You owe Rs 6,600 in two years. What lump sum clears the debt today? That fair sum is the present worth . The gap is the true discount .
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Q1. The true discount on a sum of Rs 500 due 4 years hence is Rs 250. Find the rate percent per annum.
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Answer: B
The sum (amount) due is Rs 500. The true discount is T.D. = Rs 250. The time is T = 4 years. True Discount is the simple interest earned on the Present Worth (P.W.) for this time. First find P.W.: P.W. = Amount – T.D. = 500 – 250 = Rs 250. The rate formula is Rate = (100 x T.D.) / (P.W. x T). The numerator is 100 x 250 = 25000. The denominator is 250 x 4 = 1000. So Rate = 25000 / 1000 = 25%. Check: T.D. = (P.W. x R x T) / 100 = (250 x 25 x 4) / 100 = 250.
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Q2. The true discount on a sum of Rs 8000 due 5 years hence is Rs 4000. Find the rate percent per annum.
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Answer: C
The sum (amount) due is Rs 8000. The true discount is T.D. = Rs 4000. The time is T = 5 years. True Discount is the simple interest earned on the Present Worth (P.W.) for this time. First find P.W.: P.W. = Amount – T.D. = 8000 – 4000 = Rs 4000. The rate formula is Rate = (100 x T.D.) / (P.W. x T). The numerator is 100 x 4000 = 400000. The denominator is 4000 x 5 = 20000. So Rate = 400000 / 20000 = 20%. Check: T.D. = (P.W. x R x T) / 100 = (4000 x 20 x 5) / 100 = 4000.
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Q3. The true discount on a sum of Rs 6675 due 2 years hence is Rs 2225. Find the rate percent per annum.
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Answer: A
The sum (amount) due is Rs 6675. The true discount is T.D. = Rs 2225. The time is T = 2 years. True Discount is the simple interest earned on the Present Worth (P.W.) for this time. First find P.W.: P.W. = Amount – T.D. = 6675 – 2225 = Rs 4450. The rate formula is Rate = (100 x T.D.) / (P.W. x T). The numerator is 100 x 2225 = 222500. The denominator is 4450 x 2 = 8900. So Rate = 222500 / 8900 = 25%. Check: T.D. = (P.W. x R x T) / 100 = (4450 x 25 x 2) / 100 = 2225.
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Q4. The true discount on a sum of Rs 7095 due 1 year hence is Rs 645. Find the rate percent per annum.
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Answer: D
The sum (amount) due is Rs 7095. The true discount is T.D. = Rs 645. The time is T = 1 year. True Discount is the simple interest earned on the Present Worth (P.W.) for this time. First find P.W.: P.W. = Amount – T.D. = 7095 – 645 = Rs 6450. The rate formula is Rate = (100 x T.D.) / (P.W. x T). The numerator is 100 x 645 = 64500. The denominator is 6450 x 1 = 6450. So Rate = 64500 / 6450 = 10%. Check: T.D. = (P.W. x R x T) / 100 = (6450 x 10 x 1) / 100 = 645.
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Q5. The true discount on a sum of Rs 5840 due 5 years hence is Rs 2190. Find the rate percent per annum.
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Answer: B
The sum (amount) due is Rs 5840. The true discount is T.D. = Rs 2190. The time is T = 5 years. True Discount is the simple interest earned on the Present Worth (P.W.) for this time. First find P.W.: P.W. = Amount – T.D. = 5840 – 2190 = Rs 3650. The rate formula is Rate = (100 x T.D.) / (P.W. x T). The numerator is 100 x 2190 = 219000. The denominator is 3650 x 5 = 18250. So Rate = 219000 / 18250 = 12%. Check: T.D. = (P.W. x R x T) / 100 = (3650 x 12 x 5) / 100 = 2190.
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Q6. The true discount on a sum of Rs 4588 due 3 years hence is Rs 888. Find the rate percent per annum.
