Find the percent: discount and mark-up
Key notes:
🔹 Basic Terms
- Marked Price (MP): The price written on the product 🏷️
- Selling Price (SP): The price at which the product is sold 💰
- Cost Price (CP): The price at which the shopkeeper buys the product 📦
🔹 Discount
- Discount: Reduction given on the marked price 🔻
- Discount Amount = MP − SP
👉 Discount Percent
Discount % = Discount / Marked Price × 100
✅ If MP = ₹500 and SP = ₹450
Discount = ₹50
Discount % = (50 ÷ 500) × 100 = 10%
🔹 Mark-Up
- Mark-Up: Increase in price over the cost price 🔺
- Mark-Up Amount = SP − CP
👉 Mark-Up Percent
Mark-Up % = Mark-Up / Cost Price × 100
✅ If CP = ₹400 and SP = ₹480
Mark-Up = ₹80
Mark-Up % = (80 ÷ 400) × 100 = 20%
🔹 Important Formulas
- SP after Discount:
SP = MP × (1−Discount % / 100)
- SP after Mark-Up:
SP = CP × (1 + Mark-Up % / 100)
🔹 Real-Life Examples
- Discounts are given during sales 🛍️
- Mark-ups are used by shopkeepers to make profit 📈
🔹 Key Tips 🧠
- Discount is always calculated on Marked Price
- Mark-up is always calculated on Cost Price
- Convert percentages to fractions when calculating easily ✏️
Learn with an example
A store employee creates a display of tulips priced at ₹62 apiece. The store paid ₹31 for each tulip. What percentage is the mark-up?
Write your answer using a percent sign (%).——–
The percent of change formula can be used to find percent of mark-up.
percent of mark-up=selling price − purchase price/purchase price
Plug ₹31 and ₹62 into the formula and simplify.
percent of mark-up=selling price − purchase price/purchase price
=62-31/31
=31/31
=1
Write the number as a percent.
1 → 100%
The percent of mark-up is 100%.
The buyer for a chain of stores purchased bike lights in bulk, paying ₹80 each. The stores will sell each bike light for ₹228. What is the mark-up, as a percentage?
Write your answer using a percent sign (%).——-.
The percent of change formula can be used to find percent of mark-up.
percent of mark-up=selling price − purchase price/purchase price
Plug ₹80 and ₹228 into the formula and simplify.
percent of mark-up=selling price − purchase price/purchase price
=228-80/80
=148/80
=1.85
Write the number as a percent.
1.85 → 185%
The percent of mark-up is 185%.
Juan, a sign maker for a store, makes a sign advertising boxes of plastic spoons for sale at a price of ₹116 each. However, the boxes of plastic spoons only cost the store ₹100 each. What percentage is the mark-up?
Write your answer using a percent sign (%).——–.
The percent of change formula can be used to find percent of mark-up.
percent of mark-up=selling price − purchase price/purchase price
Plug ₹100 and ₹116 into the formula and simplify.
percent of mark-up=selling price − purchase price/purchase price
=116-100/100
=16/100
=0.16
Write the number as a percent.
0.16 → 16%
The percent of mark-up is 16%.
let’s practice!
