# A worker’s salary is reduced by p%. By what percent would the salary have to be raised to bring it back to its original amount?

Jun 23, 2018

(100p)/(100-p) %

#### Explanation:

If a worker's salary, $x$ is reduced by p%, then we can say that the new salary is

$\left(1 - \frac{p}{100}\right) x$

Hence, the percentage increase of this expression back to $x$ is

$\frac{x}{\left(1 - \frac{p}{100}\right) x}$

The $x$'s cancel out leaving

$\frac{1}{1 - \frac{p}{100}} = \left(\frac{100}{100 - p}\right)$

which is the multiplier. To change this into a percentage we can finally say that the salary needs to be increased by

100((100/(100-p))-1) %

Multiplying this out and simplifying gives

(100p)/(100-p) %