Numerical aptitude · Percentages and money
Profit and loss, made easy
💡 The idea
You buy at the cost price and sell at the selling price. The difference is your profit (or loss), and the per cent is always of the cost.
🛒 Buy: $80
cost price→💰 Sell: $100
selling price→📈 Profit: $20
20 ÷ 80 = 25%
cost price→💰 Sell: $100
selling price→📈 Profit: $20
20 ÷ 80 = 25%
🧭 The method: 3 steps
- Find the profit or loss in money: selling − cost.
- Divide it by the cost price.
- Multiply by 100 to get the per cent.
🎬 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 phone costs $400 and is sold for $500. Profit %?
- Profit = 500 − 400 = $100
- On the cost: 100 ÷ 400 = 0.25
- × 100 = 25% profit
Example 2. A shop wants 20% profit on a $250 lamp. Selling price?
- 20% of 250 = 50
- Selling price = 250 + 50 = $300
⚡ Shortcut: 250 × 1.2 = 300.
Example 3. Selling a bag for $360 gives a 20% profit. What did it cost?
- Cost = 100%, so selling price = 120%
- 120% = $360, so 1% = 3
- Cost = 100% = $300
⚡ Shortcut: 360 ÷ 1.2 = 300.
⚠️ Where people go wrong
- Profit % is on the cost, not the selling price.
- To find the cost from the selling price, divide by 1.2; don’t take 20% off (that gives $288, wrong).
- Same selling price with x% profit on one and x% loss on the other always means a small loss: x² ÷ 100 %.
📌 Remember
- Profit = SP − CP
- Profit % = profit ÷ CP × 100
- SP = CP × (1 + p/100)
- CP = SP ÷ (1 + p/100)