In a sale the price of a coat is reduced by 30%. The sale price is $84. Find the price before the sale.
- A 30% decrease leaves 70%, so the multiplier is 0.70.
- original price × 0.70 = 84
- original price = 84 ÷ 0.70 = 120
Answer: $120
Percentages
Maths · Number. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
The idea
A percentage is a number out of 100, so 35% means 35/100 or 0.35. To find a percentage of a quantity, change the percentage to a decimal and multiply.
The quickest way to raise or lower an amount is a multiplier. An increase of 12% gives 112% of the starting amount, so multiply by 1.12. A decrease of 12% leaves 88%, so multiply by 0.88.
In a reverse percentage question you know the amount after the change and want the amount before it, so you divide by the multiplier. Simple interest is the same every year. Compound interest is added to the amount, so the interest grows each year.
Rules to remember
- percentage of a quantity = (percentage ÷ 100) × quantity
- A as a percentage of B = (A ÷ B) × 100, with A and B in the same units
- percentage change = (change ÷ original value) × 100
- simple interest = principal × rate × time ÷ 100 (I = PRT/100)
- compound interest: total amount = P × (1 + r/100)n after n years
- interest earned = total amount − amount invested
- reverse percentage: original amount = new amount ÷ multiplier
Common mistake
In a reverse percentage question, students take the percentage off the new amount. The percentage was worked out on the original amount, so divide the new amount by the multiplier instead.
Worked example
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