True Discount
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Solved Examples
Study MaterialSolved Examples – True Discount
Solved examples help students understand the practical application of Present Worth (PW), True Discount (TD), Amount, and Simple Interest concepts in competitive examinations. These examples are designed from basic to advanced level and cover important questions frequently asked in SSC, Banking, Railway, Insurance, Defence, and various aptitude examinations.
Topics Covered in Solved Examples
- Present Worth Problems
- True Discount Calculations
- Amount and Sum Due Questions
- Simple Interest Relations
- Compound Interest Present Worth
- Commercial Mathematics Problems
- Ratio and Percentage Applications
- Advanced Aptitude Problems
Example 1: Basic True Discount
Question: Find the True Discount on ₹480 due after 2 years at 10% per annum simple interest.
Solution:
Using formula:
TD = (Amount × R × T) / [100 + (R × T)]
= (480 × 10 × 2) / [100 + (10 × 2)]
= 9600 / 120
= ₹80
Answer: ₹80
Example 2: Present Worth Calculation
Question: Find the Present Worth of ₹720 due after 4 years at 5% per annum.
Solution:
Using formula:
PW = (100 × Amount) / [100 + (R × T)]
= (100 × 720) / [100 + (5 × 4)]
= 72000 / 120
= ₹600
Answer: ₹600
Example 3: Finding Amount
Question: The Present Worth of a sum due after 3 years at 8% per annum is ₹500. Find the Amount.
Solution:
Simple Interest:
= (500 × 8 × 3)/100
= ₹120
Amount:
= PW + SI
= 500 + 120
= ₹620
Answer: ₹620
Example 4: True Discount from PW
Question: Find the True Discount on ₹400 Present Worth for 5 years at 6% per annum.
Solution:
TD = (PW × R × T)/100
= (400 × 6 × 5)/100
= ₹120
Answer: ₹120
Example 5: Finding Present Worth from Amount
Question: Find the Present Worth of ₹1000 due after 5 years at 10% per annum.
Solution:
PW = (100 × 1000) / [100 + (10 × 5)]
= 100000 / 150
= ₹666.67
Answer: ₹666.67
Example 6: Finding True Discount Directly
Question: Find the True Discount on ₹960 due after 4 years at 25% per annum.
Solution:
R × T = 25 × 4 = 100
Shortcut:
PW = Amount / 2
= 960 / 2
= ₹480
True Discount:
= 960 − 480
= ₹480
Answer: ₹480
Example 7: Difference Between Amount and PW
Question: The Amount is ₹850 and Present Worth is ₹680. Find the True Discount.
Solution:
TD = Amount − PW
= 850 − 680
= ₹170
Answer: ₹170
Example 8: Compound Interest Present Worth
Question: Find the Present Worth of ₹1210 due after 2 years at 10% compound interest.
Solution:
PW = Amount / (1 + R/100)T
= 1210 / (1 + 10/100)2
= 1210 / (1.1)2
= 1210 / 1.21
= ₹1000
Answer: ₹1000
Example 9: Simple Interest and True Discount Relation
Question: Simple Interest on a sum for 4 years is ₹240 and True Discount is ₹200. Find the Sum Due.
Solution:
Amount = (SI × TD)/(SI − TD)
= (240 × 200)/(240 − 200)
= 48000/40
= ₹1200
Answer: ₹1200
Example 10: Finding Rate of Interest
Question: The Present Worth of ₹660 due after 2 years is ₹600. Find the rate of interest.
Solution:
TD = Amount − PW
= 660 − 600
= ₹60
Using:
TD = (PW × R × T)/100
60 = (600 × R × 2)/100
60 = 12R
R = 5%
Answer: 5% per annum
Example 11: Finding Time
Question: The Present Worth of ₹920 due at 10% simple interest is ₹800. Find the time.
Solution:
TD = 920 − 800
= ₹120
Using:
TD = (PW × R × T)/100
120 = (800 × 10 × T)/100
120 = 80T
T = 1.5 years
Answer: 1.5 years
Example 12: Shortcut-Based PW Problem
Question: Find the Present Worth of ₹1500 due after 4 years at 25% per annum.
Solution:
R × T = 25 × 4 = 100
Shortcut:
PW = Amount / 2
= 1500 / 2
= ₹750
Answer: ₹750
Example 13: Finding Amount Using PW and TD
Question: Present Worth is ₹900 and True Discount is ₹180. Find the Amount.
Solution:
Amount = PW + TD
= 900 + 180
= ₹1080
Answer: ₹1080
Example 14: Advanced TD Problem
Question: The True Discount on a sum due after 3 years at 12% per annum is ₹108. Find the Present Worth.
Solution:
PW = (100 × TD)/(R × T)
= (100 × 108)/(12 × 3)
= 10800/36
= ₹300
Answer: ₹300
Example 15: Finding Sum Due from PW
Question: A Present Worth of ₹500 amounts to what sum after 4 years at 15% per annum simple interest?
Solution:
Simple Interest:
= (500 × 15 × 4)/100
= ₹300
Amount:
= 500 + 300
= ₹800
Answer: ₹800
Important Exam Tips
- True Discount is interest on Present Worth.
- Amount is always greater than PW.
- Use shortcut formulas wherever possible.
- Practice ratio and simplification methods regularly.
- Learn compound interest PW separately.
- Verify percentage and time calculations carefully.
- Improve mental calculation speed.
Common Mistakes to Avoid
- Confusing Amount and Present Worth.
- Using wrong interest formulas.
- Ignoring percentage calculations.
- Calculation mistakes in simplification.
- Using incorrect time values.
Practicing solved examples regularly improves conceptual clarity, logical thinking, and calculation speed in solving True Discount aptitude questions in competitive examinations.