Percentage
⚡ 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 – Percentage
Shortcut techniques in Percentage help candidates solve aptitude questions quickly and accurately in SSC, Banking, Railway, CDS, NDA, CAT, UPSC, and placement examinations.
Instead of lengthy calculations, these methods focus on:
- Fast percentage conversions
- Successive percentage changes
- Mental calculation tricks
- Fraction-to-percentage shortcuts
- Profit and loss percentage concepts
- Population and depreciation methods
- Approximation techniques
Why Learn Percentage Shortcuts?
- Reduces calculation time significantly.
- Improves speed in arithmetic questions.
- Useful in Data Interpretation and Profit & Loss.
- Helps solve complex percentage problems mentally.
- Improves accuracy in competitive examinations.
Shortcut #1: Learn Important Fraction to Percentage Conversions
Memorizing common conversions saves huge calculation time.
| Fraction | Percentage |
|---|---|
| 1/2 | 50% |
| 1/3 | 33.33% |
| 2/3 | 66.66% |
| 1/4 | 25% |
| 3/4 | 75% |
| 1/5 | 20% |
| 1/8 | 12.5% |
| 1/10 | 10% |
✔ These conversions are used repeatedly in aptitude examinations.
Shortcut #2: Percentage to Decimal Conversion
To convert percentage into decimal:
Divide by 100
Example:
25% = 25/100 = 0.25
40% = 0.40
125% = 1.25
Shortcut #3: Find x% of y Quickly
Use interchange property:
x% of y = y% of x
Example:
18% of 50
= 50% of 18
= 9
✔ Very useful for mental calculations.
Shortcut #4: Successive Percentage Change Formula
If a quantity changes by a% and then by b%:
Net Change = a + b + (ab/100)
Use:
- Positive sign for increase
- Negative sign for decrease
Example:
Increase by 20% and then by 10%
= 20 + 10 + (20 × 10)/100
= 32%
Shortcut #5: Equal Percentage Increase and Decrease
If a quantity increases by x% and then decreases by x%:
Net Decrease = x²/100%
Example:
Increase by 20% and decrease by 20%
Net decrease:
= 20²/100
= 4%
✔ Equal increase and decrease never cancel each other.
Shortcut #6: Multiplication Factor Method
Convert percentage directly into multiplication factor.
| Change | Factor |
|---|---|
| Increase by 20% | 1.20 |
| Increase by 35% | 1.35 |
| Decrease by 10% | 0.90 |
| Decrease by 25% | 0.75 |
Example:
Price = 500
Increase by 20%
New price:
= 500 × 1.20
= 600
Shortcut #7: Population Growth Trick
Population increase problems can be solved quickly using factors.
Population after n years = P(1 + R/100)n
Example:
Population = 10000
Increase = 10%
After 2 years:
= 10000 × (1.1)²
= 12100
Shortcut #8: Depreciation Trick
For depreciation:
Value after n years = P(1 − R/100)n
Example:
Machine value = 50000
Depreciation = 10%
After 2 years:
= 50000 × (0.9)²
= 40500
Shortcut #9: Base Value Technique
Always identify the base value correctly.
✔ Percentage is always calculated on the original/base value.
Example:
Value increases from 80 to 100.
Increase:
= 20
Percentage increase:
= (20/80) × 100
= 25%
Shortcut #10: Percentage Error Trick
Use:
Error% = [(Wrong − Correct)/Correct] × 100
Example:
Correct answer = 80
Wrong answer = 100
Error:
= (20/80) × 100
= 25%
Shortcut #11: Consumption Reduction Trick
If price increases by R%, reduction in consumption:
[R/(100 + R)] × 100%
If price decreases by R%, increase in consumption:
[R/(100 − R)] × 100%
Shortcut #12: Reverse Percentage Technique
If a value becomes x% after increase:
Original value:
New Value × 100 / (100 + Increase%)
Example:
After 20% increase, value becomes 240.
Original value:
= 240 × 100/120
= 200
Shortcut #13: Approximation Technique
Use approximation for faster calculations in objective questions.
Example:
19% of 498
≈ 20% of 500
= 100
✔ Useful when options are widely separated.
Shortcut #14: Discount and Marked Price Trick
Final price after discount:
Marked Price × (100 − Discount)%
Example:
Marked price = 2000
Discount = 15%
Selling price:
= 2000 × 0.85
= 1700
Shortcut #15: Net Effect of Multiple Discounts
If discounts are x% and y%:
Net Discount = x + y − (xy/100)
Example:
Discounts = 20% and 10%
Net discount:
= 20 + 10 − (20 × 10)/100
= 28%
Important Exam Tips
- Memorize important fraction-percentage conversions.
- Use multiplication factors instead of lengthy percentage calculations.
- Always identify the correct base value.
- Practice successive percentage formulas regularly.
- Use approximation in objective-type questions.
- Convert percentages into decimals for quick multiplication.
- Practice mental calculations daily.
Shortcut techniques in Percentage help candidates improve speed, reduce calculation time, and solve aptitude questions efficiently in competitive examinations.