True Discount
⚡ Unlock time-saving calculation tricks and mental math techniques. Solve complex problems in seconds with proven shortcut methods used by top performers.
Shortcut Techniques
Study MaterialShortcut Techniques – True Discount
Shortcut techniques in True Discount help candidates solve present worth, discount, and commercial mathematics problems quickly and accurately in SSC, Banking, Railway, Insurance, Defence, and various competitive examinations.
Most questions from this chapter are based on:
- Present Worth (PW)
- True Discount (TD)
- Amount or Sum Due
- Simple Interest relation
- Compound Interest Present Worth
- Commercial and Banking calculations
Learning shortcut methods reduces lengthy calculations and improves solving speed significantly.
Golden Concept of True Discount
True Discount = Interest on Present Worth
Shortcut #1: Memorize the Main Formula
PW = (100 × Amount) / [100 + (R × T)]
This is the most important formula in the chapter.
Shortcut #2: Quick Formula for True Discount
TD = Amount − PW
Always calculate Present Worth first if Amount is given.
Shortcut #3: Direct TD Formula
TD = (Amount × R × T) / [100 + (R × T)]
This formula directly gives True Discount without finding PW separately.
Shortcut #4: Relationship Trick
Amount = PW + TD
Remember this simple relation for quick calculations.
Shortcut #5: Quick SI and TD Relation
SI − TD = Interest on TD
This shortcut is very useful in advanced aptitude questions.
Shortcut #6: Quick Present Worth Trick
If:
- Rate = 25%
- Time = 4 years
Then:
R × T = 100
PW = Amount / 2
This shortcut avoids lengthy calculations.
Shortcut #7: Quick Percentage Observation
If:
| R × T | PW Relation |
|---|---|
| 100 | PW = Amount/2 |
| 50 | PW = 2/3 of Amount |
| 25 | PW = 4/5 of Amount |
Shortcut #8: Direct Formula for PW Using TD
PW = (100 × TD) / (R × T)
Shortcut #9: Compound Interest PW Shortcut
For compound interest problems:
PW = Amount / (1 + R/100)T
This formula is commonly asked in Banking aptitude exams.
Shortcut #10: Quick Ratio Method
If:
PW : Amount = 100 : [100 + (R × T)]
This ratio method saves time in comparison problems.
Shortcut #11: True Discount Percentage Trick
TD as percentage of Amount:
TD% = (R × T × 100) / [100 + (R × T)]
Shortcut #12: Quick Comparison Trick
Remember:
| Concept | Behavior |
|---|---|
| Amount | Always Maximum |
| PW | Always Minimum |
| TD | Difference Between Both |
Shortcut #13: Shortcut for Equal Interest and Discount
When:
SI = TD
Then:
Rate or time values are usually very small or simplified.
Shortcut #14: Simplification Trick
Instead of solving large fractions:
Cancel common factors immediately.
Example:
(100 × 480)/(100 + 20)
= 48000/120
= 400
Shortcut #15: Present Worth Mental Calculation Trick
If:
- Rate = 10%
- Time = 2 years
Then:
R × T = 20
Therefore:
PW = Amount × 100/120
= Amount × 5/6
Shortcut #16: Difference Method
If Amount and PW are given:
TD = Amount − PW
No need to use lengthy formulas.
Shortcut #17: Memorize Common Fraction Values
| Fraction | Decimal |
|---|---|
| 1/2 | 0.5 |
| 2/3 | 0.666 |
| 3/4 | 0.75 |
| 4/5 | 0.8 |
| 5/6 | 0.833 |
These values help in quick mental calculations.
Shortcut #18: Formula Selection Trick
| If Given | Use Formula |
|---|---|
| Amount, Rate, Time | PW Formula |
| PW, Rate, Time | TD Formula |
| PW and Amount | Difference Method |
| Compound Interest | CI PW Formula |
Shortcut #19: Quick Revision Formula Table
| Concept | Shortcut Formula |
|---|---|
| Present Worth | (100 × Amount)/[100+(R×T)] |
| True Discount | Amount − PW |
| TD Formula | (Amount × R × T)/[100+(R×T)] |
| Amount | PW + TD |
| Compound Interest PW | Amount/(1+R/100)T |
Shortcut #20: Most Important Exam Tricks
- True Discount is interest on PW.
- PW is always less than Amount.
- Use direct TD formula for faster solving.
- Memorize important percentage ratios.
- Practice SI and TD relation problems.
- Use simplification methods aggressively.
- Verify time and percentage values carefully.
Common Mistakes to Avoid
- Confusing Amount and Present Worth.
- Using wrong interest formula.
- Ignoring percentage conversion.
- Calculation mistakes in simplification.
- Using SI formula instead of TD formula.
Important Exam Tips
- Memorize all important formulas thoroughly.
- Practice Present Worth calculations regularly.
- Use ratio shortcuts wherever possible.
- Improve percentage simplification speed.
- Read question conditions carefully.
- Practice previous year aptitude questions.
- Verify final answers properly.
Shortcut techniques in True Discount help candidates improve solving speed, reduce lengthy calculations, and solve commercial mathematics aptitude questions efficiently in competitive examinations.