Question

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?

Answer 1

`(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) %`