Profit and Loss – Complete Notes for Competitive Exams
Profit and Loss is one of the most important arithmetic topics for competitive examinations. Questions from this chapter are commonly based on buying price, selling price, marked price, discount, profit percentage, loss percentage and successive discounts.
The chapter becomes much easier when you clearly understand the difference between Cost Price, Selling Price and Marked Price. Once the base quantity is identified correctly, most Profit and Loss questions can be solved using a small set of formulas.
These notes are written from scratch for ExamMitra learners preparing for SSC, Railway, Banking, Assam competitive examinations and other objective-type examinations.
Table of Contents
- 1. What is Profit and Loss?
- 2. Important Terms
- 3. Cost Price
- 4. Selling Price
- 5. Marked Price
- 6. Profit
- 7. Loss
- 8. Profit Percentage
- 9. Loss Percentage
- 10. Finding Selling Price at Profit
- 11. Finding Selling Price at Loss
- 12. Finding Cost Price from Profit
- 13. Finding Cost Price from Loss
- 14. Discount
- 15. Discount Percentage
- 16. Marked Price and Selling Price
- 17. Successive Discounts
- 18. Profit After Discount
- 19. False Weight and Dishonest Dealer
- 20. Overhead Expenses
- 21. Same Selling Price Cases
- 22. Same Cost Price Cases
- 23. Reverse Profit and Loss Problems
- 24. Comparison-Based Questions
- 25. Important Shortcuts
- 26. Complete Formula Sheet
- 27. Solved Examples
- 28. Common Mistakes
- 29. Quick Revision
- 30. Preparation Strategy
- 31. Frequently Asked Questions
1. What is Profit and Loss?
Profit and Loss deals with the financial result obtained when an article is purchased and later sold.
If an article is sold for more than its cost, there is a profit. If it is sold for less than its cost, there is a loss.
An article is purchased for Rs. 500 and sold for Rs. 650.
Profit = 650 - 500
= Rs. 150
An article is purchased for Rs. 800 and sold for Rs. 700.
Loss = 800 - 700
= Rs. 100
2. Important Terms
| Term | Meaning |
|---|---|
| CP | Cost Price – price paid to acquire the article |
| SP | Selling Price – price at which the article is sold |
| MP | Marked Price – price displayed or quoted before discount |
| Profit | Amount by which SP exceeds CP |
| Loss | Amount by which CP exceeds SP |
| Discount | Reduction from the marked price |
3. Cost Price
Cost Price, usually written as CP, is the amount actually spent to acquire an article.
If additional expenses are directly associated with purchasing or preparing the article for sale, they may also be included when determining the effective cost.
An item is bought for Rs. 1,000 and Rs. 100 is spent on transportation.
Effective cost = 1,000 + 100
= Rs. 1,100
4. Selling Price
Selling Price, written as SP, is the amount received when an article is sold.
If an article is sold for Rs. 1,250, then:
SP = Rs. 1,250
5. Marked Price
Marked Price, or MP, is the price displayed by the seller before applying a discount.
An article has a marked price of Rs. 2,000 and is sold after a discount.
MP = Rs. 2,000
6. Profit
Profit occurs when the Selling Price is greater than the Cost Price.
CP = Rs. 900 and SP = Rs. 1,080.
Profit = 1,080 - 900
= Rs. 180
7. Loss
Loss occurs when the Selling Price is less than the Cost Price.
CP = Rs. 1,200 and SP = Rs. 1,020.
Loss = 1,200 - 1,020
= Rs. 180
8. Profit Percentage
Profit percentage is calculated using Cost Price as the base.
CP = Rs. 800 and SP = Rs. 920.
Profit = 920 - 800 = 120
Profit% = 120/800 × 100
= 15%
9. Loss Percentage
CP = Rs. 1,000 and SP = Rs. 850.
Loss = 1,000 - 850 = 150
Loss% = 150/1,000 × 100
= 15%
10. Finding Selling Price at Profit
If the cost price and desired profit percentage are known:
An article costs Rs. 1,200. It is sold at a profit of 25%.
