A worker's salary was reduced by m%. Find the percent by which the new salary would have to be raised to bring it back to the original amount.

jonathanxu999
Feb 9, 2018

#1**+1 **

Call S the old salary

The new salary is

S ( 1 - m ) [ where m is some percent expessed as a decimal ]

So......the percent, P , that the new salary must be raised to equal the old is

S (1 - .m) ( P + 1) = S divide both sides by S (1 - .m)

( P + 1) = S / [ S ( 1 - m ) ]

P + 1 = 1 / ( 1 - m)

P = 1 / ( 1 - m ) - 1

For example....suppose a man makes $100 per day and has his salary reduced by 5%

New salary = 100 (1 -. 05) = $95

So....the percent that this must be raised to return to the original salary is

(P + 1) = 1 / (1 - .05)

P + 1 ≈ 1.0526

P ≈ .0526 ≈ 5.26%

CPhill
Feb 9, 2018

#2**0 **

If the original salary was =S, and:

If the lower salary was = P, then we have:

S x [1 - m%] = P

S x [1 - m/100] = P divide both sides by [1 - m/100]

S = P / [ 1 - m/100], or:

S = P x 1/[1 - m/100]. Therefore:

[**1 - m%] % =[1 - m/100]** - This is the % by which the current salary P must be **divided or multiplied by its reciprocal** in order to get the original salary S.

Guest Feb 9, 2018