Profit and Loss

1Summary 重點摘要

Learn how to calculate profit and loss in business. Percentages are very useful here.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Step 1: Tell cost price and selling price apartThe cost price is what you pay to buy the goods, e.g. stock bought for $100; the selling price is what you receive selling them, e.g. sold for $150. The two must never be swapped, because every formula is based on cost. A life example: a fruit shop buys oranges at $60 a crate and sells them at $90 — cost 60, selling price 90. A common error is using the selling price as the denominator for profit per cent; write down 'cost = ..., selling price = ...' beside the question first and the slip is prevented.
2. Step 2: Find profit or lossSubtract cost from selling price: a positive result is profit (money made), a negative one a loss (money lost). Example: cost $100, sold at $150 — 150 − 100 = 50, a profit of $50; if cost $100 and sold at $80, then 80 − 100 = −20, a loss of $20. The order: compare the two prices first, then choose the word 'profit' or 'loss', and only then compute the amount. A common error is subtracting selling price from cost, getting a positive number and calling it profit — the direction is reversed and the answer is wrong.
3. Step 3: Calculate profit per centProfit per cent answers 'what fraction of the cost is the profit': profit per cent = profit ÷ cost × 100%. Example: profit $50 on cost $100 — 50 ÷ 100 × 100% = 50%, half of the cost earned. The denominator is the cost price, never the selling price. A common error: computing 50 ÷ 150 ≈ 33.3% and calling it profit per cent — that used the selling price. The check: cost × profit per cent should return the profit — 100 × 50% = 50, verified.
4. Step 4: If loss, calculate loss per centWhen the selling price falls below cost, there is a loss: loss per cent = loss ÷ cost × 100%. Example: goods costing $100 sold at $80 — the loss is 100 − 80 = 20, and the loss per cent = 20 ÷ 100 × 100% = 20%. Note the denominator is again the cost price. A life example: a bakery marks bread down in the evening; if the price drops below cost, the loss per cent helps decide how deep the cut can go. A common error is writing the loss per cent as a negative percentage; in answers, simply write 'the loss per cent is 20%'.
5. Step 5: Reverse: know profit%, find selling priceWith cost and profit per cent known, the selling price comes two ways. Method one: profit = cost × profit per cent, e.g. 100 × 20% = 20, then selling price = 100 + 20 = $120. Method two: selling price = cost × (1 + profit per cent) = 100 × 1.2 = $120, one step. Both agree. A common error is turning 20% into the number 20 and computing 100 × 20 = 2000; remember, 20% = 0.2 — convert to a decimal before multiplying.
6. Step 6: Reverse: know selling price, find costWith selling price and profit per cent known, find the cost: since selling price = cost × (1 + profit per cent), cost = selling price ÷ (1 + profit per cent). Example: sold at $120 with profit per cent 20% — cost = 120 ÷ 1.2 = $100. Division appears because cost-to-price is multiplication. A common error is computing 120 × 0.8 = 96 as the cost, treating the profit rate like a discount; the check: 100 × 1.2 = 120 returns to the selling price, so 100 is right.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Cost is how much you bought, selling price is how much you sold
• Profit = Selling − Cost (positive = earn, negative = lose)
• Profit% = Profit ÷ Cost × 100%
• Reverse: Selling price = Cost × (1 + Profit%)
• Remember denominator is always cost price