SP = 1,200 × 125/100
= Rs. 1,500
11. Finding Selling Price at Loss
An article costs Rs. 2,000 and is sold at a loss of 15%.
SP = 2,000 × 85/100
= Rs. 1,700
12. Finding Cost Price from Profit
If the Selling Price and profit percentage are known:
An article is sold for Rs. 1,380 at a profit of 15%. Find the Cost Price.
CP = 1,380 × 100/115
= Rs. 1,200
13. Finding Cost Price from Loss
An article is sold for Rs. 1,020 at a loss of 15%. Find CP.
CP = 1,020 × 100/85
= Rs. 1,200
14. Discount
Discount is the reduction offered from the marked price of an article.
MP = Rs. 2,500 and SP = Rs. 2,000.
Discount = 2,500 - 2,000
= Rs. 500
15. Discount Percentage
Discount percentage is calculated on the Marked Price.
MP = Rs. 3,000 and SP = Rs. 2,550.
Discount = 3,000 - 2,550 = 450
Discount% = 450/3,000 × 100
= 15%
16. Marked Price and Selling Price
If the marked price and discount percentage are known:
MP = Rs. 4,000 and discount = 20%.
SP = 4,000 × 80/100
= Rs. 3,200
Finding Marked Price
An article is sold for Rs. 1,700 after a discount of 15%.
MP = 1,700 × 100/85
= Rs. 2,000
17. Successive Discounts
When two or more discounts are offered one after another, they should not simply be added.
Discounts of 20% and 10% are offered successively.
Equivalent discount = 20 + 10 - (20 × 10)/100
= 30 - 2
= 28%
Three Successive Discounts
For three discounts, it is usually easiest to apply them one after another.
An article marked at Rs. 10,000 receives discounts of 10%, 20% and 5%.
After 10%: 10,000 × 90/100 = 9,000
After 20%: 9,000 × 80/100 = 7,200
After 5%: 7,200 × 95/100 = 6,840
18. Profit After Discount
An article can be marked above its cost price and then sold after giving a discount. Such questions require you to connect MP, discount and CP.
An article costs Rs. 1,000. It is marked at Rs. 1,500 and sold after a 10% discount. Find the profit percentage.
Discount = 10% of 1,500 = 150
SP = 1,500 - 150 = 1,350
Profit = 1,350 - 1,000 = 350
Profit% = 350/1,000 × 100
= 35%
Direct Relationship
If the marked price is p% above the cost price and a discount of d% is given, then:
Suppose MP is 25% above CP and a 10% discount is given.
Taking CP = 100:
MP = 125
SP = 125 × 90/100 = 112.5
Profit = 12.5
Therefore profit = 12.5%
19. False Weight and Dishonest Dealer
Some competitive-exam questions describe a dealer who sells goods at the stated price but uses a weight smaller than the stated quantity.
A shopkeeper claims to sell 1 kg but actually gives 800 g while charging the price of 1 kg.
Suppose the cost of 1 kg is Rs. 100.
Cost of 800 g = Rs. 80.
Revenue received = Rs. 100.
Profit = 100 - 80 = Rs. 20.
Profit% = 20/80 × 100
= 25%
The exact setup depends on what quantity the question treats as the cost basis, so read the wording carefully.
20. Overhead Expenses
Expenses such as transportation, packaging, repair, labour or other direct costs may need to be added to the purchase price when determining the effective cost.
Purchase price = Rs. 5,000
Transportation = Rs. 300
Repair = Rs. 200
Effective CP = 5,000 + 300 + 200
= Rs. 5,500
21. Same Selling Price Cases
A common question involves two articles sold for the same Selling Price, with one producing a profit and the other producing a loss.
Two articles are sold for Rs. 1,200 each. One gives a profit of 20% and the other gives a loss of 20%.
CP of first article:
= 1,200 × 100/120 = 1,000
CP of second article:
= 1,200 × 100/80 = 1,500
Total CP = 2,500
Total SP = 2,400
Loss = 100
Loss% = 100/2,500 × 100 = 4%
22. Same Cost Price Cases
If two articles have the same Cost Price and are sold at different profit or loss percentages, calculate their Selling Prices separately.