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Answer: A
The sum (amount) due is Rs 4588. The true discount is T.D. = Rs 888. The time is T = 3 years. True Discount is the simple interest earned on the Present Worth (P.W.) for this time. First find P.W.: P.W. = Amount – T.D. = 4588 – 888 = Rs 3700. The rate formula is Rate = (100 x T.D.) / (P.W. x T). The numerator is 100 x 888 = 88800. The denominator is 3700 x 3 = 11100. So Rate = 88800 / 11100 = 8%. Check: T.D. = (P.W. x R x T) / 100 = (3700 x 8 x 3) / 100 = 888.
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Q7. The true discount on a sum of Rs 8432 due 2 years hence is Rs 1632. Find the rate percent per annum.
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Answer: C
The sum (amount) due is Rs 8432. The true discount is T.D. = Rs 1632. The time is T = 2 years. True Discount is the simple interest earned on the Present Worth (P.W.) for this time. First find P.W.: P.W. = Amount – T.D. = 8432 – 1632 = Rs 6800. The rate formula is Rate = (100 x T.D.) / (P.W. x T). The numerator is 100 x 1632 = 163200. The denominator is 6800 x 2 = 13600. So Rate = 163200 / 13600 = 12%. Check: T.D. = (P.W. x R x T) / 100 = (6800 x 12 x 2) / 100 = 1632.
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Q8. The true discount on a certain sum of money due 5 years hence is Rs 100, and the simple interest on the same sum for the same time and at the same rate is Rs 150. Find the sum.
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Answer: D
The true discount is T.D. = Rs 100. The simple interest on the same sum, time, and rate is S.I. = Rs 150. For the same sum, time, and rate, the sum due equals (S.I. x T.D.) / (S.I. – T.D.). The numerator is S.I. x T.D. = 150 x 100 = 15000. The denominator is S.I. – T.D. = 150 – 100 = 50. So the sum due = 15000 / 50 = Rs 300. Check: Sum – T.D. = 300 – 100 = Rs 200, the present worth of the sum.
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Q9. The true discount on a certain sum of money due 5 years hence is Rs 1480, and the simple interest on the same sum for the same time and at the same rate is Rs 2072. Find the rate percent per annum.
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Answer: B
The true discount is T.D. = Rs 1480. The simple interest on the same sum, time, and rate is S.I. = Rs 2072. The time is T = 5 years. First find the sum due: Sum = (S.I. x T.D.) / (S.I. – T.D.). The numerator is S.I. x T.D. = 2072 x 1480 = 3066560. The denominator is S.I. – T.D. = 2072 – 1480 = 592. So Sum = 3066560 / 592 = Rs 5180. Now find the rate: Rate = (100 x S.I.) / (Sum x T). Rate = (100 x 2072) / (5180 x 5) = 207200 / 25900 = 8%. Check: S.I. = (Sum x R x T) / 100 = (5180 x 8 x 5) / 100 = 2072.
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Q10. The true discount on a certain sum of money due 2 years hence is Rs 520, and the simple interest on the same sum for the same time and at the same rate is Rs 728. Find the rate percent per annum.
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Answer: C
The true discount is T.D. = Rs 520. The simple interest on the same sum, time, and rate is S.I. = Rs 728. The time is T = 2 years. First find the sum due: Sum = (S.I. x T.D.) / (S.I. – T.D.). The numerator is S.I. x T.D. = 728 x 520 = 378560. The denominator is S.I. – T.D. = 728 – 520 = 208. So Sum = 378560 / 208 = Rs 1820. Now find the rate: Rate = (100 x S.I.) / (Sum x T). Rate = (100 x 728) / (1820 x 2) = 72800 / 3640 = 20%. Check: S.I. = (Sum x R x T) / 100 = (1820 x 20 x 2) / 100 = 728.
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Q11. The true discount on a certain sum of money due 4 years hence is Rs 760, and the simple interest on the same sum for the same time and at the same rate is Rs 1064. Find the rate percent per annum.
