+113 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.
+129847 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%
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.
