A banker's discount is the cut a bank takes when it buys a bill before the due date. It is simple interest on the full face value.
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Q1. The present worth of a bill due sometime hence is Rs 3800, and the true discount on the bill is Rs 380. Find the banker’s gain.
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Answer: A
Present worth (P.W.) is the sum which, invested now at the given rate, grows to the face value by the due date. Banker’s gain equals the true discount squared, divided by the present worth. Here, T.D. = Rs 380 and P.W. = Rs 3800. First square the true discount: 380 x 380 = 144400. Then divide by the present worth: 144400/3800 = Rs 38. Banker’s discount always equals true discount plus banker’s gain. B.D. = T.D. + B.G. = 380 + 38 = Rs 418.
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Q2. The present worth of a bill due sometime hence is Rs 5200, and the true discount on the bill is Rs 260. Find the banker’s discount.
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Answer: C
Present worth (P.W.) is the sum which, invested now at the given rate, grows to the face value by the due date. Banker’s gain equals the true discount squared, divided by the present worth. Here, T.D. = Rs 260 and P.W. = Rs 5200. First square the true discount: 260 x 260 = 67600. Then divide by the present worth: 67600/5200 = Rs 13. Banker’s discount always equals true discount plus banker’s gain. B.D. = T.D. + B.G. = 260 + 13 = Rs 273.
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Q3. The present worth of a bill due sometime hence is Rs 4800, and the true discount on the bill is Rs 360. Find the banker’s gain.
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Answer: A
Present worth (P.W.) is the sum which, invested now at the given rate, grows to the face value by the due date. Banker’s gain equals the true discount squared, divided by the present worth. Here, T.D. = Rs 360 and P.W. = Rs 4800. First square the true discount: 360 x 360 = 129600. Then divide by the present worth: 129600/4800 = Rs 27. Banker’s discount always equals true discount plus banker’s gain. B.D. = T.D. + B.G. = 360 + 27 = Rs 387.
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Q4. The banker’s discount on a sum of Rs 10000 due 12 months hence is Rs 600. Find the rate percent per annum.
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Answer: B
Banker’s discount is simple interest on the sum due, for the unexpired time. So the rate can be found from Rate = (100 x B.D.)/(Sum x T). Here, Sum = Rs 10000, B.D. = Rs 600, and T = 12/12 year. Using T = 12/12, this simplifies to Rate = (1200 x B.D.)/(Sum x 12). Multiply first: 1200 x 600 = 720000. Multiply the sum by the months: 10000 x 12 = 120000. Divide: 720000/120000 = 6%. So the rate is 6% per annum.
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Q5. The banker’s discount on a sum of Rs 14400 due 12 months hence is Rs 1440. Find the rate percent per annum.
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Answer: D
Banker’s discount is simple interest on the sum due, for the unexpired time. So the rate can be found from Rate = (100 x B.D.)/(Sum x T). Here, Sum = Rs 14400, B.D. = Rs 1440, and T = 12/12 year. Using T = 12/12, this simplifies to Rate = (1200 x B.D.)/(Sum x 12). Multiply first: 1200 x 1440 = 1728000. Multiply the sum by the months: 14400 x 12 = 172800. Divide: 1728000/172800 = 10%. So the rate is 10% per annum.
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Q6. The banker’s discount on a sum of Rs 18400 due 12 months hence is Rs 4600. Find the rate percent per annum.
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Answer: C
Banker’s discount is simple interest on the sum due, for the unexpired time. So the rate can be found from Rate = (100 x B.D.)/(Sum x T). Here, Sum = Rs 18400, B.D. = Rs 4600, and T = 12/12 year. Using T = 12/12, this simplifies to Rate = (1200 x B.D.)/(Sum x 12). Multiply first: 1200 x 4600 = 5520000. Multiply the sum by the months: 18400 x 12 = 220800. Divide: 5520000/220800 = 25%. So the rate is 25% per annum.
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Q7. The banker’s discount on a sum of Rs 3700 due 9 months hence is Rs 111. Find the rate percent per annum.