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Answer: A
The true discount is T.D. = Rs 760. The simple interest on the same sum, time, and rate is S.I. = Rs 1064. The time is T = 4 years. First find the sum due: Sum = (S.I. x T.D.) / (S.I. – T.D.). The numerator is S.I. x T.D. = 1064 x 760 = 808640. The denominator is S.I. – T.D. = 1064 – 760 = 304. So Sum = 808640 / 304 = Rs 2660. Now find the rate: Rate = (100 x S.I.) / (Sum x T). Rate = (100 x 1064) / (2660 x 4) = 106400 / 10640 = 10%. Check: S.I. = (Sum x R x T) / 100 = (2660 x 10 x 4) / 100 = 1064.
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Q12. The true discount on a certain sum of money due 2 years hence is Rs 1460, and the simple interest on the same sum for the same time and at the same rate is Rs 2044. Find the rate percent per annum.
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Answer: D
The true discount is T.D. = Rs 1460. The simple interest on the same sum, time, and rate is S.I. = Rs 2044. The time is T = 2 years. First find the sum due: Sum = (S.I. x T.D.) / (S.I. – T.D.). The numerator is S.I. x T.D. = 2044 x 1460 = 2984240. The denominator is S.I. – T.D. = 2044 – 1460 = 584. So Sum = 2984240 / 584 = Rs 5110. Now find the rate: Rate = (100 x S.I.) / (Sum x T). Rate = (100 x 2044) / (5110 x 2) = 204400 / 10220 = 20%. Check: S.I. = (Sum x R x T) / 100 = (5110 x 20 x 2) / 100 = 2044.
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Q13. The true discount on a certain sum of money due 1 year hence is Rs 70, and the simple interest on the same sum for the same time and at the same rate is Rs 77. Find the sum.
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Answer: B
The true discount is T.D. = Rs 70. The simple interest on the same sum, time, and rate is S.I. = Rs 77. For the same sum, time, and rate, the sum due equals (S.I. x T.D.) / (S.I. – T.D.). The numerator is S.I. x T.D. = 77 x 70 = 5390. The denominator is S.I. – T.D. = 77 – 70 = 7. So the sum due = 5390 / 7 = Rs 770. Check: Sum – T.D. = 770 – 70 = Rs 700, the present worth of the sum.
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Q14. The true discount on a certain sum of money due 4 years hence is Rs 480, and the simple interest on the same sum for the same time and at the same rate is Rs 864. Find the rate percent per annum.
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Answer: D
The true discount is T.D. = Rs 480. The simple interest on the same sum, time, and rate is S.I. = Rs 864. The time is T = 4 years. First find the sum due: Sum = (S.I. x T.D.) / (S.I. – T.D.). The numerator is S.I. x T.D. = 864 x 480 = 414720. The denominator is S.I. – T.D. = 864 – 480 = 384. So Sum = 414720 / 384 = Rs 1080. Now find the rate: Rate = (100 x S.I.) / (Sum x T). Rate = (100 x 864) / (1080 x 4) = 86400 / 4320 = 20%. Check: S.I. = (Sum x R x T) / 100 = (1080 x 20 x 4) / 100 = 864.
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Q15. The true discount on a certain sum of money due 2 years hence is Rs 880, and the simple interest on the same sum for the same time and at the same rate is Rs 1056. Find the sum.
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Answer: A
The true discount is T.D. = Rs 880. The simple interest on the same sum, time, and rate is S.I. = Rs 1056. For the same sum, time, and rate, the sum due equals (S.I. x T.D.) / (S.I. – T.D.). The numerator is S.I. x T.D. = 1056 x 880 = 929280. The denominator is S.I. – T.D. = 1056 – 880 = 176. So the sum due = 929280 / 176 = Rs 5280. Check: Sum – T.D. = 5280 – 880 = Rs 4400, the present worth of the sum.
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Q16. The true discount on a certain sum of money due 2 years hence is Rs 1900, and the simple interest on the same sum for the same time and at the same rate is Rs 2660. Find the rate percent per annum.
