Discount
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Written Lesson
A discount is an amount taken off the original price of an item. Stores often give discounts as a percentage, such as 10%, 20%, or 25%.
The marked price is the original price before the discount. The sale price is the price after the discount has been subtracted.
What You Will Learn
- Identify the marked price, discount and sale price
- Calculate a discount and sale price
- Find the change after paying with a bill or note
- Find a percentage discount
- Find the original marked price
- Interpret conditions attached to discounts
- Calculate successive discounts
- Solve problems involving markup followed by discount
Key Words
| Term | Meaning |
|---|---|
| Cost Price | The amount the merchant paid for the item |
| Marked Price | The original price before the discount |
| Discount | The amount taken off the marked price |
| Discount Rate | The discount expressed as a percentage of the marked price |
| Sale Price | The price after the discount is subtracted |
| Change | The money returned after paying |
Key Ideas
- Discount = discount rate × marked price
- Sale price = marked price − discount
- Change = amount paid − sale price
- Percentage discount = (discount ÷ marked price) × 100
- The discount is always calculated from the marked price, never the cost price or sale price.
Why Stores Offer Discounts
Businesses may offer discounts to attract customers, encourage immediate payment, reward large purchases, or clear old stock. The type of discount changes why it is given, but not how it is calculated.
| Type | When It Is Offered |
|---|---|
| Cash discount | When a customer pays immediately instead of using credit |
| Trade discount | To retailers or businesses buying goods for resale |
| Quantity discount | When a customer buys a large number of items |
| Purchase-value discount | When the total purchase is above a stated amount |
| Clearance discount | When a business wants to sell certain stock quickly |
Discount Formulas
Diagram: How Discount Works
Worked Examples
Example 1: A dress which costs $1800 is being sold at a discount of 10%. Find the amount of the discount.
- Marked price = $1800
- Discount = 10% of 1800
- Discount = 10/100 × 1800
- Discount = 180
Answer: $180
Example 2: A jacket marked $200 has a 15% discount. Find the sale price.
- Marked price = $200
- Discount = 15% of 200
- Discount = 15/100 × 200 = $30
- Sale price = marked price − discount
- Sale price = 200 − 30 = 170
Answer: $170
Example 3: A calculator marked at $120 is sold for cash at a 30% discount. How much change would Susan receive if she pays with a $100 bill?
- Marked price = $120
- Discount = 30% of 120
- Discount = 30/100 × 120 = $36
- Sale price = 120 − 36 = $84
- Susan pays $100.
- Change = 100 − 84 = 16
Answer: $16
Example 4: A bag marked $80 is sold for $68. Find the percentage discount.
- Marked price = $80
- Sale price = $68
- Discount = 80 − 68 = $12
- Percentage discount = (discount ÷ marked price) × 100
- Percentage discount = (12 ÷ 80) × 100
- Percentage discount = 15%
Answer: 15%
Example 5: A laptop marked $2000 has a 10% discount. Find the sale price.
- Marked price = $2000
- Discount = 10% of 2000
- Discount = 10/100 × 2000 = $200
- Sale price = 2000 − 200
- Sale price = 1800
Answer: $1800
A Faster Way: The Percentage-Paid Method
Instead of finding the discount first, you can jump straight to the sale price by working out what percentage is actually paid.
Example 6: A refrigerator is marked at $3200 and is discounted by 12%. Find the sale price using the percentage-paid method.
- Percentage paid = 100% − 12% = 88%
- Sale price = 88/100 × 3200
- Sale price = 2816
Answer: $2816
Finding the Original Marked Price
Sometimes you are given the sale price and need to work backwards to find the marked price.
Example 7: After receiving a discount of 20%, a customer pays $720 for a tablet. Find the original marked price.
- Percentage paid = 100% − 20% = 80%
- Marked price = (720 ÷ 80) × 100
- Marked price = 900
Answer: $900
Discounts with Qualifying Conditions
Some discounts only apply if a stated condition is met. Read the wording carefully before calculating.
At least $500 means the purchase may be $500 or more (500 itself qualifies).
Example 8: A store offers a 5% discount on purchases over $500. A customer purchases goods marked at $600. Calculate the amount paid.
- Check the condition: $600 is greater than $500, so it qualifies.
- Discount = 5/100 × 600 = $30
- Amount paid = 600 − 30 = 570
Answer: $570
Successive Discounts
Successive discounts are applied one after the other. Each new discount is worked out using the already-reduced price, not the original marked price.
Example 9: A laptop is marked at $4000. It is discounted by 20%, followed by an additional discount of 10%. Find the final price.
- Apply the first discount: 4000 × 0.80 = 3200
- Apply the second discount to the new price: 3200 × 0.90 = 2880
Answer: $2880
Markup Followed by Discount
A merchant may first increase the cost price by a markup, then offer a discount on that new marked price.
- Calculate the markup using the cost price.
- Add the markup to find the marked price.
- Calculate the discount using the marked price.
- Subtract the discount to find the sale price.
Example 10: A merchant buys an item for $80, marks it up by 50%, and then offers a discount of 20%. Find the sale price.
- Markup = 50/100 × 80 = $40
- Marked price = 80 + 40 = $120
- Sale price = 120 × 0.80 = $96
Answer: $96
Important Reminders
Common Mistakes
Lesson Summary
- A discount is an amount taken off the marked price.
- Sale price = marked price − discount. Change = amount paid − sale price.
- The percentage discount is always based on the marked price.
- The percentage-paid method finds the sale price directly: (100% − discount rate) × marked price.
- The original marked price can be found by treating the sale price as the percentage remaining.
- Conditions attached to a discount, such as "over" or "at least," must be checked before it is applied.
- Successive discounts are applied one after the other on the reduced price, and are never simply added together.
- When an item is marked up and then discounted, the discount is calculated using the marked price, not the cost price.
Practice Questions
- 1. A television marked $1500 has a 10% discount. Find the amount of the discount.
- 2. A dress marked $120 has a 25% discount. Find the sale price.
- 3. A pair of shoes marked $80 is sold at a 25% discount. A customer pays with a $100 bill. Find the change.
- 4. A watch marked $250 is sold for $200. Find the percentage discount.
- 5. A microwave marked at $1800 is discounted by 15%. Find the sale price using the percentage-paid method.
- 6. After receiving a discount of 25%, a customer pays $900 for a bicycle. Find the original marked price.
- 7. A store offers an 8% discount on purchases over $750. A customer purchases goods marked at $900. Calculate the amount paid.
- 8. A store offers successive discounts of 20% and 15% on an item marked at $2500. Calculate the final price.
- 9. A merchant buys an item for $500, marks it up by 30%, and then offers a discount of 20%. Calculate the sale price.
- 10. A school bag marked $300 has a 20% discount. Find the sale price.
Answers
- $150
- $90
- $40
- 20%
- $1530
- $1200
- $828
- $1700
- $520
- $240
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