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Answer: A
Banker’s discount is simple interest on the sum due, for the unexpired time. So the rate can be found from Rate = (100 x B.D.)/(Sum x T). Here, Sum = Rs 3700, B.D. = Rs 111, and T = 9/12 year. Using T = 9/12, this simplifies to Rate = (1200 x B.D.)/(Sum x 9). Multiply first: 1200 x 111 = 133200. Multiply the sum by the months: 3700 x 9 = 33300. Divide: 133200/33300 = 4%. So the rate is 4% per annum.
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Q8. The banker’s discount on a sum of Rs 13800 due 9 months hence is Rs 1656. Find the rate percent per annum.
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Answer: B
Banker’s discount is simple interest on the sum due, for the unexpired time. So the rate can be found from Rate = (100 x B.D.)/(Sum x T). Here, Sum = Rs 13800, B.D. = Rs 1656, and T = 9/12 year. Using T = 9/12, this simplifies to Rate = (1200 x B.D.)/(Sum x 9). Multiply first: 1200 x 1656 = 1987200. Multiply the sum by the months: 13800 x 9 = 124200. Divide: 1987200/124200 = 16%. So the rate is 16% per annum.
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Q9. The banker’s discount on a sum of Rs 19100 due 9 months hence is Rs 1719. Find the rate percent per annum.
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Answer: D
Banker’s discount is simple interest on the sum due, for the unexpired time. So the rate can be found from Rate = (100 x B.D.)/(Sum x T). Here, Sum = Rs 19100, B.D. = Rs 1719, and T = 9/12 year. Using T = 9/12, this simplifies to Rate = (1200 x B.D.)/(Sum x 9). Multiply first: 1200 x 1719 = 2062800. Multiply the sum by the months: 19100 x 9 = 171900. Divide: 2062800/171900 = 12%. So the rate is 12% per annum.
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Q10. The banker’s discount on a sum of Rs 6200 due 4 months hence is Rs 310. Find the rate percent per annum.
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Answer: C
Banker’s discount is simple interest on the sum due, for the unexpired time. So the rate can be found from Rate = (100 x B.D.)/(Sum x T). Here, Sum = Rs 6200, B.D. = Rs 310, and T = 4/12 year. Using T = 4/12, this simplifies to Rate = (1200 x B.D.)/(Sum x 4). Multiply first: 1200 x 310 = 372000. Multiply the sum by the months: 6200 x 4 = 24800. Divide: 372000/24800 = 15%. So the rate is 15% per annum.
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Q11. The banker’s discount on a sum of Rs 200 due 12 months hence is Rs 12. Find the rate percent per annum.
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Answer: B
Banker’s discount is simple interest on the sum due, for the unexpired time. So the rate can be found from Rate = (100 x B.D.)/(Sum x T). Here, Sum = Rs 200, B.D. = Rs 12, and T = 12/12 year. Using T = 12/12, this simplifies to Rate = (1200 x B.D.)/(Sum x 12). Multiply first: 1200 x 12 = 14400. Multiply the sum by the months: 200 x 12 = 2400. Divide: 14400/2400 = 6%. So the rate is 6% per annum.
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Q12. The banker’s discount on a sum of Rs 11600 due 12 months hence is Rs 696. Find the rate percent per annum.
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Answer: D
Banker’s discount is simple interest on the sum due, for the unexpired time. So the rate can be found from Rate = (100 x B.D.)/(Sum x T). Here, Sum = Rs 11600, B.D. = Rs 696, and T = 12/12 year. Using T = 12/12, this simplifies to Rate = (1200 x B.D.)/(Sum x 12). Multiply first: 1200 x 696 = 835200. Multiply the sum by the months: 11600 x 12 = 139200. Divide: 835200/139200 = 6%. So the rate is 6% per annum.
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Q13. The banker’s discount on a sum of Rs 1400 due 3 months hence is Rs 42. Find the rate percent per annum.
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Answer: A
Banker’s discount is simple interest on the sum due, for the unexpired time. So the rate can be found from Rate = (100 x B.D.)/(Sum x T). Here, Sum = Rs 1400, B.D. = Rs 42, and T = 3/12 year. Using T = 3/12, this simplifies to Rate = (1200 x B.D.)/(Sum x 3). Multiply first: 1200 x 42 = 50400. Multiply the sum by the months: 1400 x 3 = 4200. Divide: 50400/4200 = 12%. So the rate is 12% per annum.
