Practice Quantitative Aptitude questions on True Discount, covering present worth, face value, banker’s discount, simple interest, rate of interest, and the relationship between true discount and amount due. Takes about 20–25 minutes and is useful for placement tests, TCS NQT, SSC, banking and MBA entrance exams.
Question 1
If the true discount on Rs.4510 due 6 months hence is Rs.110, the rate of interest is:
Explanation
Present worth = 4510 - 110 = Rs.4400. Interest on Rs.4400 for 6 months is Rs.110. Rate of interest = 100 × 1104400 × 0.5 = 5%.
Question 2
If simple interest and true discount on a certain amount for the same time period and same rate of interest is Rs.130 and Rs.120 respectively, then find the value of the amount.
Explanation
Amount = S.I. × T.D.S.I. - T.D. = 130 × 120130 - 120 = 1560010 = Rs.1560.
Question 3
A man owes a lender Rs.20502 due 1 year hence. If the man wants to settle the account after 8 months and the rate of interest being 6% per annum, find the amount the man should pay to the lender.
Explanation
Required amount = present worth of Rs.20502 due 4 months hence (1 year - 8 months = 4 months). P.W. = amount × 100100 + (R × T) = 20502 × 100100 + (6 × 412) = 2050200102 = Rs.20100.
Question 4
A man purchased a bicycle for Rs.4800 and sold it immediately at Rs.5995, allowing the buyer a credit of one and a half years. If the rate of interest is 6%, then the man gains:
Explanation
Cost price = Rs.4800. Selling price = present worth of Rs.5995 due 1.5 years hence = 5995 × 100100 + (6 × 1.5) = 599500109 = Rs.5500. Gain = 5500 - 4800 = Rs.700.
Question 5
Gopal has to pay Rs.440 to Ajay after 1 year. Ajay asks Gopal to pay Rs.220 in cash and defer the payment of Rs.220 for 2 years. If the rate of interest is 10% per annum, in this mode of payment:
Explanation
Gopal has to pay present worth of Rs.440 due 1 year hence = 440 × 100100 + (10 × 1) = 44000110 = Rs.400. Under the new arrangement, Gopal actually pays = 220 + present worth of Rs.220 due 2 years hence = 220 + 220 × 100100 + (10 × 2) = 220 + 22000120 = 220 + 183.33 = Rs.403.33. Since Rs.403.33 > Rs.400, Gopal loses Rs.3.33, or equivalently, Ajay gains Rs.3.33.
Question 6
What is the present worth of Rs. 13,800 due in 3 years at 5% per annum simple interest?
Explanation
Present worth = Amount × 100100 + (R × T) = 13,800 × 100100 + (5 × 3) = 13,80,000115 = Rs. 12,000.
Shortcut Method
P.W. = A × 100100 + R × T
13,800 × 100115
∴ P.W. = Rs. 12,000 ✓
13,800 × 100115
∴ P.W. = Rs. 12,000 ✓
Question 7
Find the present worth of a sum of Rs. 9,600 due 2 years hence, the rate of simple interest being 12.5% per annum.
Explanation
Present worth = Amount × 100100 + (R × T) = 9,600 × 100100 + (12.5 × 2) = 9,60,000125 = Rs. 7,680.
Shortcut Method
P.W. = A × 100100 + R × T
9,600 × 100125
∴ P.W. = Rs. 7,680 ✓
9,600 × 100125
∴ P.W. = Rs. 7,680 ✓
Question 8
The true discount on Rs. 3,150 due 6 months hence is Rs. 150. The rate percent per annum is:
Explanation
Present worth = 3,150 − 150 = Rs. 3,000.
The true discount is the simple interest on the present worth, so 150 = 3,000 × R × 1100 × 2.
R = 150 × 100 × 23,000 = 10%.
The true discount is the simple interest on the present worth, so 150 = 3,000 × R × 1100 × 2.
R = 150 × 100 × 23,000 = 10%.
