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?

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Answer 1 · 2018-06-23T20:05:52

#(100p)/(100-p) %#

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) %#