True Discount— Concepts, Formulas & Shortcuts
- Present Worth (PW) = Amount × 100 / (100 + R × T).
- True Discount (TD) = Amount − PW = interest on the PRESENT WORTH.
- TD = (PW × R × T)/100 — never use the face value here.
- Amount = PW + TD, so PW = Amount − TD.
- TD = (Amount × R × T)/(100 + R × T) is the direct one-step formula.
- PW = (TD × 100)/(R × T) recovers the present worth when only the discount is known.
True Discount Practice Questions with Answers
Attempt each question first, then open the explanation. All 16 questions below are free to read and require no signup.
Q1.True discount is the interest on the:
Easy- AAmount due
- BPresent worth
- CBanker's gain
- DFace value
True Discount question 1 of 16+Show Answer & Explanation
Answer: B. Present worth
Explanation: By definition TD is the simple interest on the present worth for the unexpired time.
Q2.The present worth of ₹1,320 due 2 years hence at 10% per annum simple interest is:
Moderate- A₹1,000
- B₹1,100
- C₹1,200
- D₹1,250
True Discount question 2 of 16+Show Answer & Explanation
Answer: B. ₹1,100
Explanation: PW = 1320 × 100/(100 + 20) = 1320 × 100/120 = ₹1,100.
Q3.In the previous case, the true discount is:
Moderate- A₹120
- B₹200
- C₹220
- D₹264
True Discount question 3 of 16+Show Answer & Explanation
Answer: C. ₹220
Explanation: TD = Amount − PW = 1320 − 1100 = ₹220.
Q4.The true discount on ₹2,160 due after 1 year at 8% per annum is:
Moderate- A₹120
- B₹160
- C₹172.80
- D₹180
True Discount question 4 of 16+Show Answer & Explanation
Answer: B. ₹160
Explanation: PW = 2160 × 100/108 = ₹2,000 → TD = 2160 − 2000 = ₹160.
Q5.The relation between amount, present worth and true discount is:
Easy- AAmount = PW − TD
- BAmount = PW + TD
- CPW = Amount + TD
- DTD = Amount + PW
True Discount question 5 of 16+Show Answer & Explanation
Answer: B. Amount = PW + TD
Explanation: The present worth grows by exactly the true discount to become the amount due.
Q6.If the true discount on a sum due 2 years hence at 14% per annum is ₹168, the sum due is:
Difficult- A₹600
- B₹700
- C₹768
- D₹800
True Discount question 6 of 16+Show Answer & Explanation
Answer: C. ₹768
Explanation: PW = 168 × 100/(14 × 2) = ₹600 → Amount = 600 + 168 = ₹768.
Q7.The present worth of ₹1,100 due 1 year hence at 10% per annum is:
Easy- A₹990
- B₹1,000
- C₹1,010
- D₹1,050
True Discount question 7 of 16+Show Answer & Explanation
Answer: B. ₹1,000
Explanation: PW = 1100 × 100/110 = ₹1,000.
Q8.In the previous case the true discount is:
Easy- A₹90
- B₹100
- C₹110
- D₹120
True Discount question 8 of 16+Show Answer & Explanation
Answer: B. ₹100
Explanation: TD = 1100 − 1000 = ₹100.
Q9.The true discount on ₹1,860 due 3 years hence at 8% per annum is:
Moderate- A₹340
- B₹360
- C₹380
- D₹400
True Discount question 9 of 16+Show Answer & Explanation
Answer: B. ₹360
Explanation: PW = 1860 × 100/124 = ₹1,500 → TD = 1860 − 1500 = ₹360.
Q10.If the present worth of a sum due 2 years hence at 5% is ₹800, the sum due is:
Moderate- A₹840
- B₹860
- C₹880
- D₹900
True Discount question 10 of 16+Show Answer & Explanation
Answer: C. ₹880
Explanation: TD = 800 × 5 × 2/100 = ₹80 → amount = 800 + 80 = ₹880.
Q11.The true discount is always ___ the simple interest on the same amount for the same period.
Moderate- AGreater than
- BLess than
- CEqual to
- DDouble
True Discount question 11 of 16+Show Answer & Explanation
Answer: B. Less than
Explanation: TD is interest on the smaller present worth, so it is always less than SI computed on the face value.
Q12.The present worth of ₹2,200 due 1 year hence at 10% per annum is:
Easy- A₹1,900
- B₹2,000
- C₹2,100
- D₹2,150
True Discount question 12 of 16+Show Answer & Explanation
Answer: B. ₹2,000
Explanation: PW = 2200 × 100/110 = ₹2,000.
Q13.In the previous case the true discount is:
Easy- A₹150
- B₹180
- C₹200
- D₹220
True Discount question 13 of 16+Show Answer & Explanation
Answer: C. ₹200
Explanation: TD = 2200 − 2000 = ₹200.
Q14.The true discount on ₹1,200 due 2 years hence at 10% per annum is:
Moderate- A₹150
- B₹180
- C₹200
- D₹240
True Discount question 14 of 16+Show Answer & Explanation
Answer: C. ₹200
Explanation: PW = 1200 × 100/(100 + 20) = ₹1,000, so TD = 1200 − 1000 = ₹200.
Q15.If the present worth is ₹1,500 and the true discount ₹150, the sum due is:
Easy- A₹1,350
- B₹1,600
- C₹1,650
- D₹1,700
True Discount question 15 of 16+Show Answer & Explanation
Answer: C. ₹1,650
Explanation: Amount = PW + TD = 1500 + 150 = ₹1,650.
Q16.The true discount on a bill is the interest on the:
Easy- AFace value
- BPresent worth
- CBanker's gain
- DDiscounted value
True Discount question 16 of 16+Show Answer & Explanation
Answer: B. Present worth
Explanation: By definition true discount is simple interest on the present worth.
True Discount — Frequently Asked Questions
What is the difference between true discount and simple interest?+
Simple interest is charged on the sum you actually hold now, while true discount is the interest on the present worth of a future amount. TD is always slightly less than the SI computed on the face value.
How do I find the sum due when only the true discount is given?+
First find the present worth using PW = TD × 100/(R × T), then add the true discount back: Amount = PW + TD.
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