Shortcut Method
P.W. = 3,150 − 150 = 3,000
S.I. on 3,000 for 6 months = 150
∴ Rate = 150 × 2003,000 = 10% ✓
S.I. on 3,000 for 6 months = 150
∴ Rate = 150 × 2003,000 = 10% ✓
Question 9
The true discount on a bill of Rs. 5,300 due 8 months hence is Rs. 300. What is the rate percent per annum?
Explanation
Present worth = 5,300 − 300 = Rs. 5,000.
The true discount is the simple interest on the present worth for 8 months, so 300 = 5,000 × R × 812 × 100.
R = 300 × 1,2005,000 × 8 = 9%.
The true discount is the simple interest on the present worth for 8 months, so 300 = 5,000 × R × 812 × 100.
R = 300 × 1,2005,000 × 8 = 9%.
Shortcut Method
P.W. = 5,300 − 300 = 5,000
S.I. on 5,000 for 8 months = 300
∴ Rate = 300 × 1,2005,000 × 8 = 9% ✓
S.I. on 5,000 for 8 months = 300
∴ Rate = 300 × 1,2005,000 × 8 = 9% ✓
Question 10
A bill of Rs. 8,400 is due 8 months hence and its true discount is Rs. 400. Find the rate of interest per annum.
Explanation
Present worth = 8,400 − 400 = Rs. 8,000.
The true discount is the simple interest on the present worth for 8 months, so 400 = 8,000 × R × 812 × 100.
R = 400 × 1,2008,000 × 8 = 7.5%.
The true discount is the simple interest on the present worth for 8 months, so 400 = 8,000 × R × 812 × 100.
R = 400 × 1,2008,000 × 8 = 7.5%.
Shortcut Method
P.W. = 8,400 − 400 = 8,000
S.I. on 8,000 for 8 months = 400
∴ Rate = 400 × 1,2008,000 × 8 = 7.5% ✓
S.I. on 8,000 for 8 months = 400
∴ Rate = 400 × 1,2008,000 × 8 = 7.5% ✓
Question 11
What rate of interest per annum is implied if the true discount on Rs. 5,600 due 1 year 6 months hence is Rs. 600?
Explanation
Present worth = 5,600 − 600 = Rs. 5,000.
The true discount is the simple interest on the present worth for 1.5 years, so 600 = 5,000 × R × 1.5100.
R = 600 × 1005,000 × 1.5 = 8%.
The true discount is the simple interest on the present worth for 1.5 years, so 600 = 5,000 × R × 1.5100.
R = 600 × 1005,000 × 1.5 = 8%.
Shortcut Method
P.W. = 5,600 − 600 = 5,000
S.I. on 5,000 for 1.5 years = 600
∴ Rate = 600 × 1005,000 × 1.5 = 8% ✓
S.I. on 5,000 for 1.5 years = 600
∴ Rate = 600 × 1005,000 × 1.5 = 8% ✓
Question 12
The true discount on a bill due 6 months hence at 12% per annum is Rs. 360. The amount of the bill is:
Explanation
Let the present worth be Rs. x. Then simple interest on x at 12% for 6 months = 360.
x × 12 × 1100 × 2 = 360, so 6x100 = 360 and x = Rs. 6,000.
Amount of the bill = P.W. + T.D. = 6,000 + 360 = Rs. 6,360.
x × 12 × 1100 × 2 = 360, so 6x100 = 360 and x = Rs. 6,000.
Amount of the bill = P.W. + T.D. = 6,000 + 360 = Rs. 6,360.
Shortcut Method
P.W. = 360 × 10012 × 0.5 = 6,000
Bill = P.W. + T.D.
∴ Bill = 6,000 + 360 = Rs. 6,360 ✓
Bill = P.W. + T.D.
∴ Bill = 6,000 + 360 = Rs. 6,360 ✓
Question 13
The true discount on a bill due 15 months hence at 8% per annum is Rs. 450. What is the amount of the bill?