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Answer: C
The true discount is T.D. = Rs 1900. The simple interest on the same sum, time, and rate is S.I. = Rs 2660. The time is T = 2 years. First find the sum due: Sum = (S.I. x T.D.) / (S.I. – T.D.). The numerator is S.I. x T.D. = 2660 x 1900 = 5054000. The denominator is S.I. – T.D. = 2660 – 1900 = 760. So Sum = 5054000 / 760 = Rs 6650. Now find the rate: Rate = (100 x S.I.) / (Sum x T). Rate = (100 x 2660) / (6650 x 2) = 266000 / 13300 = 20%. Check: S.I. = (Sum x R x T) / 100 = (6650 x 20 x 2) / 100 = 2660.
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Q17. The true discount on a certain sum of money due 4 years hence is Rs 200, and the simple interest on the same sum for the same time and at the same rate is Rs 400. Find the rate percent per annum.
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Answer: B
The true discount is T.D. = Rs 200. The simple interest on the same sum, time, and rate is S.I. = Rs 400. The time is T = 4 years. First find the sum due: Sum = (S.I. x T.D.) / (S.I. – T.D.). The numerator is S.I. x T.D. = 400 x 200 = 80000. The denominator is S.I. – T.D. = 400 – 200 = 200. So Sum = 80000 / 200 = Rs 400. Now find the rate: Rate = (100 x S.I.) / (Sum x T). Rate = (100 x 400) / (400 x 4) = 40000 / 1600 = 25%. Check: S.I. = (Sum x R x T) / 100 = (400 x 25 x 4) / 100 = 400.
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Q18. The true discount on a certain sum of money due 5 years hence is Rs 1050, and the simple interest on the same sum for the same time and at the same rate is Rs 2100. Find the sum.
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Answer: C
The true discount is T.D. = Rs 1050. The simple interest on the same sum, time, and rate is S.I. = Rs 2100. For the same sum, time, and rate, the sum due equals (S.I. x T.D.) / (S.I. – T.D.). The numerator is S.I. x T.D. = 2100 x 1050 = 2205000. The denominator is S.I. – T.D. = 2100 – 1050 = 1050. So the sum due = 2205000 / 1050 = Rs 2100. Check: Sum – T.D. = 2100 – 1050 = Rs 1050, the present worth of the sum.
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Q19. The true discount on a certain sum of money due 5 years hence is Rs 820, and the simple interest on the same sum for the same time and at the same rate is Rs 984. Find the sum.
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Answer: D
The true discount is T.D. = Rs 820. The simple interest on the same sum, time, and rate is S.I. = Rs 984. For the same sum, time, and rate, the sum due equals (S.I. x T.D.) / (S.I. – T.D.). The numerator is S.I. x T.D. = 984 x 820 = 806880. The denominator is S.I. – T.D. = 984 – 820 = 164. So the sum due = 806880 / 164 = Rs 4920. Check: Sum – T.D. = 4920 – 820 = Rs 4100, the present worth of the sum.
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Q20. The true discount on a certain sum of money due 3 years hence is Rs 720, and the simple interest on the same sum for the same time and at the same rate is Rs 1152. Find the rate percent per annum.
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Answer: B
The true discount is T.D. = Rs 720. The simple interest on the same sum, time, and rate is S.I. = Rs 1152. The time is T = 3 years. First find the sum due: Sum = (S.I. x T.D.) / (S.I. – T.D.). The numerator is S.I. x T.D. = 1152 x 720 = 829440. The denominator is S.I. – T.D. = 1152 – 720 = 432. So Sum = 829440 / 432 = Rs 1920. Now find the rate: Rate = (100 x S.I.) / (Sum x T). Rate = (100 x 1152) / (1920 x 3) = 115200 / 5760 = 20%. Check: S.I. = (Sum x R x T) / 100 = (1920 x 20 x 3) / 100 = 1152.
