Quantitative Aptitude

Banker’s Discount and True Discount: Practice Questions with Answers

14 practice questions on Banker’s Discount and True Discount, with answers; most also have an explanation or a worked solution. Try each one before you open its answer.

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1. Q.1

   Find the banker’s discount (BD) on ₹1,200 due 2 years hence at 10% per annum.

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   Answer: ₹240

   Solution:

   1. BD = A×R×T / 100 = 1,200 × 10 × 2 / 100 = ₹240.

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2. Q.2

   The banker’s discount on a bill due 2 years hence at 10% per annum is ₹360. Find the true discount.

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   Answer: ₹300

   Solution:

   1. From BD, find the Amount first: A = BD × 100 / (R×T) = 360 × 100 / 20 = ₹1,800.
   2. TD = A × R×T / (100 + R×T) = 1,800 × 20 / 120 = ₹300.

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3. Q.3

   For the same bill, BD = ₹240 and TD = ₹200. Find the banker’s gain (BG).

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   Answer: ₹40

   Solution:

   1. BG = BD − TD = 240 − 200 = ₹40.

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4. Q.4

   On a bill of ₹2,200, the true discount is ₹200 and the banker's discount is ₹220. Verify the banker's gain using both BG = BD − TD and BG = (BD × TD)/A.

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   Answer: ₹20

   Solution:

   1. Directly: BG = BD − TD = 220 − 200 = ₹20.
   2. Shortcut: BG = (BD × TD)/A = (220 × 200)/2,200 = 44,000/2,200 = ₹20.
   3. Both methods agree.

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5. Q.5

   The banker's discount and true discount on a bill due in 1 year are ₹120 and ₹100 respectively. Find the amount of the bill and the rate of interest.

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   Answer: Amount = ₹600, Rate = 20% per annum

   Solution:

   1. BG = BD − TD = 120 − 100 = 20. Then PW = TD²/BG = 100²/20 = 10,000/20 = ₹500.
   2. Amount = PW + TD = 500 + 100 = ₹600.
   3. Using TD = A×RT/(100+RT) with T = 1: 100 = 600R/(100+R) → 10,000 + 100R = 600R → R = 10,000/500 = 20%.

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6. Q.6

   If the true discount on a bill is ₹40 and the present worth is ₹400, find the banker's gain using the shortcut formula.

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   Answer: ₹4

   Solution:

   1. BG = TD² / PW.
   2. = 40² / 400 = 1,600 / 400
   3. = ₹4.

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7. Q.7

   Find the present worth (PW) and the true discount (TD) on ₹1,200 due 2 years hence at 10% per annum simple interest.

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   Answer: PW = ₹1,000, TD = ₹200

   Solution:

   1. PW = 100 × 1,200 / (100 + 10×2) = 120,000 / 120 = ₹1,000.
   2. TD = A − PW = 1,200 − 1,000 = ₹200.

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8. Q.8

   The banker’s discount on a bill due 2 years hence at 10% per annum is ₹480. Find the true discount.

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   Answer: ₹400

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9. Q.9

   The banker's discount and true discount on a bill due in 1 year are ₹216 and ₹200 respectively. Find the amount of the bill and the rate of interest.

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   Answer: Amount = ₹2,700, Rate = 8%. BG=16, PW=TD²/BG=2,500, A=PW+TD=2,700; then solve 200=2,700R/(100+R).

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10. Q.10

    If the true discount on a bill is ₹60 and the present worth is ₹900, find the banker's gain using the shortcut formula.

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    Answer: ₹4. BG = TD²/PW = 3,600/900.

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11. Q.11

    Find the present worth and true discount on ₹3,600 due 2 years hence at 10% per annum simple interest.

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    Answer: PW = ₹3,000, TD = ₹600.

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12. Q.12

    On a bill of ₹1,320, the true discount is ₹120 and the banker's discount is ₹132. Verify the banker's gain using both formulas.

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    Answer: ₹12 by both methods: 132−120, and (132×120)/1,320.

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13. Q.13

    Find the present worth and the true discount on ₹2,400 due 2 years hence at 10% per annum simple interest.

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    Answer: PW = ₹2,000, TD = ₹400

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14. Q.14

    Find the banker’s discount on ₹2,400 due 2 years hence at 10% per annum.

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    Answer: ₹480

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