Percentage problems can be tricky at times when you are careless.
Let's us look at one maths word problem related to it.
There are 3 persons, John, Mary and Jane.
John is richer than Mary by 10%, and Mary is richer than Jane by 20%.
Is John richer than Jane by (10 + 20)% = 30% ?
Most students, upon quick thinking, will acknowledge that 30% is the correct answer.
Is it so?
To verify the answer, let us assume that Jane has $1000.
As such, Mary will have (100+20)% of $1000 = 1.2 x $1000 = $1200.
John is then 1.1 x $1200 = $1320 richer than Jane ==> By 32%.
If 30% is correct, we should get 1.3 X $1000 = $1300.
The latter number (dollar) is not the same as the first worked out solution.
Mistake in understanding what is percentage:
To assume that John is 10% + 20% richer than Jane is incorrect.
This is due to the fact that percentage has to take a common reference for this to be correct.
In the word problem, the percentages of comparison are not to a common reference.
The first one is to Mary, while the next is to Jane.
These made the denominator of the ratio different.
Thus adding the percentage up is a mistake, and an easy one too!