Percentage increases, decreases

Question

Why does a % decrease of a number not equal the same % increase when you reverse the calculation?

ie: $30 less 20% = $24.00

Reverse calculation

$24 plus 20% = $28.80

Please explain

Answer 1

That's easy. The key to understanding this is to realize that you shouldn't speak of subtracting "twenty percent"; you are really subtracting "twenty percent of thirty". That is, you are subtracting (0.20)(30) = 6 from 30, resulting in 24.

Now, surely you see that "twenty percent of twenty four" is smaller than "twenty percent of thirty", right? So you can't possibly get back to where you started by adding the same fraction of a smaller number.

The 6 you need to add back is a larger fraction of 24 than it is of 30: 6 is 25% of 24, but it is only 20% of 30.

This happens because you usually are considering the second stage to be a whole new problem, forgetting about the original amount. So at that point, you are basing your computation on the current amount (24), not the original amount (30).