Banker's Discount
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Solved Examples
Study MaterialSolved Examples – Banker's Discount
Solved examples help students understand the practical application of Banker's Discount (BD), True Discount (TD), Banker’s Gain (BG), Face Value (FV), and Present Worth (PW) 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, CAT, CDS, and various aptitude examinations.
Topics Covered in Solved Examples
- Banker's Discount Problems
- True Discount Calculations
- Banker’s Gain Questions
- Present Worth Problems
- Bills of Exchange
- Rate and Time Calculations
- Ratio-Based Problems
- Advanced Banking Aptitude Questions
Example 1: Finding Banker's Discount
Question: Find the Banker's Discount on a bill of ₹5000 due after 2 years at 10% per annum.
Solution:
Using formula:
BD = (FV × R × T)/100
= (5000 × 10 × 2)/100
= ₹1000
Answer: ₹1000
Example 2: Finding True Discount
Question: Find the True Discount on ₹4800 due after 3 years at 8% per annum.
Solution:
Using formula:
TD = (FV × R × T)/[100 + (R × T)]
= (4800 × 8 × 3)/[100 + (8 × 3)]
= 115200/124
= ₹929.03
Answer: ₹929.03
Example 3: Finding Banker’s Gain
Question: The Banker's Discount is ₹750 and True Discount is ₹700. Find the Banker’s Gain.
Solution:
BG = BD − TD
= 750 − 700
= ₹50
Answer: ₹50
Example 4: Finding Present Worth
Question: A bill of ₹2400 is due after 2 years at 10% per annum. Find the Present Worth.
Solution:
PW = (100 × FV)/[100 + (R × T)]
= (100 × 2400)/[100 + (10 × 2)]
= 240000/120
= ₹2000
Answer: ₹2000
Example 5: Finding Face Value
Question: Banker's Discount is ₹240 and True Discount is ₹200. Find the Face Value of the bill.
Solution:
Using formula:
FV = (BD × TD)/(BD − TD)
= (240 × 200)/(240 − 200)
= 48000/40
= ₹1200
Answer: ₹1200
Example 6: Finding TD Using BG
Question: Banker’s Gain is ₹36, rate is 12% per annum, and time is 3 years. Find the True Discount.
Solution:
TD = (BG × 100)/(R × T)
= (36 × 100)/(12 × 3)
= 3600/36
= ₹100
Answer: ₹100
Example 7: Banker’s Gain Using TD and PW
Question: True Discount is ₹150 and Present Worth is ₹750. Find Banker’s Gain.
Solution:
BG = (TD)2/PW
= (150 × 150)/750
= 22500/750
= ₹30
Answer: ₹30
Example 8: Finding Rate of Interest
Question: The Banker's Discount on ₹4000 for 2 years is ₹800. Find the rate of interest.
Solution:
BD = (FV × R × T)/100
800 = (4000 × R × 2)/100
800 = 80R
R = 10%
Answer: 10% per annum
Example 9: Finding Time
Question: The Banker's Discount on ₹6000 at 15% per annum is ₹900. Find the time.
Solution:
BD = (FV × R × T)/100
900 = (6000 × 15 × T)/100
900 = 900T
T = 1 year
Answer: 1 year
Example 10: Comparing BD and TD
Question: The Face Value of a bill is ₹5000, rate is 10%, and time is 2 years. Find both BD and TD.
Solution:
Banker's Discount:
BD = (5000 × 10 × 2)/100
= ₹1000
True Discount:
TD = (5000 × 10 × 2)/[100 + (10 × 2)]
= 100000/120
= ₹833.33
Answer:
BD = ₹1000
TD = ₹833.33
Example 11: Banker’s Gain from BD and TD
Question: If Banker's Discount is ₹960 and True Discount is ₹800, find Banker’s Gain.
Solution:
BG = BD − TD
= 960 − 800
= ₹160
Answer: ₹160
Example 12: Ratio-Based Problem
Question: The Banker's Discount on a sum due after 2 years is 11/10 of the True Discount. Find the rate of interest.
Solution:
Using:
BD/TD = 1 + (R × T)/100
11/10 = 1 + (R × 2)/100
1/10 = 2R/100
10 = 2R
R = 5%
Answer: 5% per annum
Example 13: Advanced Banker’s Gain Problem
Question: The Banker’s Gain on a sum due after 3 years at 12% per annum is ₹270. Find the Banker's Discount.
Solution:
R × T = 12 × 3 = 36
Using shortcut:
BD/TD = 1 + 36/100
= 1.36
BG = BD − TD
270 = BD − BD/1.36
270 = 0.36BD/1.36
BD = (270 × 1.36)/0.36
= ₹1020
Answer: ₹1020
Example 14: Business Transaction Problem
Question: A trader owes ₹10028 due after 1 year. He wants to settle the account after 3 months at 12% per annum. Find the cash he should pay immediately.
Solution:
Remaining time:
= 9 months = 9/12 year
Present Worth:
PW = 10028/[1 + (12 × 9)/(100 × 12)]
= 10028/1.09
= ₹9200
Answer: ₹9200
Example 15: True Value Business Problem
Question: A man purchased a cow for ₹3000 and sold it the same day for ₹3600 on 2 years credit at 10% per annum. Find his gain.
Solution:
Present Value:
= 3600/[1 + (10 × 2)/100]
= 3600/1.2
= ₹3000
Gain:
= 3000 − 3000
= ₹0
Answer: No Gain
Important Exam Tips
- Banker's Discount is always greater than True Discount.
- Memorize all important formulas thoroughly.
- Use ratio shortcuts wherever possible.
- Practice Banker’s Gain problems regularly.
- Remember grace day rules carefully.
- Improve simplification and percentage calculations.
- Practice previous year aptitude questions.
Common Mistakes to Avoid
- Confusing BD with TD.
- Ignoring grace days.
- Using incorrect formulas.
- Calculation mistakes in percentages.
- Using wrong time values.
Practicing solved examples regularly improves conceptual clarity, logical thinking, and calculation speed in solving Banker's Discount aptitude questions in competitive examinations.