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Q21. The true discount on a certain sum of money due 5 years hence is Rs 2500, and the simple interest on the same sum for the same time and at the same rate is Rs 5625. Find the rate percent per annum.
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Answer: A
The true discount is T.D. = Rs 2500. The simple interest on the same sum, time, and rate is S.I. = Rs 5625. The time is T = 5 years. First find the sum due: Sum = (S.I. x T.D.) / (S.I. – T.D.). The numerator is S.I. x T.D. = 5625 x 2500 = 14062500. The denominator is S.I. – T.D. = 5625 – 2500 = 3125. So Sum = 14062500 / 3125 = Rs 4500. Now find the rate: Rate = (100 x S.I.) / (Sum x T). Rate = (100 x 5625) / (4500 x 5) = 562500 / 22500 = 25%. Check: S.I. = (Sum x R x T) / 100 = (4500 x 25 x 5) / 100 = 5625.
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Q22. The true discount on a certain sum of money due 5 years hence is Rs 600, and the simple interest on the same sum for the same time and at the same rate is Rs 840. Find the sum.
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Answer: B
The true discount is T.D. = Rs 600. The simple interest on the same sum, time, and rate is S.I. = Rs 840. For the same sum, time, and rate, the sum due equals (S.I. x T.D.) / (S.I. – T.D.). The numerator is S.I. x T.D. = 840 x 600 = 504000. The denominator is S.I. – T.D. = 840 – 600 = 240. So the sum due = 504000 / 240 = Rs 2100. Check: Sum – T.D. = 2100 – 600 = Rs 1500, the present worth of the sum.
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Q23. The true discount on a certain sum of money due 5 years hence is Rs 60, and the simple interest on the same sum for the same time and at the same rate is Rs 96. Find the rate percent per annum.
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Answer: A
The true discount is T.D. = Rs 60. The simple interest on the same sum, time, and rate is S.I. = Rs 96. The time is T = 5 years. First find the sum due: Sum = (S.I. x T.D.) / (S.I. – T.D.). The numerator is S.I. x T.D. = 96 x 60 = 5760. The denominator is S.I. – T.D. = 96 – 60 = 36. So Sum = 5760 / 36 = Rs 160. Now find the rate: Rate = (100 x S.I.) / (Sum x T). Rate = (100 x 96) / (160 x 5) = 9600 / 800 = 12%. Check: S.I. = (Sum x R x T) / 100 = (160 x 12 x 5) / 100 = 96.
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Q24. The true discount on a bill due 2 years hence at 4% per annum is Rs 744. Find the present worth of the bill.
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Answer: C
The true discount is T.D. = Rs 744. The rate is R = 4% per year. The time is T = 2 years. Let the amount due be x. True Discount equals interest on x: T.D. = (x x R x T) / (100 + R x T). Here 100 + R x T = 100 + 4 x 2 = 108. So 744 = (x x 8) / 108. Cross-multiplying gives x x 8 = 744 x 108 = 80352. So x = 80352 / 8 = Rs 10044. Present Worth (P.W.) = Amount – T.D. = 10044 – 744 = Rs 9300. Check: P.W. + T.D. = 9300 + 744 = 10044, which matches the Amount.
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Q25. The true discount on a bill due 4 years hence at 6% per annum is Rs 2160. Find the amount of the bill.
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Answer: D
The true discount is T.D. = Rs 2160. The rate is R = 6% per year. The time is T = 4 years. Let the amount due be x. True Discount equals interest on x: T.D. = (x x R x T) / (100 + R x T). Here 100 + R x T = 100 + 6 x 4 = 124. So 2160 = (x x 24) / 124. Cross-multiplying gives x x 24 = 2160 x 124 = 267840. So x = 267840 / 24 = Rs 11160. Present Worth (P.W.) = Amount – T.D. = 11160 – 2160 = Rs 9000. Check: P.W. + T.D. = 9000 + 2160 = 11160, which matches the Amount.
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