Practice Quantitative Aptitude questions on Banker's Discount, covering face value, present worth, simple interest, rate of interest, time periods, and calculations involving banker’s discount and true discount. Takes about 20–25 minutes and is useful for placement tests, TCS NQT, SSC, banking and MBA entrance exams.
Question 1
What is the banker's discount, if the true discount on a bill of Rs.840 is Rs.105?
Explanation
Present worth (P.W.) = 840 - 105 = Rs.735. Therefore, S.I. on Rs.735 = Rs.105. Banker's discount = S.I. on Rs.840 = 105 × 840735 = Rs.120.
Question 2
Find the banker's gain, if the present worth of a certain amount is Rs.2400 and the true discount is Rs.120.
Explanation
Banker's gain = (T.D.)2P.W. = (120)22400 = 144002400 = Rs.6.
Question 3
The banker's gain on a bill due 2 years hence at 10% per annum is Rs.10. What is the true discount?
Explanation
True discount = B.G. × 100R × T = 10 × 10010 × 2 = Rs.50.
Question 4
If the banker's discount on a certain amount of money is Rs.80 and the true discount on the same amount for the same time duration is Rs.64, then the amount due is:
Explanation
Amount due = B.D. × T.D.B.D. - T.D. = 80 × 6480 - 64 = 512016 = Rs.320.
Question 5
Find the rate percent if the banker's gain on a certain sum due two and a half year hence is 15 of the banker's discount.
Explanation
Let banker's discount = Rs.10. Then, banker's gain = 15 × 10 = Rs.2. True discount = (B.D. - B.G.) = (10 - 2) = Rs.8. Sum = 10 × 810 - 8 = 802 = Rs.40. S.I. on Rs.40 for 2.5 years is Rs.10 (the banker's discount). Therefore, rate = 100 × 1040 × 2.5 = 10%.
Question 6
What is the true discount if a banker’s discount on a bill due 4 months hence is 420 at 15%?
Explanation
Banker's discount = 420, time = 4 months = 13 year and rate = 15%.
True discount = BD × 100100 + (R × T) = 420 × 100100 + 5 = 42000105 = 400.
True discount = BD × 100100 + (R × T) = 420 × 100100 + 5 = 42000105 = 400.
Question 7
The present worth of a sum due some time hence is Rs. 2,500 and the true discount is Rs. 150. The banker's gain is:
Explanation
Banker's gain = (T.D.)2P.W. = 150 × 1502,500 = 22,5002,500 = Rs. 9.
Shortcut Method
B.G. = (T.D.)2P.W.
150 × 1502,500
∴ B.G. = Rs. 9 ✓
150 × 1502,500
∴ B.G. = Rs. 9 ✓
Question 8
If the present worth of a bill due some time hence is Rs. 1,500 and the true discount is Rs. 150, find the banker's gain.
Explanation
Banker's gain = (T.D.)2P.W. = 150 × 1501,500 = 22,5001,500 = Rs. 15.
Shortcut Method
B.G. = (T.D.)2P.W.
150 × 1501,500
∴ B.G. = Rs. 15 ✓
150 × 1501,500
∴ B.G. = Rs. 15 ✓
Question 9
The present worth of a bill due some time hence is Rs. 1,250 and the true discount is Rs. 50. The banker's discount is:
Explanation
Banker's gain = (T.D.)2P.W. = 50 × 501,250 = Rs. 2.
Banker's discount = T.D. + B.G. = 50 + 2 = Rs. 52.
Banker's discount = T.D. + B.G. = 50 + 2 = Rs. 52.
Shortcut Method
B.G. = 50 × 501,250 = 2
B.D. = T.D. + B.G.
∴ B.D. = 50 + 2 = Rs. 52 ✓
B.D. = T.D. + B.G.
∴ B.D. = 50 + 2 = Rs. 52 ✓
Question 10
A bill is due after some time. Its present worth is Rs. 600 and the true discount is Rs. 30. What is the banker's discount?
