Percentage problems can be tricky at times when you are careless.

Let's us look at one maths word problem related to it.

Question:

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.

Why?

**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!

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## 1 comment:

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