Explanation
Let the present worth be Rs. x. Then simple interest on x at 8% for 15 months (1.25 years) = 450.
x × 8 × 1.25100 = 450, so 10x100 = 450 and x = Rs. 4,500.
Amount of the bill = P.W. + T.D. = 4,500 + 450 = Rs. 4,950.
x × 8 × 1.25100 = 450, so 10x100 = 450 and x = Rs. 4,500.
Amount of the bill = P.W. + T.D. = 4,500 + 450 = Rs. 4,950.
Shortcut Method
P.W. = 450 × 1008 × 1.25 = 4,500
Bill = P.W. + T.D.
∴ Bill = 4,500 + 450 = Rs. 4,950 ✓
Bill = P.W. + T.D.
∴ Bill = 4,500 + 450 = Rs. 4,950 ✓
Question 14
The true discount on Rs. 3,300 due after a certain time at 15% per annum is Rs. 300. The time after which it is due is:
Explanation
Present worth = 3,300 − 300 = Rs. 3,000.
Simple interest on Rs. 3,000 at 15% for t years = 300.
t = 100 × 3003,000 × 15 = 23 year = 23 × 12 = 8 months.
Simple interest on Rs. 3,000 at 15% for t years = 300.
t = 100 × 3003,000 × 15 = 23 year = 23 × 12 = 8 months.
Shortcut Method
P.W. = 3,300 − 300 = 3,000
t = 100 × 3003,000 × 15 = 23 yr
∴ t = 8 months ✓
t = 100 × 3003,000 × 15 = 23 yr
∴ t = 8 months ✓
Question 15
The true discount on Rs. 2,520 due after some time at 10% per annum is Rs. 120. After how long is it due?
Explanation
Present worth = 2,520 − 120 = Rs. 2,400.
Simple interest on Rs. 2,400 at 10% for t years = 120.
t = 100 × 1202,400 × 10 = 12 year = 6 months.
Simple interest on Rs. 2,400 at 10% for t years = 120.
t = 100 × 1202,400 × 10 = 12 year = 6 months.
Shortcut Method
P.W. = 2,520 − 120 = 2,400
t = 100 × 1202,400 × 10 = 12 yr
∴ t = 6 months ✓
t = 100 × 1202,400 × 10 = 12 yr
∴ t = 6 months ✓
Question 16
A man owes Rs. 8,560 due 1 year hence. If he settles the account after 6 months and the rate of interest is 14% per annum, how much cash should he pay?
Explanation
The money is due 6 months after the settlement date, so he should pay the present worth of Rs. 8,560 due 6 months hence.
Present worth = 8,560 × 100100 + (14 × 0.5) = 8,56,000107 = Rs. 8,000.
Present worth = 8,560 × 100100 + (14 × 0.5) = 8,56,000107 = Rs. 8,000.
Shortcut Method
due after 12 − 6 = 6 months
P.W. = 8,560 × 100100 + 14 × 0.5 = 8,560 × 100107
∴ Pays Rs. 8,000 ✓
P.W. = 8,560 × 100100 + 14 × 0.5 = 8,560 × 100107
∴ Pays Rs. 8,000 ✓
Question 17
A trader owes a supplier Rs. 11,550 due 15 months hence. He wants to settle the account after 3 months. If money is worth 10% per annum, how much cash should he pay?
Explanation
The money is then due 15 − 3 = 12 months, that is 1 year, after the settlement date.
Present worth = 11,550 × 100100 + (10 × 1) = 11,55,000110 = Rs. 10,500.
Present worth = 11,550 × 100100 + (10 × 1) = 11,55,000110 = Rs. 10,500.
Shortcut Method
due after 15 − 3 = 12 months
P.W. = 11,550 × 100110
∴ Pays Rs. 10,500 ✓
P.W. = 11,550 × 100110
∴ Pays Rs. 10,500 ✓
Question 18
A shopkeeper bought a refrigerator for Rs. 14,000 and sold it the same day for Rs. 16,500, allowing the buyer a credit of 2 years. If the rate of interest is 10% per annum, he:
Explanation
The cash value of the sale is the present worth of Rs. 16,500 due 2 years hence.
