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?

1 Answer
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

(1-p/100)x

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

x/((1-p/100)x)

The x's cancel out leaving

1/(1-p/100) = (100/(100-p))

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) %