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Profit, loss, and discount questions are a natural extension of percentage calculations and appear frequently in QR data sets involving shops, businesses, or financial scenarios. This lesson covers the key terms, formulas, and the specific question types you will encounter.
| Term | Definition | Formula |
|---|---|---|
| Cost Price (CP) | The price paid to acquire or produce the item | Given in the question |
| Selling Price (SP) | The price at which the item is sold | Given or calculated |
| Profit | The gain from selling above cost price | SP − CP |
| Loss | The shortfall from selling below cost price | CP − SP |
| Mark-up | The amount added to the cost price | SP − CP (same as profit) |
| Discount | The amount reduced from the listed/original price | Original Price − Sale Price |
| VAT | Value Added Tax, added to the price | Usually 20% in the UK |
Profit = Selling Price − Cost Price
Example: A shopkeeper buys a toy for £12 and sells it for £18.
Profit = £18 − £12 = £6
Profit Percentage = (Profit ÷ Cost Price) × 100
Using the same example:
Profit % = (6 ÷ 12) × 100 = 50%
Loss = Cost Price − Selling Price
Example: A trader buys goods for £250 and sells them for £200.
Loss = £250 − £200 = £50
Loss % = (50 ÷ 250) × 100 = 20%
Mark-up is the percentage added to the cost price to determine the selling price.
Selling Price = Cost Price × (1 + Mark-up%/100)
Example: A shop buys shirts for £20 and applies a 60% mark-up.
Selling Price = £20 × 1.60 = £32
Mark-up % = ((SP − CP) ÷ CP) × 100
Note: This is the same formula as profit percentage (mark-up = profit as a percentage of cost).
Sale Price = Original Price × (1 − Discount%/100)
Example: A jacket originally costs £85. There is a 20% discount.
Sale Price = £85 × 0.80 = £68
Discount % = ((Original − Sale Price) ÷ Original) × 100
Example: A TV originally priced at £600 is sold for £480.
Discount = £600 − £480 = £120
Discount % = (120 ÷ 600) × 100 = 20%
Original = Sale Price ÷ (1 − Discount%/100)
Example: A dress costs £63 after a 30% discount. What was the original price?
Original = £63 ÷ 0.70 = £90
In the UK, the standard VAT rate is 20%.
Price including VAT = Price excluding VAT × 1.20
Example: A service costs £450 plus VAT.
Total = £450 × 1.20 = £540
Price excluding VAT = Price including VAT ÷ 1.20
Example: A bill is £360 including VAT. What is the pre-VAT amount?
Pre-VAT = £360 ÷ 1.20 = £300
Common Trap: Do not calculate 20% of £360 (= £72) and subtract. This gives £288, which is wrong. The VAT was 20% of £300 (= £60), not 20% of £360.
Many QR questions follow this chain:
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