Two articles each cost Rs. 1,000. One is sold at 20% profit and the other at 10% loss.
First SP = 1,000 × 120/100 = 1,200
Second SP = 1,000 × 90/100 = 900
Total CP = 2,000
Total SP = 2,100
Overall profit = 100
Profit% = 5%
23. Reverse Profit and Loss Problems
Reverse questions provide the Selling Price and the profit or loss percentage and ask you to find the Cost Price.
An article is sold for Rs. 1,440 at a profit of 20%.
CP = 1,440 × 100/120
= Rs. 1,200
An article is sold for Rs. 1,020 at a loss of 15%.
CP = 1,020 × 100/85
= Rs. 1,200
24. Comparison-Based Questions
Some questions compare two selling prices, two cost prices or two profit percentages.
A seller earns 25% profit by selling an article for Rs. 1,000. At what price should it be sold to earn 40% profit?
First find CP:
CP = 1,000 × 100/125 = 800
Required SP = 800 × 140/100
= Rs. 1,120
25. Important Shortcuts
Shortcut 1: Profit as a Percentage of CP
Example: At 30% profit, if CP is assumed to be 100, SP becomes 130.
Shortcut 2: Loss as a Percentage of CP
Shortcut 3: Profit Percentage to SP:CP Ratio
If profit is p%, then:
Profit = 25%.
SP : CP = 125 : 100 = 5 : 4
Shortcut 4: Loss Percentage to SP:CP Ratio
Loss = 20%.
SP : CP = 80 : 100 = 4 : 5
Shortcut 5: Profit from SP:CP Ratio
SP : CP = 6 : 5.
Profit% = (6 - 5)/5 × 100
= 20%
Shortcut 6: Loss from SP:CP Ratio
SP : CP = 7 : 10.
Loss% = (10 - 7)/10 × 100
= 30%
26. Complete Formula Sheet
27. Solved Examples
An article is bought for Rs. 600 and sold for Rs. 750. Find the profit.
Profit = 750 - 600
= Rs. 150
An article costs Rs. 900 and is sold for Rs. 765. Find the loss percentage.
Loss = 900 - 765 = 135
Loss% = 135/900 × 100
= 15%
An article costing Rs. 1,500 is sold at a profit of 20%. Find SP.
SP = 1,500 × 120/100
= Rs. 1,800
An article costing Rs. 2,000 is sold at a loss of 12%. Find SP.
SP = 2,000 × 88/100
= Rs. 1,760
An article is sold for Rs. 1,500 at a profit of 25%. Find CP.
CP = 1,500 × 100/125
= Rs. 1,200
An article is sold for Rs. 1,360 at a loss of 15%. Find CP.
CP = 1,360 × 100/85
= Rs. 1,600
A shirt marked at Rs. 2,500 is sold at a discount of 12%. Find SP.
SP = 2,500 × 88/100
= Rs. 2,200
An article marked at Rs. 3,000 is sold for Rs. 2,400. Find the discount percentage.
Discount = 3,000 - 2,400 = 600
Discount% = 600/3,000 × 100
= 20%
A product receives successive discounts of 10% and 20%. Find the equivalent discount.
= 10 + 20 - 10 × 20/100
= 30 - 2
= 28%
A shopkeeper buys an article for Rs. 800, marks it at Rs. 1,200 and gives a discount of 10%. Find the profit percentage.
SP = 1,200 × 90/100 = 1,080
Profit = 1,080 - 800 = 280
Profit% = 280/800 × 100
= 35%
Two articles are sold for Rs. 1,000 each. One gives a 20% profit and the other a 20% loss. Find the overall result.
CP of first = 1,000 × 100/120 = 833.33...
CP of second = 1,000 × 100/80 = 1,250
Total CP = 2,083.33...
Total SP = 2,000
Overall loss percentage = 4%
A trader sells an article at 30% profit. If the Cost Price is Rs. 700, find the Selling Price.
