The answer is correct. But how can one say for sure that "1/5" is 450 i.e. It is half of 1/3?

Because after spending 1/5 of remaining, he had 2/3 of his total salary left. It also means that 1/5 of remaining spent also means 4/5 left... and the 4/5 left is equivalent to the 2/3 of his TOTAL salary.. so i drew up a model to match this.. from this, i find out that 1unit of the 1/5 remaining is half of 1unit of the 1/3 salary. So i can conclude that the "1/5" + $450 is equivalent to 1/3 of his TOTAL salary and that $450 is "1/5" which is 1/6 of the TOTAL salary.

Hope this helps... :) you can redraw the model to make it clearer..