Numerical aptitude · Percentages and money
Discount, made easy
💡 The idea
The marked price is on the tag. A discount is taken off it, and what is left is the sale price you pay.
🧭 The method: 3 steps
- Take the discount away from 100% to see what you pay (25% off → you pay 75%).
- Work out that per cent of the marked price.
- For two discounts, do them one after the other, on 100.
🎬 Every kind of question, in pictures
Pick a kind. Guess the answer first, then watch the picture work it out. Tap any step to see it in the picture.
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✏️ Worked examples
Example 1. A $120 jacket has 25% off. Sale price?
- 25% off → you pay 75%
- 75% of 120 = 0.75 × 120 = $90
⚡ Shortcut: ¾ of 120 = 90.
Example 2. 20% off, then another 10% off. What single discount is that?
- Start with 100
- 20% off → 80
- 10% off 80 = 8 → 72
- 100 → 72 is 28% off (not 30%)
⚡ Shortcut: 20 + 10 − (20 × 10 ÷ 100) = 28.
Example 3. Goods marked 50% above cost, sold with 20% off. Profit %?
- Cost = 100
- Marked = 150
- 20% off 150 = 30 → sold at 120
- Profit = 20%
⚠️ Where people go wrong
- Two discounts do not simply add: the second one is on a smaller price.
- Discount is on the marked price; profit is on the cost. Keep them apart.
- To get the marked price back, divide by what you pay (e.g. ÷ 0.75); don’t add the discount on.
📌 Remember
- Sale price = marked × (1 − d/100)
- Two discounts a and b = a + b − ab/100