Previous-year Profit and Loss questions often repeat a limited set of structures even when the wording changes. The fastest preparation strategy is not to memorise individual questions, but to recognise the recurring pattern behind them: direct profit or loss, reverse cost-price calculation, marked price with discount, ratio conversion, successive percentage change, same-selling-price comparison and mixed objective traps.
This guide studies those recurring SSC- and Railway-style patterns without attaching an unverified year or shift to any question. Use it as a pattern-recognition and revision chapter, then practise with verified question sets where official or reliably sourced attribution is available.
1. Previous-Year Pattern 1: Direct Profit
A common form gives CP and profit% and asks for SP.
SP = CP × (100 + profit%) ÷ 100
Example: CP = ₹800, profit = 25%.
SP = 800 × 125/100 = ₹1,000.
2. Previous-Year Pattern 2: Direct Loss
If CP and loss% are given:
SP = CP × (100 − loss%) ÷ 100
Example: CP = ₹700, loss = 20%.
SP = 700 × 80/100 = ₹560.
3. Previous-Year Pattern 3: Reverse CP from Profit SP
Example: SP = ₹880 at 10% profit.
₹880 is 110% of CP.
CP = 880 × 100/110 = ₹800.
4. Previous-Year Pattern 4: Reverse CP from Loss SP
Example: SP = ₹600 at 25% loss.
SP is 75% of CP.
CP = 600 × 100/75 = ₹800.
5. Previous-Year Pattern 5: Ratio-Based Option Solving
Percentage-to-ratio conversion is useful when objective options are close.
- 20% profit → SP:CP = 120:100 = 6:5
- 20% loss → SP:CP = 80:100 = 4:5
- 25% profit → SP:CP = 125:100 = 5:4
- 25% loss → SP:CP = 75:100 = 3:4
For speed techniques, see Profit and Loss Tricks for Faster Solving.
6. Previous-Year Pattern 6: Marked Price and Single Discount
Example: MP = ₹1,250 and SP = ₹1,000.
Discount = ₹250.
Discount% = 250/1,250 × 100 = 20%.
For deeper MP-SP problems, use Discount and Marked Price Questions.
7. Previous-Year Pattern 7: Discount Plus Profit
Example: An article marked at ₹1,500 is sold at 20% discount and the seller still earns 20% profit.
SP = 1,500 × 80/100 = ₹1,200.
₹1,200 is 120% of CP.
CP = 1,200 × 100/120 = ₹1,000.
8. Previous-Year Pattern 8: Successive Discounts
Two successive discounts must be applied one after another.
Example: 10% and 20% discounts.
Effective discount = 10 + 20 − (10×20/100) = 28%.
If MP = ₹2,000, SP = 2,000 × 0.90 × 0.80 = ₹1,440.
Changing-base logic is covered in Successive Profit and Loss Changes.
9. Previous-Year Pattern 9: Markup Followed by Discount
Example: MP is 25% above CP and then a 10% discount is given.
Take CP = 100.
MP = 125 and SP = 125 × 0.90 = 112.5.
Profit = 12.5%.
10. Previous-Year Pattern 10: Same Selling Price
Two articles are sold at the same SP of ₹1,200. One is sold at 20% profit and the other at 20% loss.
First CP = 1,200 × 100/120 = ₹1,000.
Second CP = 1,200 × 100/80 = ₹1,500.
Total CP = ₹2,500; total SP = ₹2,400.
Net loss = ₹100, so loss% = 4%.
11. Previous-Year Pattern 11: Equal Gain and Loss Do Not Cancel
A familiar trap is to assume +20% and −20% cancel. They do not when applied successively to a changing base.
100 → 120 → 96.
Net result = 4% loss.
12. Previous-Year Pattern 12: More Than / Less Than Reverse Base
If A is 25% more than B, take B = 100 and A = 125.
Then B is 25/125 × 100 = 20% less than A.
The reverse percentage changes because the base changes.
13. Previous-Year Pattern 13: Required MP for Target Profit
Example: CP = ₹900. The seller wants 20% profit after giving 10% discount.
Required SP = 900 × 120/100 = ₹1,080.
₹1,080 is 90% of MP.
MP = 1,080 × 100/90 = ₹1,200.
14. Previous-Year Pattern 14: Hidden Word-Problem Translation
Previous-year style questions often hide CP, SP and MP inside ordinary language such as “bought for”, “sold for”, “marked at”, “after discount” or “still gains”.
The safe translation flow is:
Words → Symbols → Base → Formula → Answer
For dedicated translation practice, see Profit and Loss Word Problems.
15. Previous-Year Pattern 15: Quantity and Short-Weight Awareness
Some objective questions change quantity instead of price. If a trader charges for 1 kg but gives 900 g, the customer receives only 90% of the stated quantity.
Translate such questions into effective quantity or effective cost before applying profit percentage.
16. Option-Elimination Technique
In objective questions, exact calculation is not always necessary.
- If there is profit, SP must normally be above CP.
- If there is loss, SP must normally be below CP.
- After discount, SP should normally be below MP.
- Two positive increases must produce a final value above the original.
- A 20% loss followed by a 20% gain cannot return exactly to the original.
These direction checks can eliminate impossible options quickly.
17. Common Previous-Year Pattern Traps
- Using SP as the base for ordinary profit% or loss%.
- Using CP as the base for discount%.
- Adding successive percentages directly.
- Reversing profit/loss percentages by simple subtraction.
- Assuming equal gain and loss always cancel.
- Confusing markup with actual profit.
- Ignoring whether a value is per-unit or total.
For a full error guide, read Common Profit and Loss Mistakes.
18. Mixed Previous-Year-Style Practice
- CP = ₹640, SP = ₹800. Find profit%.
- SP = ₹720 at 20% profit. Find CP.
- MP = ₹1,500 and discount = 12%. Find SP.
- Find the effective discount for 20% and 25% successive discounts.
- At 25% loss, write SP:CP.
- CP = ₹1,000, markup = 25%, discount = 10%. Find profit%.
- SP = ₹680 at 15% loss. Find CP.
- MP = ₹2,400, SP = ₹2,040. Find discount%.
Answers: (1) 25%; (2) ₹600; (3) ₹1,320; (4) 40%; (5) 3:4; (6) 12.5%; (7) ₹800; (8) 15%.
19. Exam-Speed Decision Path
- Direct CP→SP → multiplier.
- Reverse SP→CP → reverse percentage or ratio.
- Clean percentage → ratio.
- Two discounts → effective-discount formula.
- Three or more changes → multipliers.
- Mixed wording → translate first.
- Close objective options → ratio or elimination may be faster.
Formula revision is available in Profit and Loss Formulas for Exams.
20. Next Step
Return to the Profit and Loss Master Guide for the complete chapter map.
Then practise these recurring patterns in Exam-Based Profit and Loss Questions and Profit and Loss Practice Set 1.