Explanation
Banker's gain = (T.D.)2P.W. = 30 × 30600 = Rs. 1.50.
Banker's discount = T.D. + B.G. = 30 + 1.50 = Rs. 31.50.
Banker's discount = T.D. + B.G. = 30 + 1.50 = Rs. 31.50.
Shortcut Method
B.G. = 30 × 30600 = 1.50
B.D. = T.D. + B.G.
∴ B.D. = 30 + 1.50 = Rs. 31.50 ✓
B.D. = T.D. + B.G.
∴ B.D. = 30 + 1.50 = Rs. 31.50 ✓
Question 11
The present worth of a bill due some time hence is Rs. 1,500 and the true discount is Rs. 60. What is the banker's discount?
Explanation
Face value of the bill = P.W. + T.D. = 1,500 + 60 = Rs. 1,560.
T.D. is the interest on the present worth, so rate × time = 601,500 = 125.
Banker's discount = interest on the face value = 125 × 1,560 = Rs. 62.40.
T.D. is the interest on the present worth, so rate × time = 601,500 = 125.
Banker's discount = interest on the face value = 125 × 1,560 = Rs. 62.40.
Shortcut Method
F = 1,500 + 60 = 1,560
rate × time = 601,500 = 0.04
∴ B.D. = 0.04 × 1,560 = Rs. 62.40 ✓
rate × time = 601,500 = 0.04
∴ B.D. = 0.04 × 1,560 = Rs. 62.40 ✓
Question 12
The present worth of a certain bill is Rs. 1,600 and the true discount on it is Rs. 120. Find the banker's discount.
Explanation
Banker's gain = (T.D.)2P.W. = 120 × 1201,600 = 14,4001,600 = Rs. 9.
Banker's discount = T.D. + B.G. = 120 + 9 = Rs. 129.
Banker's discount = T.D. + B.G. = 120 + 9 = Rs. 129.
Shortcut Method
B.G. = 120 × 1201,600 = 9
B.D. = T.D. + B.G.
∴ B.D. = 120 + 9 = Rs. 129 ✓
B.D. = T.D. + B.G.
∴ B.D. = 120 + 9 = Rs. 129 ✓
Question 13
The true discount on a bill of Rs. 630 is Rs. 90. The banker's discount is:
Explanation
Present worth = 630 − 90 = Rs. 540.
The interest on Rs. 540 is Rs. 90, so rate × time = 90540 = 16.
Banker's discount = interest on the bill of Rs. 630 = 16 × 630 = Rs. 105.
The interest on Rs. 540 is Rs. 90, so rate × time = 90540 = 16.
Banker's discount = interest on the bill of Rs. 630 = 16 × 630 = Rs. 105.
Shortcut Method
P.W. = 630 − 90 = 540
rate × time = 90540 = 16
∴ B.D. = 6306 = Rs. 105 ✓
rate × time = 90540 = 16
∴ B.D. = 6306 = Rs. 105 ✓
Question 14
The true discount on a bill of Rs. 770 is Rs. 70. What is the banker's discount?
Explanation
Present worth = 770 − 70 = Rs. 700.
The interest on Rs. 700 is Rs. 70, so rate × time = 70700 = 110.
Banker's discount = interest on the bill of Rs. 770 = 110 × 770 = Rs. 77.
The interest on Rs. 700 is Rs. 70, so rate × time = 70700 = 110.
Banker's discount = interest on the bill of Rs. 770 = 110 × 770 = Rs. 77.
Shortcut Method
P.W. = 770 − 70 = 700
rate × time = 70700 = 0.1
∴ B.D. = 0.1 × 770 = Rs. 77 ✓
rate × time = 70700 = 0.1
∴ B.D. = 0.1 × 770 = Rs. 77 ✓
Question 15
The banker's discount on a bill due 6 months hence at 10% per annum is Rs. 735. What is the true discount?
Explanation
Rate × time = 10% × 12 year = 5%.
True discount = B.D. × 100100 + (rate × time) = 735 × 100100 + 5 = 73,500105 = Rs. 700.
