CP, SP, Profit & Loss Basics

🎯 Learning Objective

Identify CP and SP in any transaction and compute profit, loss and their percentages correctly.

💡 Concept

• CP (Cost Price) = price at which an article is bought
• SP (Selling Price) = price at which it is sold
• SP > CP → Profit = SP − CP; SP < CP → Loss = CP − SP
• Profit% = (Profit/CP) × 100; Loss% = (Loss/CP) × 100
• Profit% and Loss% are ALWAYS calculated on CP, never on SP (unless the question says so)

🧮 Key Formulas

Profit = SP − CP

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Loss = CP − SP

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Profit% = (Profit × 100)/CP

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Loss% = (Loss × 100)/CP

✏️ Easy Example

Q. A shopkeeper buys a pen for ₹40 and sells it for ₹50. Find his profit per cent.

1. Profit = 50 − 40 = ₹10
2. Profit% = (10/40) × 100

Answer: 25%

🇮🇳 Real-Life Example

A sabzi-wala buys tomatoes at ₹30/kg from the mandi and sells at ₹36/kg — profit ₹6 on ₹30, a clean 20%.

📝 Exam-Level Example

Q. A cycle bought for ₹1,250 is sold for ₹1,000. Find the loss per cent.

1. Loss = 1250 − 1000 = ₹250
2. Loss% = (250/1250) × 100

Answer: 20%

📝 Exam-Level Example

Q. Ravi buys a watch for ₹800 and sells it at a 10% loss. Find the selling price.

1. Loss = 10% of 800 = ₹80
2. SP = 800 − 80

Answer: ₹720

🪄 Memory Trick

Money paid = CP, money received = SP. Underline both in the question first — half the mistakes vanish there.

⚠️ Common Mistakes

• ❌ Calculating profit% on SP instead of CP
• ❌ Confusing profit in rupees with profit per cent
• ❌ Subtracting in the wrong order and calling a loss a profit

🏆 Exam Tips

• ✅ Write CP and SP separately on paper before touching any formula
• ✅ If profit% and CP are known, SP = CP + profit — no need for a fresh formula

📌 Summary

• CP = buying price, SP = selling price
• Profit = SP − CP, Loss = CP − SP
• Profit% and Loss% are always on CP
• Rupee profit and percentage profit are different things