SP = 700 × 130/100
= Rs. 910
A trader wants a profit of 25% after giving a discount of 20%. If the Cost Price is Rs. 1,000, find the required Marked Price.
Required SP = 1,000 × 125/100 = 1,250
Since SP is 80% of MP:
MP = 1,250 × 100/80
= Rs. 1,562.50
An article is sold at a 10% loss. If its Cost Price is Rs. 1,500, find the loss amount.
Loss = 10/100 × 1,500
= Rs. 150
A product is sold at 20% profit instead of 10% profit. If its Cost Price is Rs. 900, how much additional money is earned?
Difference in profit = 10% of 900
= Rs. 90
28. Common Mistakes
Mistake 1: Using SP as the Base for Profit Percentage
Standard profit percentage is calculated using Cost Price as the base.
Mistake 2: Using CP as the Base for Discount
Discount percentage is calculated on Marked Price.
Mistake 3: Adding Successive Discounts
A 20% discount followed by a 10% discount is not a 30% discount. The equivalent discount is 28%.
Mistake 4: Ignoring Additional Expenses
If the question includes transportation, repair, packaging or similar expenses as part of the effective cost, include them before calculating profit or loss.
Mistake 5: Confusing Marked Price and Cost Price
The marked price is not automatically the Cost Price. The seller may mark an article above its cost and then offer a discount.
Mistake 6: Ignoring the Wording of the Question
Words such as "profit on CP", "discount on MP", "sold at a loss", and "marked above CP" determine which formula should be used.
29. Quick Revision
Profit/Loss percentage → Cost Price
Discount percentage → Marked Price
Percentage comparison → The quantity specified as the reference
30. Preparation Strategy
Step 1: Master CP, SP and MP
Do not start with shortcuts. First understand exactly what each price represents.
Step 2: Learn Profit and Loss Formulas
Practise direct profit, loss, profit percentage and loss percentage questions until the relationships become automatic.
Step 3: Practise Discount
Learn how marked price, discount and selling price are connected.
Step 4: Move to Mixed Problems
Practise questions combining marked price, discount and profit.
Step 5: Learn Ratio Methods
The ratio approach can make many profit and loss questions faster, especially when only percentages are given.
Step 6: Practise Timed Questions
Once your accuracy is strong, solve mixed Profit and Loss questions under a time limit.
31. Frequently Asked Questions
What is Cost Price?
Cost Price is the amount paid to acquire an article. Additional expenses may also form part of the effective cost when specified in the question.
What is Selling Price?
Selling Price is the amount for which an article is sold.
What is Marked Price?
Marked Price is the price displayed or quoted by the seller before a discount is applied.
On what value is profit percentage calculated?
Standard profit percentage is calculated on Cost Price.
On what value is discount percentage calculated?
Discount percentage is calculated on Marked Price.
Is a 20% profit and 20% loss on two articles equal overall?
Not when the two articles are sold for the same Selling Price. In that particular case, the combined result is a loss of 4%.
Are successive discounts added directly?
No. Each later discount is applied to the price remaining after the previous discount.
How can I solve Profit and Loss questions faster?
Build a strong understanding of CP, SP and MP, remember the core formulas, practise percentage-to-ratio conversions and use a convenient base such as 100 when actual values are not required.
Is Profit and Loss important for competitive exams?
Yes. It is a fundamental arithmetic chapter and is also connected with discount, percentage, ratio and other commercial arithmetic questions.
Final Revision Advice
Profit and Loss becomes much easier when you keep the three main prices separate: Cost Price, Selling Price and Marked Price. Most questions can then be reduced to a simple percentage or ratio calculation.
Remember that profit and loss percentages normally use Cost Price as their base, while discount percentage uses Marked Price. This distinction is one of the most important ideas in the chapter.
Start with direct formula-based questions and gradually move to discount, successive discount, false-weight, overhead-expense and mixed application problems. With regular practice, Profit and Loss can become one of the faster-scoring arithmetic topics in competitive examinations.
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