Present worth = 16,500 × 100100 + (10 × 2) = 16,50,000120 = Rs. 13,750.
Cost price = Rs. 14,000, so loss = 14,000 − 13,750 = Rs. 250.
Present worth = 16,500 × 100100 + (10 × 2) = 16,50,000120 = Rs. 13,750.
Cost price = Rs. 14,000, so loss = 14,000 − 13,750 = Rs. 250.
Shortcut Method
P.W. of 16,500 = 16,500 × 100120 = 13,750
cost 14,000 > 13,750
∴ Loses Rs. 250 ✓
cost 14,000 > 13,750
∴ Loses Rs. 250 ✓
Question 19
A trader purchased a machine for Rs. 20,000 and sold it the same day for Rs. 26,250 on a credit of 2 years. If the rate of interest is 12.5% per annum, he:
Explanation
The cash value of the sale is the present worth of Rs. 26,250 due 2 years hence.
Present worth = 26,250 × 100100 + (12.5 × 2) = 26,25,000125 = Rs. 21,000.
Cost price = Rs. 20,000, so gain = 21,000 − 20,000 = Rs. 1,000.
Present worth = 26,250 × 100100 + (12.5 × 2) = 26,25,000125 = Rs. 21,000.
Cost price = Rs. 20,000, so gain = 21,000 − 20,000 = Rs. 1,000.
Shortcut Method
P.W. of 26,250 = 26,250 × 100125 = 21,000
cost 20,000 < 21,000
∴ Gains Rs. 1,000 ✓
cost 20,000 < 21,000
∴ Gains Rs. 1,000 ✓
Question 20
A man buys a camera for Rs. 8,500 in cash and sells it for Rs. 9,900 at a credit of 1 year. If the rate of interest is 10% per annum, he:
Explanation
The cash value of the sale is the present worth of Rs. 9,900 due 1 year hence.
Present worth = 9,900 × 100100 + (10 × 1) = 9,90,000110 = Rs. 9,000.
Cost price = Rs. 8,500, so gain = 9,000 − 8,500 = Rs. 500.
Present worth = 9,900 × 100100 + (10 × 1) = 9,90,000110 = Rs. 9,000.
Cost price = Rs. 8,500, so gain = 9,000 − 8,500 = Rs. 500.
Shortcut Method
P.W. of 9,900 = 9,900 × 100110 = 9,000
9,000 − 8,500
∴ Gains Rs. 500 ✓
9,000 − 8,500
∴ Gains Rs. 500 ✓
Question 21
A person buys a laptop for Rs. 31,000 in cash and sells it for Rs. 36,000 at a credit of 2 years. If the rate of interest is 10% per annum, he:
Explanation
The cash value of the sale is the present worth of Rs. 36,000 due 2 years hence.
Present worth = 36,000 × 100100 + (10 × 2) = 36,00,000120 = Rs. 30,000.
Cost price = Rs. 31,000, so loss = 31,000 − 30,000 = Rs. 1,000.
Present worth = 36,000 × 100100 + (10 × 2) = 36,00,000120 = Rs. 30,000.
Cost price = Rs. 31,000, so loss = 31,000 − 30,000 = Rs. 1,000.
Shortcut Method
P.W. of 36,000 = 36,000 × 100120 = 30,000
cost 31,000 > 30,000
∴ Loses Rs. 1,000 ✓
cost 31,000 > 30,000
∴ Loses Rs. 1,000 ✓
Question 22
A man wants to sell a motorcycle. He gets two offers: Rs. 45,000 in cash, or Rs. 49,500 to be paid after 1 year. Money is worth 10% per annum. Which offer is better?
Explanation
Compare the cash offer with the present worth of the credit offer.
