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 shopkeeper marks an article at ₹800. He offers a discount of 15% on the marked price. What is the selling price of the article?
Practice 2medium
A merchant offers a discount of 25% on the marked price of an article. Even after giving this discount, he makes a profit of 20%. If the cost price is ₹600, what is the marked price?
Practice 3medium
A retailer buys goods at ₹2400 per dozen. He marks them at 50% above cost price and offers a discount of 20% on the marked price. What is his profit per dozen?
Practice 4medium
A shopkeeper marks articles at 40% above cost price. He gives a discount of 10% on the marked price to the first 50 customers and a discount of 15% to the remaining customers. If the cost price of each article is ₹500, what is the difference in profit between the two groups of customers?
Practice 5medium
A shopkeeper marks an article at ₹1,200. He offers a discount of 15% on the marked price. However, he still makes a profit of 20% on the cost price. What is the cost price of the article?
Practice 6hard
A shopkeeper marks up goods at 80% above cost price. He offers two successive discounts of 20% and 15% to customers. If a customer pays ₹1,224 for an item, what is the cost price of that 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)%