Percentages (I) · Ages 12–13
Profit and loss
Profit and loss percentages are of the cost.
How to do it
Method
Profit and loss percentages are of the cost
Cost 80, sold at 100: 20 ÷ 80 × 100% = 25%
Another way
One multiplication
Selling price = 80 × 1.25 = 100
In full
The cost price is what it was bought for; the selling price, what it sold for. Selling above cost makes a profit: profit = selling price − cost; below cost, a loss: loss = cost − selling price. Profit and loss percentages both take the cost as the base: profit % = profit ÷ cost × 100%. Cost $80, sold for $100: the profit is $20, and the profit percentage is 20 ÷ 80 × 100% = 25%, not 20 ÷ 100. From the cost and the profit percentage to the selling price: one way, the profit first, 80 × 25% = 20, plus the cost, 100; another, in one step, 80 × 1.25 = 100. From the selling price back to the cost: cost × 1.25 = 100, so cost = 100 ÷ 1.25 = 80.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Selling price $210, a 50% loss: cost = $
Show the answer and working
Answer: 420
The loss is of the cost: cost × 0.5 = 210, so cost = 210 ÷ 0.5 = 420. Not 210 plus 50% of 210.
Example 2
An item sells for $700 at a 25% profit. What did it cost?
Show the answer and working
Answer: 560 dollars
Cost × 1.25 = 700, so cost = 700 ÷ 1.25 = 560. Check: 560 × 1.25 = 700.
Example 3
Two items each sell for $1,188: one at a 10% profit, the other at a 10% loss. Overall, what happens?
- A. No profit, no loss
- B. A profit of $24
- C. A loss of $132
- D. A loss of $24
Choose the right answer
Show the answer and working
Answer: D. A loss of $24
The costs are 1188 ÷ (1 + 10%) = 1080 and 1188 ÷ (1 − 10%) = 1320, 2400 in all; they sell for 2376, a loss of $24.
Practice questions to try
Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.
1.Cost $100, 60% profit: selling price = $
Answer:
2.Cost $200, selling price $160: the loss percentage is 25%.
True or false?
Answer:
3.Selling price $275, a 45% loss: cost = $
Answer:
4.An item sells for $324 at a 35% profit. What did it cost?
Answer:
5.Two items each sell for $120: one at a 20% profit, the other at a 20% loss. Overall, what happens?
- A. No profit, no loss
- B. A loss of $10
- C. A profit of $10
- D. A loss of $30
Choose the right answer
Answer:
All the answers
- 1. 160
- 2. False
- 3. 500
- 4. 240 dollars
- 5. B. A loss of $10
VIP practice notes and papers
Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.
- Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
- Practice paper: Set out in parts like a school paper, marked, with answers and full working
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