Present worth of Rs. 49,500 due 1 year hence = 49,500 × 100100 + (10 × 1) = 49,50,000110 = Rs. 45,000.
This is equal to the cash offer of Rs. 45,000, so both offers are equally good.
Present worth of Rs. 49,500 due 1 year hence = 49,500 × 100100 + (10 × 1) = 49,50,000110 = Rs. 45,000.
This is equal to the cash offer of Rs. 45,000, so both offers are equally good.
Shortcut Method
P.W. of 49,500 = 49,500 × 100110 = 45,000
cash = 45,000
∴ Both equally good ✓
cash = 45,000
∴ Both equally good ✓
Question 23
A farmer is offered Rs. 24,000 in cash for his tractor, or Rs. 27,000 to be paid after 6 months, money being worth 8% per annum. Which offer is better?
Explanation
Compare the cash offer with the present worth of the credit offer.
Present worth of Rs. 27,000 due 6 months hence = 27,000 × 100100 + (8 × 0.5) = 27,00,000104 = Rs. 25,961.54 (approximately).
This is more than the cash offer of Rs. 24,000, so the credit offer is better.
Present worth of Rs. 27,000 due 6 months hence = 27,000 × 100100 + (8 × 0.5) = 27,00,000104 = Rs. 25,961.54 (approximately).
This is more than the cash offer of Rs. 24,000, so the credit offer is better.
Shortcut Method
P.W. of 27,000 = 27,000 × 100104 ≈ 25,962
25,962 > 24,000
∴ Credit offer is better ✓
25,962 > 24,000
∴ Credit offer is better ✓
Question 24
If Rs. 30 is allowed as true discount on a bill of Rs. 130 due at the end of a certain time, then the discount allowed on the same sum due at the end of double the time is:
Explanation
Present worth for the certain time = 130 − 30 = Rs. 100, so the simple interest on Rs. 100 for that time = Rs. 30.
For double the time, the simple interest on Rs. 100 = Rs. 60, so a sum of Rs. 160 has present worth Rs. 100.
True discount on Rs. 160 = Rs. 60, so on Rs. 130 the true discount = 60160 × 130 = Rs. 48.75.
For double the time, the simple interest on Rs. 100 = Rs. 60, so a sum of Rs. 160 has present worth Rs. 100.
True discount on Rs. 160 = Rs. 60, so on Rs. 130 the true discount = 60160 × 130 = Rs. 48.75.
Shortcut Method
S.I. on 100 for the time = 30; for double = 60
T.D. on Rs. 160 = 60
∴ T.D. on Rs. 130 = 60160 × 130 = Rs. 48.75 ✓
T.D. on Rs. 160 = 60
∴ T.D. on Rs. 130 = 60160 × 130 = Rs. 48.75 ✓
Question 25
If Rs. 50 is allowed as true discount on a bill of Rs. 150 due at the end of a certain time, then the discount allowed on the same sum due at the end of double the time is:
Explanation
Present worth for the certain time = 150 − 50 = Rs. 100, so the simple interest on Rs. 100 for that time = Rs. 50.
For double the time, the simple interest on Rs. 100 = Rs. 100, so a sum of Rs. 200 has present worth Rs. 100.
True discount on Rs. 200 = Rs. 100, so on Rs. 150 the true discount = 100200 × 150 = Rs. 75.
For double the time, the simple interest on Rs. 100 = Rs. 100, so a sum of Rs. 200 has present worth Rs. 100.
True discount on Rs. 200 = Rs. 100, so on Rs. 150 the true discount = 100200 × 150 = Rs. 75.
Shortcut Method
S.I. on 100 for the time = 50; for double = 100
T.D. on Rs. 200 = 100
∴ T.D. on Rs. 150 = 100200 × 150 = Rs. 75 ✓
T.D. on Rs. 200 = 100
∴ T.D. on Rs. 150 = 100200 × 150 = Rs. 75 ✓
