This equation is is not the computed on the delta between the old rate and the new rate.
First, they are stating that they want to bill at a rate increased by +30%of the old rate.
To accomplish this, They assume that the old rate was 70% of what the new rate will be.
Thus, working in decimal equivalents:
175/((100 - 30)/100) = 250
partial solution:
175/ (1 - 0.3) = 250
or
175/ (.7) = 250
This is not dissimilar to the slight of hand used by businesses in the aspect of retail pricing when they are operating on margin and selling on markup.
Essentially, by their definition, it is a 30% increase.