Percentage Profit and Loss

1Cost price, selling price, profit and loss

• The cost price is what the trader paid for the goods.
• The selling price is what the trader receives when selling them.
• If the selling price is more than the cost price, there is a profit: profit = selling price − cost price.
• If the selling price is less than the cost price, there is a loss: loss = cost price − selling price.

Mutesi's avocados.
Selling price = 50 × 150 = 7 500 Frw.
Cost price = 6 000 Frw.
7 500 is more than 6 000, so she made a profit of 7 500 − 6 000 = 1 500 Frw.

2Percentage profit and percentage loss

To judge whether 1 500 Frw is a lot, compare it with what she paid:

percentage profit = profit ÷ cost price × 100
percentage loss = loss ÷ cost price × 100

Mutesi: 1 500 ÷ 6 000 × 100 = 25% profit.

3Finding the selling price

Gatete buys a radio for 25 000 Frw and wants a profit of 20%.
Profit = 20% of 25 000 = 5 000 Frw.
Selling price = 25 000 + 5 000 = 30 000 Frw. You can also do it in one step: 120% of 25 000 = 1.2 × 25 000 = 30 000 Frw.

4Discount

A discount is an amount taken off the marked price. A shirt is marked 15 000 Frw, and the shop gives a 10% discount.
Discount = 10% of 15 000 = 1 500 Frw.
You pay 15 000 − 1 500 = 13 500 Frw.

Try it yourself

1. Cost price 4 000 Frw, selling price 5 000 Frw. Find the profit and the percentage profit.
2. Cost price 20 000 Frw, selling price 17 000 Frw. Find the loss and the percentage loss.
3. A trader buys a phone for 12 000 Frw and wants a 15% profit. What should the selling price be?
4. A book is marked 8 000 Frw and has a 5% discount. What do you pay?

Answers

1. Profit = 1 000 Frw. 1 000 ÷ 4 000 × 100 = 25%.
2. Loss = 3 000 Frw. 3 000 ÷ 20 000 × 100 = 15%.
3. 15% of 12 000 = 1 800, so the selling price is 13 800 Frw.
4. 5% of 8 000 = 400, so you pay 7 600 Frw.