Maths · Ratio, proportion and rates of change. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
Per cent means "out of 100". To write one amount as a percentage of another, make a fraction and multiply by 100.
The fastest way to change an amount by a percentage is a multiplier. An increase of 15% leaves you with 115% of the amount, so multiply by 1.15. A decrease of 15% leaves 85%, so multiply by 0.85. For two changes in a row, multiply by both multipliers.
In a reverse percentage question you know the amount after the change and want the amount before. Divide by the multiplier. With simple interest, the same interest is added every year, worked out on the starting amount only.
To undo a 20% reduction, students add 20% to the sale price. The 20% was taken from the original price, so divide the sale price by 0.8.
Answer: £25 000
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