# When a number is decreased by 20% of itself, the result is 20. What is the number?

May 2, 2017

25

#### Explanation:

Since the number is reduced by 20% we have 80% left. That 80% is equal to 20. We can use cross multiplication to relate the two.

80% is equal to $\frac{80}{100} = \frac{8}{10} = \frac{4}{5}$
We know that 20 is 80% of something so we have $\frac{20}{x}$

These two should be equal so we can do the following
$\frac{4}{5} = \frac{20}{x}$

Using cross multiplication we get
$4 x = 100$

Solving we get
$x = 25$