Discount & MP

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)

SP = MP - Discount Basic Formulas: - Discount = MP - SP - Discount% = (Discount/MP) × 100 - SP = MP × (100 - Discount%)/100 - MP = SP × 100/(100 - Discount%)

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

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

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

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%

When solving discount problems, always identify what is given and what needs to be found

CP → MP → SP. Mark the percentages between each step. This visual approach prevents calculation errors and saves time in exams.