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Q14. The banker’s discount and the true discount on a sum of money due 8 months hence are Rs 104 and Rs 100 respectively. Find the sum.
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Answer: C
When both the banker’s discount and true discount are known, a standard formula gives the sum. Sum = (B.D. x T.D.)/(B.D. – T.D.). Here, B.D. = Rs 104 and T.D. = Rs 100. First find the difference: B.D. – T.D. = 104 – 100 = 4. Multiply B.D. by T.D.: 104 x 100 = 10400. Divide: 10400/4 = Rs 2600. So the sum is Rs 2600. Check: this difference, Rs 4, is exactly the banker’s gain on this sum.
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Q15. The banker’s discount and the true discount on a sum of money due 8 months hence are Rs 2450 and Rs 2100 respectively. Find the sum.
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Answer: D
When both the banker’s discount and true discount are known, a standard formula gives the sum. Sum = (B.D. x T.D.)/(B.D. – T.D.). Here, B.D. = Rs 2450 and T.D. = Rs 2100. First find the difference: B.D. – T.D. = 2450 – 2100 = 350. Multiply B.D. by T.D.: 2450 x 2100 = 5145000. Divide: 5145000/350 = Rs 14700. So the sum is Rs 14700. Check: this difference, Rs 350, is exactly the banker’s gain on this sum.
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Q16. The banker’s discount and the true discount on a sum of money due 12 months hence are Rs 1428 and Rs 1275 respectively. Find the sum.
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Answer: B
When both the banker’s discount and true discount are known, a standard formula gives the sum. Sum = (B.D. x T.D.)/(B.D. – T.D.). Here, B.D. = Rs 1428 and T.D. = Rs 1275. First find the difference: B.D. – T.D. = 1428 – 1275 = 153. Multiply B.D. by T.D.: 1428 x 1275 = 1820700. Divide: 1820700/153 = Rs 11900. So the sum is Rs 11900. Check: this difference, Rs 153, is exactly the banker’s gain on this sum.
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Q17. The banker’s discount and the true discount on a sum of money due 4 months hence are Rs 312 and Rs 300 respectively. Find the sum.
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Answer: A
When both the banker’s discount and true discount are known, a standard formula gives the sum. Sum = (B.D. x T.D.)/(B.D. – T.D.). Here, B.D. = Rs 312 and T.D. = Rs 300. First find the difference: B.D. – T.D. = 312 – 300 = 12. Multiply B.D. by T.D.: 312 x 300 = 93600. Divide: 93600/12 = Rs 7800. So the sum is Rs 7800. Check: this difference, Rs 12, is exactly the banker’s gain on this sum.
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Q18. The banker’s discount and the true discount on a sum of money due 12 months hence are Rs 2800 and Rs 2240 respectively. Find the sum.
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Answer: A
When both the banker’s discount and true discount are known, a standard formula gives the sum. Sum = (B.D. x T.D.)/(B.D. – T.D.). Here, B.D. = Rs 2800 and T.D. = Rs 2240. First find the difference: B.D. – T.D. = 2800 – 2240 = 560. Multiply B.D. by T.D.: 2800 x 2240 = 6272000. Divide: 6272000/560 = Rs 11200. So the sum is Rs 11200. Check: this difference, Rs 560, is exactly the banker’s gain on this sum.
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Q19. The banker’s discount and the true discount on a sum of money due 4 months hence are Rs 560 and Rs 525 respectively. Find the sum.
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Answer: B
When both the banker’s discount and true discount are known, a standard formula gives the sum. Sum = (B.D. x T.D.)/(B.D. – T.D.). Here, B.D. = Rs 560 and T.D. = Rs 525. First find the difference: B.D. – T.D. = 560 – 525 = 35. Multiply B.D. by T.D.: 560 x 525 = 294000. Divide: 294000/35 = Rs 8400. So the sum is Rs 8400. Check: this difference, Rs 35, is exactly the banker’s gain on this sum.
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Q20. If the true discount on a certain sum due 12 months hence at 25% per annum is Rs 1980, what is the banker’s discount on the same sum for the same time and at the same rate?
