Profit & Loss — shortcuts that build on real formulas, not guesses
Almost every profit-and-loss question reduces to the relationship between cost price (CP), selling price (SP), and marked price (MP). Once that relationship is automatic, the 'shortcuts' below are just faster arithmetic paths to the same answer.
The core relationship
Profit % = (SP − CP)/CP × 100. Loss % = (CP − SP)/CP × 100. Everything else in profit-and-loss questions is a rearrangement of this — if you know any two of CP, SP, and profit%, you can find the third.
Marked price and discount are not profit/loss directly
Discount is calculated on the marked price, but profit/loss is calculated on the cost price. A shopkeeper can offer a discount on MP and still make a profit relative to CP — these are two separate base values, and mixing them up is the single most common exam error.
Successive discounts use the same formula as successive percentage change
Two successive discounts of a% and b% combine to a single effective discount of a + b − (ab/100), not a simple sum — the same logic covered on the percentage shortcuts page, since a discount is really just a percentage decrease applied to a changing base value.
Examples
- CP = ₹800, SP = ₹920: Profit% = (920−800)/800 × 100 = 15%.
- Marked price ₹1000, two successive discounts of 10% and 10%: effective discount = 10+10−1 = 19%, so final price = ₹810, not ₹800.
- A trader marks goods 40% above cost, then gives a 20% discount: net profit% = 40 − 20 − (40×20)/100 = 12%.
Common mistakes
- Calculating profit/loss percentage on selling price instead of cost price.
- Treating marked-price discount and cost-price profit as the same base value.
- Adding two successive discounts directly instead of using the combined-discount formula.
Try it yourself
A shopkeeper buys an item for ₹500 and sells it at a 20% loss. What is the selling price?
Show answer
₹400 — Loss% = (CP−SP)/CP × 100, so SP = CP × (1 − 0.20) = 500 × 0.8 = ₹400.
Frequently asked questions
Is this the same logic used in banking and SSC exams?
Yes — profit and loss formulas are identical across exams; only word-problem complexity changes.
Can Learn2Plus AI show the working, not just the answer?
Yes — every solved example includes the full working, and you can ask for a slower step-by-step walkthrough at any point.
What if I confuse CP and SP in a specific question?
Ask Learn2Plus AI to identify CP, SP, and MP in that exact question first — separating the identification step from the calculation step fixes most errors.
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