109
= ? 4600
- 8. Aarti has to pay ? 440 to Babita after 1 yr. Babita asks Aarti to pay ? 220 in cash and defer the payment of ? 220 for 2 yr. Aarti agrees to it. If the rate of interest be 10 % per annum, find Aarti's gain or loss?
Options- A. Aarti gains ? 3.33
- B. Aarti gains ? 8
- C. Aarti losses ? 9
- D. Aarti losses ? 3.33 Discuss
Correct Answer: Aarti losses ? 3.33
Explanation:
Money to be paid by Aarti
= PW of ? 440 due 1 yr hence
= {440 x 100}/{100 + (10 x 1)} = {440 x 100}/110
= 4 x 100 = ? 400
Aarti actually pays ? 220 + PW of ? 220 due yr hence
i.e. 220 + {(220 x 100) / (100 + 10 x 2)}
= 220 + (220 x 100)/120
= [220 + 183.33]
= ? 403.33
? Loss of Aarti = 403.33 - 400
= ? 3.33
- 9. M owes N ? 3146 payable 1 1/ 2 yr hence. Also, N owes M, ? 2889 payable 6 months hence. If they want to settle the account forthwith, keeping 14% the rate of interest, who should pay and how much?
Options- A. N should pay ? 100
- B. N should pay ? 50
- C. M should pay ? 100
- D. M should pay ? 50 Discuss
Correct Answer: N should pay ? 100
Explanation:
N owes PW of ? 3146 due 3/2 yr hence
i.e. {3146 x 100} / {100 + (14 x 3/2)} = (3146 x 100) / (100 + 21)
= 314600 / 121
= ? 2600
N owes PW of ? 2889 due 6 months hence
i.e. {2889 x 100}/{100 + (14 x 1/2)} = (2889 x 100)/(100 + 7)
= (2889 x 100)/107 = ? 2700
? N must pay ? (2700 - 2600) i.e. ? 100 to M.
- 10. A company offers three types of successive discounts : (i) 25% and 15%, (ii) 30% and 10%, (iii) 35% and 5%. Which offer is the best for a customer?
Options- A. First offer
- B. Second offer
- C. Third offer
- D. Any one; all are equally good Discuss
Correct Answer: Third offer
Explanation:
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