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Answer: C
Banker’s gain (B.G.) equals simple interest on the true discount, for the unexpired time. Here, T.D. = Rs 1980, the rate is R = 25% per annum, and the time is 12 months hence. B.G. = (T.D. x R x 12)/1200. Multiply first: 1980 x 25 x 12 = 594000. Then divide by 1200: 594000/1200 = Rs 495. Banker’s discount is always true discount plus banker’s gain. B.D. = T.D. + B.G. = 1980 + 495 = Rs 2475. Check: B.D. must exceed T.D., and Rs 2475 is indeed more than Rs 1980.
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Q21. If the true discount on a certain sum due 12 months hence at 25% per annum is Rs 3440, what is the banker’s discount on the same sum for the same time and at the same rate?
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Answer: D
Banker’s gain (B.G.) equals simple interest on the true discount, for the unexpired time. Here, T.D. = Rs 3440, the rate is R = 25% per annum, and the time is 12 months hence. B.G. = (T.D. x R x 12)/1200. Multiply first: 3440 x 25 x 12 = 1032000. Then divide by 1200: 1032000/1200 = Rs 860. Banker’s discount is always true discount plus banker’s gain. B.D. = T.D. + B.G. = 3440 + 860 = Rs 4300. Check: B.D. must exceed T.D., and Rs 4300 is indeed more than Rs 3440.
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Q22. If the true discount on a certain sum due 6 months hence at 25% per annum is Rs 2000, what is the banker’s discount on the same sum for the same time and at the same rate?
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Answer: C
Banker’s gain (B.G.) equals simple interest on the true discount, for the unexpired time. Here, T.D. = Rs 2000, the rate is R = 25% per annum, and the time is 6 months hence. B.G. = (T.D. x R x 6)/1200. Multiply first: 2000 x 25 x 6 = 300000. Then divide by 1200: 300000/1200 = Rs 250. Banker’s discount is always true discount plus banker’s gain. B.D. = T.D. + B.G. = 2000 + 250 = Rs 2250. Check: B.D. must exceed T.D., and Rs 2250 is indeed more than Rs 2000.
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Q23. If the true discount on a certain sum due 8 months hence at 10% per annum is Rs 975, what is the banker’s discount on the same sum for the same time and at the same rate?
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Answer: D
Banker’s gain (B.G.) equals simple interest on the true discount, for the unexpired time. Here, T.D. = Rs 975, the rate is R = 10% per annum, and the time is 8 months hence. B.G. = (T.D. x R x 8)/1200. Multiply first: 975 x 10 x 8 = 78000. Then divide by 1200: 78000/1200 = Rs 65. Banker’s discount is always true discount plus banker’s gain. B.D. = T.D. + B.G. = 975 + 65 = Rs 1040. Check: B.D. must exceed T.D., and Rs 1040 is indeed more than Rs 975.
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Q24. If the true discount on a certain sum due 4 months hence at 5% per annum is Rs 300, what is the banker’s discount on the same sum for the same time and at the same rate?
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Answer: B
Banker’s gain (B.G.) equals simple interest on the true discount, for the unexpired time. Here, T.D. = Rs 300, the rate is R = 5% per annum, and the time is 4 months hence. B.G. = (T.D. x R x 4)/1200. Multiply first: 300 x 5 x 4 = 6000. Then divide by 1200: 6000/1200 = Rs 5. Banker’s discount is always true discount plus banker’s gain. B.D. = T.D. + B.G. = 300 + 5 = Rs 305. Check: B.D. must exceed T.D., and Rs 305 is indeed more than Rs 300.
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Q25. If the true discount on a certain sum due 6 months hence at 16% per annum is Rs 400, what is the banker’s discount on the same sum for the same time and at the same rate?
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Answer: A
Banker’s gain (B.G.) equals simple interest on the true discount, for the unexpired time. Here, T.D. = Rs 400, the rate is R = 16% per annum, and the time is 6 months hence. B.G. = (T.D. x R x 6)/1200. Multiply first: 400 x 16 x 6 = 38400. Then divide by 1200: 38400/1200 = Rs 32. Banker’s discount is always true discount plus banker’s gain. B.D. = T.D. + B.G. = 400 + 32 = Rs 432. Check: B.D. must exceed T.D., and Rs 432 is indeed more than Rs 400.
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