Pet peeve – math errors involving percentages

I hate it when someone sees that an item is 10% off, then there is another 20% off, and concludes that the item is 30% off the original price. The item is actually 28% off the original price – if the original price is X, then the sale price is (1- 0.10)(1-0.20)X, which comes to 0.72X, which is 28% off.

I also hate it when someone says something like “My wife and I each got a 10% pay cut. That means we got a 20% pay cut.” AARGH! That is a 10% pay cut for the household!!! To see this, suppose that the husband’s salary is X and the wife’s salary is Y. After the pay cuts, the husband makes 0.90X and the wife makes 0.90Y. The combined salary is 0.90(X + Y), which is a 10% cut from the original combined salary.

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