Profit and Loss is a high-frequency arithmetic topic in SSC, Banking and Railway exams. The chapter is not difficult because of formulas alone; the real challenge is identifying the correct base, connecting Cost Price (CP), Selling Price (SP) and Marked Price (MP), and choosing a short calculation path when discount or successive percentage changes are involved.
This master guide builds that complete framework. Learn the core logic here, then use the linked topic guides for deeper formula practice, shortcuts, mistakes, word problems, exam patterns and timed practice.
1. Understand CP, SP, MP, Profit, Loss and Discount
Every Profit and Loss question starts with a few basic quantities. Cost Price (CP) is the amount paid to acquire an item. Selling Price (SP) is the amount received when it is sold. Marked Price (MP) is the displayed or listed price before discount.
- If SP > CP, there is a profit.
- If SP < CP, there is a loss.
- If SP = CP, there is neither profit nor loss.
- Discount is normally measured against Marked Price, while profit or loss percentage is normally measured against Cost Price.
This difference in the base is one of the most important ideas in the chapter. For a foundation-first explanation, study Profit and Loss Basics.
2. Essential Profit and Loss Formulas
- Profit = SP − CP
- Loss = CP − SP
- Profit% = (Profit ÷ CP) × 100
- Loss% = (Loss ÷ CP) × 100
- SP at p% profit = CP × (100 + p) ÷ 100
- SP at p% loss = CP × (100 − p) ÷ 100
- CP when SP and profit% are known = SP × 100 ÷ (100 + p)
- CP when SP and loss% are known = SP × 100 ÷ (100 − p)
The denominator matters. Unless a question explicitly changes the reference quantity, profit% and loss% use CP as the base. Keep the complete formula set together in Profit and Loss Formulas for Exams.
3. Direct Questions: Find SP from CP
When CP and profit or loss percentage are given, the multiplier method is usually faster than calculating the profit or loss separately.
Example: An article costs ₹800 and is sold at a profit of 25%. Since 125% of CP is received, SP = 800 × 1.25 = ₹1,000.
If the same article were sold at a 15% loss, SP would be 85% of CP: 800 × 0.85 = ₹680.
The mental model is simple: profit moves SP above 100% of CP; loss moves SP below 100% of CP.
4. Reverse Questions: Find CP from SP
Reverse questions cause mistakes because students sometimes subtract the given percentage directly from SP. Instead, first identify what percentage of CP the final SP represents.
Example: An item is sold for ₹720 at a 20% profit. SP is 120% of CP, so CP = 720 × 100 ÷ 120 = ₹600.
Example: An item is sold for ₹680 at a 15% loss. SP is 85% of CP, so CP = 680 × 100 ÷ 85 = ₹800.
Whenever the final value is known, think in terms of a reverse multiplier rather than reversing the percentage by subtraction.
5. Marked Price and Discount
Discount questions introduce another base. Discount percentage is calculated on MP, not on CP. If an item marked at ₹2,000 receives a 15% discount, the customer pays 85% of MP: SP = 2,000 × 0.85 = ₹1,700.
If CP is also given, first calculate the discounted SP and then compare SP with CP to determine profit or loss. This two-stage structure is common in exams.
For deeper combinations of marked price, discount and profit margin, continue to Discount and Marked Price Questions.
6. Successive Discounts and Percentage Changes
Two successive percentage changes should not normally be added. A 10% discount followed by a 20% discount means the price is multiplied by 0.90 and then by 0.80.
Example: MP = ₹1,000. After successive discounts of 10% and 20%, SP = 1,000 × 0.90 × 0.80 = ₹720. The effective discount is 28%, not 30%.
For two successive changes of a% and b%, the multiplier method is the safest general approach. The shortcut a + b + ab/100 can also be used when increases are treated as positive and decreases as negative.
Practice this logic separately in Successive Profit and Loss Changes.
7. Ratio and Multiplier Method for Faster Solving
Many exam questions become shorter when percentages are converted into ratios. A 20% profit means SP:CP = 120:100 = 6:5. A 25% loss means SP:CP = 75:100 = 3:4.
If a question says that SP at 20% profit is ₹600, the ratio 6:5 immediately gives CP = ₹500. This avoids writing a full percentage equation.
Ratio thinking is especially useful when two selling prices, two profit rates, or a change in profit condition must be compared. More speed-oriented patterns are covered in Profit and Loss Tricks for Faster Solving.
8. When Profit, Loss and Discount Appear Together
Do not mix the bases. Discount connects MP to SP, while profit or loss connects CP to SP. Build the chain in the correct order:
MP → apply discount → SP → compare with CP → profit or loss.
