Exam-based Profit and Loss questions become faster when you recognise the pattern before choosing a formula. SSC, Banking and Railway questions often repeat the same structures: direct CP-SP conversion, reverse percentage, marked price with discount, successive changes, same selling price, target profit and mixed ratio-percentage problems.
This guide is designed as a pattern-recognition chapter. Instead of memorising more formulas, learn to identify what the examiner is actually asking and which representation—formula, ratio, multiplier or base-100—will solve it most efficiently.
1. Pattern 1: CP Given, Find SP
If CP and profit% are given:
SP = CP × (100 + profit%) ÷ 100
Example: CP = ₹800 and profit = 25%.
SP = 800 × 125/100 = ₹1,000.
2. Pattern 2: CP Given, Find SP at Loss
If CP and loss% are given:
SP = CP × (100 − loss%) ÷ 100
Example: CP = ₹900 and loss = 20%.
SP = 900 × 80/100 = ₹720.
3. Pattern 3: SP Given, Find CP at Profit
Reverse questions require you to divide by the final percentage base.
Example: SP = ₹880 at 10% profit.
SP represents 110% of CP.
CP = 880 × 100/110 = ₹800.
4. Pattern 4: SP Given, Find CP at Loss
Example: SP = ₹680 at 15% loss.
SP represents 85% of CP.
CP = 680 × 100/85 = ₹800.
5. Pattern 5: Marked Price and Single Discount
If MP and discount% are given:
SP = MP × (100 − discount%) ÷ 100
Example: MP = ₹1,500 and discount = 20%.
SP = 1,500 × 80/100 = ₹1,200.
For deeper MP-SP questions, see Discount and Marked Price Questions.
6. Pattern 6: Successive Discounts
Two discounts should not be added directly.
For 10% and 20% discounts:
Effective discount = 10 + 20 − 2 = 28%.
On MP ₹1,500:
SP = 1,500 × 0.90 × 0.80 = ₹1,080.
For changing-base logic, use Successive Profit and Loss Changes.
7. Pattern 7: Markup Plus Discount
Example: MP is 25% above CP and a 10% discount is given.
Take CP = 100.
MP = 125 and SP = 125 × 0.90 = 112.5.
Therefore actual profit = 12.5%.
Markup and profit are not the same because discount changes the final SP.
8. Pattern 8: Target Profit After Discount
Example: CP = ₹800. The seller wants 20% profit after giving 20% discount.
Required SP = 800 × 120/100 = ₹960.
₹960 is 80% of MP.
MP = 960 × 100/80 = ₹1,200.
9. Pattern 9: Same SP on Two Articles
Two articles are sold for ₹1,200 each. One gives 20% profit and the other 20% loss.
First CP = 1,200 × 100/120 = ₹1,000.
Second CP = 1,200 × 100/80 = ₹1,500.
Total CP = ₹2,500 and total SP = ₹2,400.
Net loss = ₹100, so loss% = 4%.
10. Pattern 10: Equal Profit and Loss Percentages
Equal gain and loss percentages do not automatically cancel.
If the same percentage x applies to equal selling prices, the result can still be a net loss because the cost bases differ.
Always compare total CP with total SP instead of cancelling the percentages mentally.
11. Pattern 11: More Than / Less Than Reverse Percentage
If A is 25% more than B, take B = 100 and A = 125.
B is then 25/125 × 100 = 20% less than A.
This base-change pattern appears frequently in objective arithmetic.
12. Pattern 12: Ratio Conversion
At 20% profit:
SP:CP = 120:100 = 6:5
At 25% loss:
SP:CP = 75:100 = 3:4
Ratio form is often faster when the percentage converts cleanly.
For speed methods, use Profit and Loss Tricks for Faster Solving.
13. Pattern 13: Hidden Word-Problem Translation
Exam questions may hide CP, SP and MP inside language such as “bought for”, “sold for”, “marked at”, “after discount”, “still gains” or “sold at a loss”.
The safest sequence is:
Words → Symbols → Base → Formula → Answer
For dedicated translation practice, see Profit and Loss Word Problems.
14. Pattern 14: Quantity or Short-Weight Awareness
Some questions change quantity instead of price. If a trader charges for 1 kg but gives only 900 g, the effective quantity delivered is 90% of the stated amount.
Such questions must be translated into effective quantity or effective cost before applying profit percentage.
15. Exam Trap Checklist
- Profit/loss percentage normally uses CP as base.
- Discount percentage normally uses MP as base.
- Reverse percentage is not solved by simple subtraction.
- Successive percentages use changing bases.
- Equal gain and loss percentages do not always cancel.
- Markup is not the same as profit.
- Ratio must be written in the correct direction.
For a complete trap guide, read Common Profit and Loss Mistakes.
16. Mixed Objective Examples
Q1: CP = ₹600, profit = 20%. SP = ₹720.
Q2: SP = ₹900 at 25% profit. CP = ₹720.
Q3: MP = ₹2,000, discount = 15%. SP = ₹1,700.
Q4: 20% and 10% successive discounts give an effective discount of 28%.
Q5: CP = ₹1,000, markup = 25%, discount = 10%. Profit% = 12.5%.
17. Quick Exam Practice
- CP = ₹750, profit = 20%. Find SP.
- SP = ₹960 at 20% profit. Find CP.
- MP = ₹1,800, discount = 15%. Find SP.
- Find effective discount for 20% and 25% successive discounts.
- At 25% loss, write SP:CP.
- CP = ₹900. Find required MP for 20% profit after 10% discount.
Answers: (1) ₹900; (2) ₹800; (3) ₹1,530; (4) 40%; (5) 3:4; (6) ₹1,200.
18. Which Method Should You Choose in the Exam?
- Direct CP→SP → multiplier.
- Reverse SP→CP → reverse percentage or ratio.
- Clean percentage → ratio can be faster.
- Two discounts → effective-discount formula.
- Three or more changes → multipliers.
- Mixed wording → translate first, calculate second.
For formula revision, use Profit and Loss Formulas for Exams.
19. Next Step
Return to the Profit and Loss Master Guide for the complete chapter structure.
Then test these patterns in Profit and Loss Practice Set 1.