Marked Price — CP, MP and SP Together

🎯 Learning Objective

Connect CP, MP and SP in one equation and find markup or profit when a discount is involved.

💡 Concept

• MP (Marked Price) = label/tag price printed on the article
• Chain: CP —(markup)→ MP —(discount)→ SP
• Markup% is on CP; discount% is on MP; profit% is again on CP
• Master equation: CP × (100 + Profit%) = MP × (100 − Discount%)
• Markup m% then discount d% → net profit% = m − d − md/100 (signs matter)

🧮 Key Formulas

CP × (100 + P%) = MP × (100 − D%)

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Net profit% = m − d − md/100

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SP = MP × (100 − D%)/100

✏️ Easy Example

Q. A shopkeeper marks a shirt 30% above its cost price of ₹500. Find the marked price.

1. Markup = 30% of 500 = ₹150
2. MP = 500 + 150

Answer: ₹650

🇮🇳 Real-Life Example

A jacket tagged ₹2,000 in Sarojini market sells after haggling at ₹1,400 — the seller's cost was ₹1,000, so he still walked away with 40% profit.

📝 Exam-Level Example

Q. A trader marks his goods 40% above cost price and allows a discount of 20%. Find his profit per cent.

1. Net MF = 1.40 × 0.80 = 1.12
2. Or: 40 − 20 − (40 × 20)/100 = 12

Answer: 12% profit

📝 Exam-Level Example

Q. A shopkeeper wants 20% profit even after giving a 25% discount. By what per cent above CP must he mark the goods?

1. MP/CP = (100 + 20)/(100 − 25)
2. = 120/75 = 1.60
3. MP is 160% of CP

Answer: 60% above CP

🪄 Memory Trick

One line solves everything: CP(100 + profit) = MP(100 − discount). Put in the two knowns, the third pops out.

⚠️ Common Mistakes

• ❌ Taking the discount on CP instead of MP
• ❌ Adding markup% and subtracting discount% directly (40 − 20 = 20 ✗)
• ❌ Treating MP as the selling price when a discount exists

🏆 Exam Tips

• ✅ Assume CP = ₹100 in confusing questions — every % becomes a rupee value
• ✅ Markup and discount combine exactly like successive percentage changes

📌 Summary

• CP → MP (markup on CP) → SP (discount on MP)
• CP(100 + P) = MP(100 − D)
• Net profit% = m − d − md/100
• Discount does not mean loss — always check against CP