Marked Price (MP) is the price tag on an item - what the seller claims is the original price. Discount is the reduction given on this marked price. The final price customer pays is called Selling Price (SP)
finding MP when SP and discount% are given, calculating profit when discount is involved, successive discounts, and false discount problems.
Shortcut #1 - Direct SP Formula: When discount% is given, SP = MP × (100-d)/100. For 20% discount: SP = 0.8 × MP
Shortcut #2 - Successive Discounts: For two discounts of a% and b%, combined discount = a + b - (ab/100). For 10% and 20%: Combined = 10 + 20 - (200/100) = 28%
Worked Example 1: A shopkeeper marks an article 40% above cost price. He gives 25% discount and still makes Rs. 20 profit.
Find the cost price
→Solution
Let CP = 100
MP = CP + 40% = 100 + 40 = 140
After 25% discount: SP = 140 × 75/100 = 105
Profit = SP - CP = 105 - 100 = 5
If profit of 5 gives Rs. 20, then CP = 20 × 100/5 = Rs. 400
Worked Example 2: A trader allows 16% discount on marked price and still gains 5%. If the article costs Rs. 50, what is the marked price
→Solution
CP = Rs. 50
Gain = 5%, so SP = 50 × 105/100 = Rs. 52.50
Discount = 16%, so SP = MP × 84/100
52.50 = MP × 84/100
MP = 52.50 × 100/84 = Rs. 62.50
Shortcut #3 - Quick MP Calculation: When SP and discount% are known, use MP = SP ÷ (1 - d/100). For 20% discount: MP = SP ÷ 0.8
Most Common Trap: Students confuse discount% base. Discount% is ALWAYS calculated on Marked Price, never on Cost Price or Selling Price. Many students calculate discount on CP and get wrong answers
💡Remember
Discount% = (Discount/MP) × 100, not (Discount/CP) × 100.
Another frequent error is in successive discount problems. Students simply add the percentages instead of using the formula. For 10% and 15% discounts, combined is NOT 25%, but 23.5%
💡Practical Tip
When solving discount problems, always identify what is given and what needs to be found
→Draw the relationship
CP → MP → SP. Mark the percentages between each step. This visual approach prevents calculation errors and saves time in exams.
A retailer buys a product for ₹600 and wants to make a profit of 30%. He marks the price 50% above the cost price. What discount percentage should he offer to achieve his target profit?
Practice 2easy
A merchant offers a discount of 25% on the marked price of a shirt. The cost price is ₹240 and he makes a profit of 20%. What is the marked price?
Practice 3easy
The selling price of an item is ₹450 after a discount of 10% on the marked price. If the cost price is ₹300, what is the profit percentage?
Practice 4easy
A store marks up a product by 60% above its cost price. During a sale, it offers a discount of 30% on the marked price. What is the overall profit or loss percentage?
Practice 5easy
A shopkeeper marks an article at ₹800. He gives a discount of 15% on the marked price. What is the selling price?
Practice 6easy
The marked price of a book is ₹500. After giving a discount of 20%, the shopkeeper still makes a profit of 25% on the cost price. What is the cost price of the book?
Practice 7medium
A shopkeeper offers a discount of 30% on the marked price of an item. After giving the discount, he makes a profit of 40% on the cost price. If the cost price is ₹350, what is the marked price?
Practice 8medium
A merchant buys goods at ₹2400 per dozen. He marks them up by 50% and then gives a discount of 20% on the marked price. What is his profit percentage?
Practice 9medium
The marked price of a book is 40% more than its cost price. A customer buys it at a discount of 25% on the marked price. If the customer pays ₹420, what is the cost price of the book?
Practice 10medium
A retailer marks goods at 60% above cost price. During a sale, he offers two successive discounts of 10% and 15%. What is his overall profit or loss percentage?
Practice 11medium
A vendor purchases items at ₹80 each. He marks them at ₹120 each. During a clearance sale, he offers a discount such that he makes a profit of 10% on each item. What is the discount percentage?
Practice 12medium
A shopkeeper marks an article at ₹800. He offers a discount of 15% on the marked price. If he still makes a profit of 25% on the cost price, what is the cost price of the article?
Practice 13hard
A retailer buys goods at ₹500 per unit. He marks them up by 80%. During a festival sale, he gives two successive discounts of 20% and 15%. What is his profit percentage on each unit sold?
Practice 14hard
A wholesaler buys 100 units at ₹40 per unit. He marks them up by 50% and sells 60 units at the marked price. The remaining 40 units are sold at a 20% discount on the marked price. What is his overall profit percentage?
Practice 15hard
A shopkeeper marks up goods by 60% above cost price. He offers a discount of 25% on the marked price during a sale. If a customer pays ₹1,080 for an item after the discount, what is the cost price of the item?
60-Second Revision — Discount & MP
Formula: SP = MP × (100-discount%)/100 for quick calculations
Remember: Discount% base is always Marked Price, not Cost Price
Shortcut: Successive discounts a% and b% = a+b-(ab/100)%