True discount = B.D. × 100100 + (rate × time) = 735 × 100100 + 5 = 73,500105 = Rs. 700.
Shortcut Method
r × t = 10% × 12 = 5%
T.D. = 735 × 100105
∴ T.D. = Rs. 700 ✓
T.D. = 735 × 100105
∴ T.D. = Rs. 700 ✓
Question 16
The banker's discount on a bill due 3 months hence at 16% per annum is Rs. 520. The true discount is:
Explanation
Rate × time = 16% × 14 year = 4%.
True discount = B.D. × 100100 + (rate × time) = 520 × 100100 + 4 = 52,000104 = Rs. 500.
True discount = B.D. × 100100 + (rate × time) = 520 × 100100 + 4 = 52,000104 = Rs. 500.
Shortcut Method
r × t = 16% × 14 = 4%
T.D. = 520 × 100104
∴ T.D. = Rs. 500 ✓
T.D. = 520 × 100104
∴ T.D. = Rs. 500 ✓
Question 17
The present worth of a sum due some time hence is Rs. 900 and the banker's gain is Rs. 25. The true discount is:
Explanation
B.G. = (T.D.)2P.W., so (T.D.)2 = P.W. × B.G. = 900 × 25 = 22,500.
T.D. = √22,500 = Rs. 150.
T.D. = √22,500 = Rs. 150.
Shortcut Method
(T.D.)2 = P.W. × B.G.
900 × 25 = 22,500
∴ T.D. = Rs. 150 ✓
900 × 25 = 22,500
∴ T.D. = Rs. 150 ✓
Question 18
The present worth of a certain sum due sometime hence is Rs. 1,764 and the banker's gain is Rs. 9. The true discount is:
Explanation
B.G. = (T.D.)2P.W., so (T.D.)2 = P.W. × B.G. = 1,764 × 9 = 15,876.
T.D. = √15,876 = Rs. 126.
T.D. = √15,876 = Rs. 126.
Shortcut Method
(T.D.)2 = P.W. × B.G.
1,764 × 9 = 15,876 = 1262
∴ T.D. = Rs. 126 ✓
1,764 × 9 = 15,876 = 1262
∴ T.D. = Rs. 126 ✓
Question 19
A bill of Rs. 2,40,000 is due in 2 years. At 10% per annum, find the banker's gain.
Explanation
Banker's discount = interest on the face value = 2,40,000 × 10% × 2 = Rs. 48,000.
Present worth = 2,40,000 × 100100 + (10 × 2) = 2,40,000 × 100120 = Rs. 2,00,000, so true discount = 2,40,000 − 2,00,000 = Rs. 40,000.
Banker's gain = B.D. − T.D. = 48,000 − 40,000 = Rs. 8,000.
Present worth = 2,40,000 × 100100 + (10 × 2) = 2,40,000 × 100120 = Rs. 2,00,000, so true discount = 2,40,000 − 2,00,000 = Rs. 40,000.
Banker's gain = B.D. − T.D. = 48,000 − 40,000 = Rs. 8,000.
Shortcut Method
B.D. = 2,40,000 × 20% = 48,000
P.W. = 2,40,000 ÷ 1.2 = 2,00,000 → T.D. = 40,000
∴ B.G. = 48,000 − 40,000 = Rs. 8,000 ✓
P.W. = 2,40,000 ÷ 1.2 = 2,00,000 → T.D. = 40,000
∴ B.G. = 48,000 − 40,000 = Rs. 8,000 ✓
Question 20
The banker's discount on a certain sum due some time hence is Rs. 90 and the true discount on the same sum for the same time is Rs. 75. The sum due is:
Explanation
Sum due = B.D. × T.D.B.D. − T.D. = 90 × 7590 − 75 = 6,75015 = Rs. 450.
Shortcut Method
Sum = B.D. × T.D.B.D. − T.D.
90 × 7515
∴ Sum = Rs. 450 ✓
90 × 7515
∴ Sum = Rs. 450 ✓
Question 21
The banker's discount on a sum due some time hence is Rs. 154 and the true discount on it for the same time is Rs. 140. What is the sum due?
