Percentages, profit, discount and interest are all the same idea wearing different clothes: a part compared with a whole. Learn the comparison and the rest is arithmetic.
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A percentage is just a fraction with 100 underneath. Turning it into a fraction makes every calculation easier.
💯 Learn these conversions
| Percent | Fraction | Percent | Fraction |
|---|---|---|---|
| 50% | 1/2 | 20% | 1/5 |
| 25% | 1/4 | 10% | 1/10 |
| 75% | 3/4 | 12½% | 1/8 |
| 33⅓% | 1/3 | 5% | 1/20 |
💯 The three percentage questions
Find a percent of a number: 15% of 240 = 15/100 × 240 = 36.
Express as a percent: 36 out of 240 = 36/240 × 100 = 15%.
Percentage change: change ÷ original × 100. Always divide by the original.
Profit and loss are always worked out on the cost price. Discount is always worked out on the marked price.
💰 The formulas
| Quantity | Formula |
|---|---|
| Profit | SP − CP |
| Loss | CP − SP |
| Profit % | Profit ÷ CP × 100 |
| Loss % | Loss ÷ CP × 100 |
| SP with profit | CP × (100 + profit%) ÷ 100 |
| Discount | MP − SP |
| Discount % | Discount ÷ MP × 100 |
The single commonest error: dividing by the selling price when finding profit %. Profit and loss percentages are always on the cost price. Discount alone uses the marked price.
Interest is the rent paid for money. In simple interest it is charged on the original sum every year.
🏦 One formula, three rearrangements
SI = (P × R × T) ÷ 100, where P is principal, R is rate per year, T is years.
Amount = P + SI — the total you pay back.
Rearrange for anything: R = (SI × 100) ÷ (P × T), and T = (SI × 100) ÷ (P × R).
Watch the time units. If a question gives months, convert to years first: 6 months = ½ year, 9 months = ¾ year. Putting 6 into the formula instead of 0.5 gives an answer twelve times too big.
12 questions on percentage, profit, loss and interest. Write the formula first. 🍀
