Discount – Reducing the Price
A discount is a reduction in the original price of an item. Shops, websites, and businesses use discounts to attract customers. Knowing how to calculate discounts helps you find the actual price you will pay and compare deals accurately.
Seasonal discounting has a surprisingly long commercial history — Boxing Day sales in the UK trace back to Victorian-era shop clearances, while the term “Black Friday” for the day after American Thanksgiving became associated with steep discounts by the 1980s. The maths behind “successive discounts” below is one of the most commonly misunderstood ideas in everyday shopping: retailers sometimes advertise stacked percentages (e.g. “20% off, plus an extra 10% off”) precisely because most shoppers instinctively (and wrongly) add them to 30%, when the true combined discount is always slightly less.
Key Terms
| Term | Meaning |
|---|---|
| Marked Price (MP) | The original price before any reduction |
| Discount Amount | How much money is taken off |
| Sale Price (SP) | The price after the discount is applied |
| Discount % | The discount expressed as a percentage of the marked price |
Formulas
Discount Amount = (Discount % / 100) times Marked Price. Sale Price = Marked Price minus Discount Amount. Or: Sale Price = Marked Price times (1 - Discount%/100).
Worked Examples
Discount = 25% of 120 = 0.25 times 120 = 30. Sale price = 120 - 30 = 90. Or: 120 times 0.75 = 90.
Discount = 800 - 680 = 120. Discount % = (120 / 800) times 100 = 15%.
Sale price = MP times 0.70. MP = 105 / 0.70 = 150.
Successive Discounts
When two discounts are applied one after the other, you cannot simply add them.
After 20%: 500 times 0.80 = 400. After 10%: 400 times 0.90 = 360. (A single equivalent discount would be 28%, not 30%.)
Real-Life Tips
- Always check whether the discount is on the original or a previously reduced price.
- Voucher codes and sale percentages stack differently — read the small print.
- Comparing two deals: convert both to their final sale price before choosing.
Key Takeaways
- Discount amount = discount% times marked price / 100.
- Sale price = marked price times (1 - discount%/100).
- To find the marked price from the sale price: divide by (1 - discount%/100).
- Successive discounts are not additive — apply them one at a time.