Profit & Loss
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Shortcut Techniques
Study MaterialShortcut Techniques – Profit & Loss
Shortcut techniques in Profit & Loss 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:
- Quick profit and loss calculations
- Percentage-based shortcuts
- Successive discount tricks
- False weight concepts
- Marked price calculations
- Mental multiplication methods
- Approximation techniques
Why Learn Profit & Loss Shortcuts?
- Reduces calculation time significantly.
- Improves speed in arithmetic questions.
- Useful in Banking and SSC examinations.
- Helps solve discount and marked price questions quickly.
- Improves mental calculation ability.
Shortcut #1: Profit and Loss Are Always Calculated on CP
✔ Profit% and Loss% are always calculated on Cost Price unless otherwise stated.
This is the most important rule in Profit & Loss.
Example:
CP = 400
SP = 500
Profit:
= 100
Profit%:
= (100/400) × 100
= 25%
Shortcut #2: Direct Selling Price Formula
Instead of lengthy calculations, directly use:
For Profit
SP = CP × (100 + Profit%)/100
For Loss
SP = CP × (100 − Loss%)/100
Example:
CP = 800
Profit = 25%
SP:
= 800 × 125/100
= 1000
Shortcut #3: Percentage Conversion Trick
Convert profit or loss directly into percentage form.
| Condition | SP Relation |
|---|---|
| 20% Profit | SP = 120% of CP |
| 25% Profit | SP = 125% of CP |
| 10% Loss | SP = 90% of CP |
| 40% Loss | SP = 60% of CP |
✔ Very useful for mental calculations.
Shortcut #4: Multiplication Factor Method
Convert percentages into multiplication factors.
| Change | Factor |
|---|---|
| 20% Profit | 1.20 |
| 35% Profit | 1.35 |
| 10% Loss | 0.90 |
| 25% Loss | 0.75 |
Example:
CP = 500
Profit = 20%
SP:
= 500 × 1.20
= 600
Shortcut #5: Equal Profit and Loss Shortcut
If two articles are sold:
- One at x% gain
- Another at x% loss
Then overall result is always:
Net Loss = x²/100%
Example:
Gain = 20%
Loss = 20%
Net loss:
= 20²/100
= 4%
✔ Equal profit and loss percentages never cancel each other.
Shortcut #6: Cost Price Formula Trick
Use direct formulas to avoid multiple calculations.
For Profit
CP = SP × 100/(100 + Profit%)
For Loss
CP = SP × 100/(100 − Loss%)
Shortcut #7: Successive Discount Formula
If two discounts are x% and y%:
Net Discount = x + y − (xy/100)
Example:
Discounts = 20% and 10%
Net discount:
= 20 + 10 − (20 × 10)/100
= 28%
Shortcut #8: Marked Price Shortcut
Selling price after discount:
SP = MP × (100 − Discount%)/100
Example:
MP = 2000
Discount = 15%
SP:
= 2000 × 85/100
= 1700
Shortcut #9: False Weight Technique
When a trader uses false weights:
Gain% = [Error/(True Value − Error)] × 100
Example:
A trader gives 900g instead of 1kg.
Error = 100g
Gain%:
= [100/(1000 − 100)] × 100
= 11.11%
Shortcut #10: Reverse Percentage Technique
If SP after profit is given:
CP = SP × 100/(100 + Profit%)
If SP after loss is given:
CP = SP × 100/(100 − Loss%)
Shortcut #11: Ratio Method
If profit percentage is known:
- CP : SP can be directly formed.
| Profit/Loss | CP : SP |
|---|---|
| 20% Profit | 5 : 6 |
| 25% Profit | 4 : 5 |
| 20% Loss | 5 : 4 |
| 40% Loss | 5 : 3 |
✔ Useful in ratio-based aptitude questions.
Shortcut #12: Approximation Technique
Use approximation in objective-type questions when options are widely separated.
Example:
19% profit on 498
Approximate:
20% of 500
= 100
Shortcut #13: Quick Mental Discount Trick
To calculate discounts mentally:
- 10% means divide by 10
- 20% means divide by 5
- 25% means divide by 4
- 50% means divide by 2
Example:
25% of 800
= 800 ÷ 4
= 200
Shortcut #14: Formula Reduction Method
Many Profit & Loss questions can be solved using:
SP = CP(1 ± Profit/Loss%)
Use:
- + for profit
- − for loss
Example:
CP = 1000
Profit = 15%
SP:
= 1000(1 + 0.15)
= 1150
Shortcut #15: Combined Discount and Profit Technique
If a shopkeeper gives discount and still earns profit:
- Use multiplication factors together.
Example:
MP = 2000
Discount = 10%
SP = 1800
If CP = 1500
Profit:
= 300
Profit%:
= 20%
Important Exam Tips
- Always calculate profit and loss on CP.
- Memorize direct SP and CP formulas.
- Use percentage-to-factor conversion for fast calculations.
- Practice successive discount questions regularly.
- Remember equal gain-loss shortcut formula.
- Use approximation techniques in MCQs.
- Practice mental percentage calculations daily.
Shortcut techniques in Profit & Loss help candidates improve speed, reduce calculation time, and solve arithmetic aptitude questions efficiently in competitive examinations.