Question

What single percentage change is equivalent to a 18% increase followed by a 13% decrease?

Answer 1

Given:

18% increase followed by a 13% decrease.

To find:

The single percentage equivalent to a 18% increase followed by a 13% decrease.

Solution:

Let a number be 100.

If it is increased by 18% then the number becomes

`Number=100+(18)/(100)* 100`

`=100+18`

`=118`

Then, it is decreased by 13%.

`Number=118-(13)/(100)* 118`

`=118-15.34`

`=102.66`

New number is 102.66.

Now, the percentage change is

`\%\text{ Change}=\frac{\text{New number - Initial number}}{\text{Initial number}}* 100`

`\%\text{ Change}=(102.66-100)/(100)* 100`

`\%\text{ Change}=(2.66)/(100)* 100`

`\%\text{ Change}=2.66\%`

Therefore, the Single percentage change is 2.66%.