Profit and Loss
About 6 min · Mathematics · English
Time worked out from the lesson's 422 words at 150 words a minute, plus a minute for each question.
The topic revolves around commercial transactions: buying goods at a Cost Price (CP), selling them at a Selling Price (SP), and calculating the profit or loss. You'll also encounter Marked Price (MP) and discount scenarios where shopkeepers mark prices higher than CP and then offer discounts to attract buyers.
Key ideas
- Cost Price (CP): The amount paid to acquire or produce a good. This is your baseline for profit or loss calculations.
- Selling Price (SP): The amount received when the good is sold. If SP > CP, there's a profit; if SP < CP, there's a loss.
- Profit: Profit = SP − CP. Always expressed as a positive number. Profit% = (Profit / CP) × 100.
- Loss: Loss = CP − SP. Loss% = (Loss / CP) × 100. Note the percentage is always calculated on CP, not SP, unless stated otherwise.
- Marked Price (MP): The price tag on an item before any discount. Shopkeepers mark goods above CP to absorb discount and still earn profit.
Watch out for
- Calculating percentage on SP instead of CP for profit/loss: Always remember profit% and loss% are based on Cost Price unless explicitly stated otherwise. Students often compute (SP − CP)/SP, which is incorrect.
- Adding successive discounts directly: If discounts are 10% and 20%, the net discount is not 30%. Use the formula d₁ + d₂ − (d₁ × d₂)/100. Direct addition underestimates the selling price.
- Confusing MP with CP: When a question states "marked 30% above cost price," students sometimes apply discount on CP instead of MP. Always: CP → calculate MP → apply discount → get SP.
Quick reference
- Profit = SP − CP; Loss = CP − SP. Base percentages on CP.
- SP = CP × (100 ± Profit or Loss %) / 100. Use + for profit, − for loss.
- Discount is always on Marked Price (MP), not on CP or SP.
- Successive discounts d₁% and d₂%: Net% = d₁ + d₂ − d₁×d₂/100.
- To find CP from SP and profit%: CP = SP × 100 / (100 + Profit%).
Check yourself: 3 questions
1. A shopkeeper bought a watch for Rs. 800 and sold it for Rs. 920. What is his profit percentage?
2. A trader marks his goods 40% above the cost price and allows a discount of 20%. What is his profit percentage?
3. A fruit seller sells apples at a loss of 10%. If he had sold them for Rs. 60 more, he would have gained 5%. What was the cost price of the apples?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
Read the full noteFlashcards for this topic
Saves this lesson and its 3 questions in this browser on this phone. No sign-in; nothing about you is saved or sent. A saved copy is not updated until you save it again. Parts that load from the server when you use them (the AI tutor, adaptive practice, sign-in) still need a connection.