Well, purple tang I see at LFS are about 2.5 inch and my yellow tang is little bit bigger than 3 inch. That why I am thinking to put Purple Tang in 20 gal for few week and change rock work in my 90.

+1 for the purple, they are very shy and your yellow will be the dominant one and like other have said, I'd stick to just those two

I have to agree with nickguay that the YT are dominant. My YT use to attack my blonde naso tang whenever it got to the end of the 120g tank when the YT likes to spend most of its time.

I think this is a recipe for disaster no matter what tang you get or how big it is. You have a resident yellow tang in at most a 4 foot long tank. By now it think it owns that tank. There's no amount of rock work rearranging you could do in such small of a space for it to think it wasn't its tank.

Purple tangs are the same genus, with a nearly identical body shape. I would be shocked if within moments of adding the purple to your tank one of them wasn't seriously injured. At the very least you're going to be dealing with constant, mid-level aggression between the two, with the dominant one keeping the subordinate one in a near constant state of stress.

I've tried to do what you're doing in 90 gallon tank. It didn't matter what species, or what genus, Zebrasomas were utterly intolerant of another tang in a tank that size. There might be people on here who've gotten away with it for a time, but the chances are good this is not going to work long term.