Explanation
Sum due = B.D. × T.D.B.D. − T.D. = 154 × 140154 − 140 = 21,56014 = Rs. 1,540.
Shortcut Method
Sum = B.D. × T.D.B.D. − T.D.
154 × 14014
∴ Sum = Rs. 1,540 ✓
154 × 14014
∴ Sum = Rs. 1,540 ✓
Question 22
The banker's gain on a sum due 3 years hence at 8% per annum is Rs. 36. The present worth is:
Explanation
Rate × time = 8% × 3 = 24%.
Banker's gain is the interest on the true discount, so T.D. = B.G. × 100rate × time = 36 × 10024 = Rs. 150.
True discount is the interest on the present worth, so P.W. = T.D. × 100rate × time = 150 × 10024 = Rs. 625.
Banker's gain is the interest on the true discount, so T.D. = B.G. × 100rate × time = 36 × 10024 = Rs. 150.
True discount is the interest on the present worth, so P.W. = T.D. × 100rate × time = 150 × 10024 = Rs. 625.
Shortcut Method
r × t = 8% × 3 = 24%
T.D. = 36 × 10024 = 150
∴ P.W. = 150 × 10024 = Rs. 625 ✓
T.D. = 36 × 10024 = 150
∴ P.W. = 150 × 10024 = Rs. 625 ✓
Question 23
The banker's gain on a certain sum due 2 years hence at 5% per annum is Rs. 15. What is the present worth?
Explanation
Rate × time = 5% × 2 = 10%.
Banker's gain is the interest on the true discount, so T.D. = B.G. × 100rate × time = 15 × 10010 = Rs. 150.
True discount is the interest on the present worth, so P.W. = T.D. × 100rate × time = 150 × 10010 = Rs. 1,500.
Banker's gain is the interest on the true discount, so T.D. = B.G. × 100rate × time = 15 × 10010 = Rs. 150.
True discount is the interest on the present worth, so P.W. = T.D. × 100rate × time = 150 × 10010 = Rs. 1,500.
Shortcut Method
r × t = 5% × 2 = 10%
T.D. = 15 × 10010 = 150
∴ P.W. = 150 × 10010 = Rs. 1,500 ✓
T.D. = 15 × 10010 = 150
∴ P.W. = 150 × 10010 = Rs. 1,500 ✓
Question 24
The banker's discount on a certain sum due 2 years hence is 65 of the true discount. The rate percent is:
Explanation
B.D. ÷ T.D. = 1 + (rate × time), because B.D. is the interest on the sum and T.D. is the interest on the present worth.
65 = 1 + (rate × time), so rate × time = 15.
Time = 2 years, so rate = 15 × 1002 = 10%.
65 = 1 + (rate × time), so rate × time = 15.
Time = 2 years, so rate = 15 × 1002 = 10%.
Shortcut Method
B.D. ÷ T.D. = 1 + r × t
65 = 1 + r × t → r × t = 15
∴ r = 10010 = 10% ✓
65 = 1 + r × t → r × t = 15
∴ r = 10010 = 10% ✓
Question 25
The banker's discount on a certain sum due 112 years hence is 2825 of the true discount. The rate percent is:
Explanation
B.D. ÷ T.D. = 1 + (rate × time), because B.D. is the interest on the sum and T.D. is the interest on the present worth.
2825 = 1 + (rate × time), so rate × time = 325.
Time = 112 years = 32 years, so rate = 325 × 23 × 100 = 8%.
2825 = 1 + (rate × time), so rate × time = 325.
Time = 112 years = 32 years, so rate = 325 × 23 × 100 = 8%.
Shortcut Method
B.D. ÷ T.D. = 1 + r × t
2825 = 1 + r × t → r × t = 325
∴ r = 325 ÷ 32 = 8% ✓
2825 = 1 + r × t → r × t = 325
∴ r = 325 ÷ 32 = 8% ✓