Example: MP = ₹1,500 and discount = 20%, so SP = ₹1,200. If CP = ₹1,000, profit = ₹200 and profit% = 20%.
The same SP can therefore represent both a discount from MP and a profit over CP. These are not contradictory because their reference values are different.
9. Common Profit and Loss Traps
- Wrong denominator: using SP instead of CP for ordinary profit% or loss%.
- Adding successive percentages: forgetting that the base changes after the first change.
- Confusing discount with loss: discount is measured from MP; loss is measured from CP.
- Reversing percentages directly: a 20% profit cannot be reversed by simply subtracting 20% from SP.
- Ignoring units or quantities: some word problems change the number of items, weight or effective cost.
- Using a shortcut without checking its condition: a memorised formula is useful only when its assumptions match the question.
Review these patterns in detail in Common Profit and Loss Mistakes.
10. Worked Example: Required Marked Price
A shopkeeper buys an item for ₹800. He wants a 20% profit after giving a 20% discount. Find the required marked price.
Required SP for 20% profit = 800 × 1.20 = ₹960. After a 20% discount, SP is 80% of MP. Therefore MP = 960 × 100 ÷ 80 = ₹1,200.
The key is to work from the required profit first, because profit fixes the required SP. Then reverse the discount to obtain MP.
11. Worked Example: Same Selling Price, Profit and Loss
Suppose two articles are sold for the same selling price. One is sold at a profit and the other at a loss. Do not assume the two percentages cancel. Their cost prices can be different, so the overall result depends on the actual values or the precise conditions given.
This is a classic example of why percentage questions should be solved from their bases rather than from surface wording alone.
12. Word-Problem Translation Strategy
Before calculating, convert the statement into CP, SP, MP, profit, loss and discount relationships. Words such as “bought for,” “sold for,” “marked at,” “discounted by,” and “gains” tell you which quantity is being described.
For multi-line questions, write the base first and then the percentage relation. This prevents the arithmetic from starting before the problem structure is understood. Apply this method to Profit and Loss Word Problems.
13. Exam-Speed Decision Path
- If CP and profit/loss% are given, use an SP multiplier.
- If SP and profit/loss% are given, reverse the multiplier to find CP.
- If MP and discount% are given, calculate SP first.
- If two percentage changes occur, use successive multipliers.
- If the percentage converts to a clean ratio, consider ratio solving.
- If the question feels confusing, identify the base before touching the numbers.
The fastest method is not always the shortest-looking formula. It is the method that keeps the base clear and reduces calculation risk.
14. Exam Question Patterns to Recognise
Competitive exams repeatedly test direct profit/loss, reverse CP, marked-price discount, successive discount, required MP for a target profit, comparison of two transactions and mixed word problems. Learning the pattern helps you decide the method before performing arithmetic.
Use Exam-Based Profit and Loss Questions for application-focused practice. For recurring historical styles, study Previous Year Profit and Loss Patterns.
15. Quick Revision Checklist
- Can you identify CP, SP and MP immediately?
- Do you remember which base is used for profit, loss and discount?
- Can you convert common percentages into multipliers or ratios?
- Can you reverse a profit or loss condition to recover CP?
- Can you handle two successive percentage changes without adding them blindly?
- Can you separate discount from actual profit or loss?
If any answer is uncertain, revise that concept before attempting a timed set.
16. Practice Ladder
Start with five direct CP-SP questions, then five reverse questions, followed by discount and successive-change problems. After accuracy becomes stable, mix the types so that the method is not revealed by the section heading.
Use Profit and Loss Practice Set 1 as the first mixed checkpoint. Record whether each error came from concept selection, base selection, formula recall or arithmetic. That error label tells you what to revise next.
17. Profit and Loss Learning Path
Use this pillar as the map rather than reading every cluster in one sitting. Choose the next step according to the skill you need to strengthen:
- Foundation: start with Profit and Loss Basics if CP, SP, MP or the percentage base is still unclear.
- Formula and speed revision: use Profit and Loss Formulas for Exams when formula recall is the main weakness.
- Discount and changing-base questions: move to Discount and Marked Price Questions for MP-SP combinations.
- Error repair: review Common Profit and Loss Mistakes when repeated base, reverse-percentage or shortcut errors appear.
- Mixed exam practice: finish with Profit and Loss Practice Set 1 to test whether the concepts work together under mixed conditions.
The other specialist guides are linked exactly where their concepts are taught above. After practice, return to the weak layer that caused the error instead of rereading the complete chapter.