Formulas & Concepts
Profit & Loss · Study material
Profit & Loss
Profit and Loss is one of the most important and scoring topics in Quantitative Aptitude. Questions from this chapter are frequently asked in SSC, Banking, Railway, CDS, NDA, CAT, UPSC, and placement examinations.
This topic is based on buying and selling of goods, calculation of profit, loss, discount, marked price, and percentage changes in business transactions.
Profit and Loss problems are widely used in:
- Business mathematics
- Commercial calculations
- Data Interpretation
- Percentage applications
- Discount and taxation problems
Why Profit & Loss is Important?
- Frequently asked in competitive examinations.
- Directly connected with Percentage chapter.
- Useful in real-life business calculations.
- Improves calculation speed and logical thinking.
- Important for commerce and banking aptitude.
Basic Terminologies
1. Cost Price (CP)
The price at which an article is purchased is called:
Cost Price (CP)
It represents the buying price of an article.
2. Selling Price (SP)
The price at which an article is sold is called:
Selling Price (SP)
It represents the final selling amount of an article.
3. Profit or Gain
If:
SP > CP
Then the seller earns:
Profit = SP − CP
4. Loss
If:
CP > SP
Then the seller incurs:
Loss = CP − SP
5. Overhead Charges
Extra expenditures on purchased goods apart from actual cost price are called overhead charges.
Examples:
- Transport charges
- Repair charges
- Packing charges
- Salary expenses
- Maintenance cost
✔ If overhead charges are not mentioned in the question, they are generally ignored.
Important Formulae of Profit & Loss
| Concept | Formula |
|---|---|
| Profit | SP − CP |
| Loss | CP − SP |
| Profit Percentage | (Profit / CP) × 100 |
| Loss Percentage | (Loss / CP) × 100 |
| Selling Price (Profit) | CP × (100 + Profit%)/100 |
| Selling Price (Loss) | CP × (100 − Loss%)/100 |
| Cost Price (Profit) | SP × 100/(100 + Profit%) |
| Cost Price (Loss) | SP × 100/(100 − Loss%) |
Profit Percentage Formula
Profit percentage is always calculated on:
Cost Price (CP)
Formula:
Profit% = (Profit / CP) × 100
Example:
CP = 500
SP = 600
Profit:
= 600 − 500
= 100
Profit percentage:
= (100/500) × 100
= 20%
Loss Percentage Formula
Formula:
Loss% = (Loss / CP) × 100
Example:
CP = 800
SP = 680
Loss:
= 800 − 680
= 120
Loss percentage:
= (120/800) × 100
= 15%
Selling Price Formula
1. Selling Price with Profit
SP = CP × (100 + Profit%)/100
2. Selling Price with Loss
SP = CP × (100 − Loss%)/100
Cost Price Formula
1. Cost Price with Profit
CP = SP × 100/(100 + Profit%)
2. Cost Price with Loss
CP = SP × 100/(100 − Loss%)
Important Profit & Loss Concepts
1. Profit is Always Calculated on CP
✔ Profit percentage and loss percentage are always calculated on Cost Price unless stated otherwise.
2. Selling at Profit
If profit = 25%
Then:
SP = 125% of CP
3. Selling at Loss
If loss = 20%
Then:
SP = 80% of CP
Discount and Marked Price
1. Marked Price (MP)
The price marked on an article before discount is called:
Marked Price (MP)
2. Discount
Reduction given on marked price is called:
Discount
3. Discount Formula
Discount = MP − SP
4. Discount Percentage
Discount% = (Discount / MP) × 100
Successive Discount Formula
If two successive discounts are x% and y%:
Net Discount = x + y − (xy/100)
False Weight Concept
Sometimes traders use false weights while claiming no profit.
In such cases:
Gain% = [Error / (True Value − Error)] × 100
Equal Gain and Loss Percentage Concept
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%
Important Formula Summary
| Concept | Formula |
|---|---|
| Profit | SP − CP |
| Loss | CP − SP |
| Profit% | (Profit/CP) × 100 |
| Loss% | (Loss/CP) × 100 |
| SP with Profit | CP × (100 + Profit%)/100 |
| SP with Loss | CP × (100 − Loss%)/100 |
| CP with Profit | SP × 100/(100 + Profit%) |
| CP with Loss | SP × 100/(100 − Loss%) |
| Net Discount | x + y − xy/100 |
| Equal Gain-Loss | x²/100 loss |
Common Mistakes in Profit & Loss
- Calculating profit percentage on SP instead of CP.
- Ignoring overhead charges.
- Using incorrect discount formulas.
- Confusing marked price with selling price.
- Mistakes in successive discount calculations.
Important Exam Tips
- Always calculate profit and loss on CP.
- Memorize basic profit-loss formulas.
- Use percentage conversion shortcuts.
- Practice discount and marked price problems regularly.
- Use approximation methods in MCQs.
- Remember equal gain-loss shortcut formula.
- Verify calculations carefully in percentage questions.
Profit & Loss is one of the most fundamental arithmetic topics in Quantitative Aptitude. Strong understanding of formulas, discount concepts, and percentage applications helps candidates solve competitive exam questions quickly and accurately.