Profit-Loss % & the MF Method

🎯 Learning Objective

Use multiplying factors to jump between CP and SP in a single step.

💡 Concept

• 20% profit → SP = CP × 1.20; 20% loss → SP = CP × 0.80
• General: SP = CP × (100 + P%)/100 or CP × (100 − L%)/100
• Reverse: CP = SP × 100/(100 + P%) for profit; CP = SP × 100/(100 − L%) for loss
• Never subtract the % from SP directly — always divide by the MF
• Same SP, one article at x% profit and another at x% loss → net is ALWAYS a loss of (x/10)²%

🧮 Key Formulas

SP = CP × (100 ± x)/100

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CP = SP × 100/(100 ± x)

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Same SP, ±x% → net loss = (x/10)²%

✏️ Easy Example

Q. A bag costing ₹500 is sold at 20% profit. Find the selling price.

1. MF = 1.20
2. SP = 500 × 1.20

Answer: ₹600

🇮🇳 Real-Life Example

A mobile shop owner buys a phone for ₹10,000 and wants 15% profit — he simply types 10000 × 1.15 on his calculator: ₹11,500.

📝 Exam-Level Example

Q. A fridge is sold for ₹9,200 at a loss of 8%. Find the cost price.

1. MF for 8% loss = 0.92
2. CP = 9200 ÷ 0.92

Answer: ₹10,000

📝 Exam-Level Example

Q. A man sells two articles at ₹600 each — one at 20% profit, the other at 20% loss. Find his net loss per cent.

1. CP of 1st = 600/1.2 = 500; CP of 2nd = 600/0.8 = 750
2. Total CP = 1250, total SP = 1200
3. Loss% = (50/1250) × 100

Answer: 4% loss

🪄 Memory Trick

Same-SP, same-% questions: skip all working — net loss = (x/10)²%. For 20% it is 4%, for 10% it is 1%.

⚠️ Common Mistakes

• ❌ Finding CP by subtracting x% from SP (division by MF is the only correct way)
• ❌ Thinking equal % profit and loss cancel out to zero
• ❌ Using 100 + x in place of 100 − x for a loss

🏆 Exam Tips

• ✅ Memorise MF pairs: +10%→1.1, +25%→1.25, −10%→0.9, −25%→0.75
• ✅ In same-SP questions the answer is always a loss — options showing profit are instantly wrong

📌 Summary

• Profit x% → ×(100+x)/100; loss x% → ×(100−x)/100
• CP from SP → divide by the MF
• Same SP with ±x% → guaranteed loss of (x/10)²%
• MF method turns two steps into one