Thanks for all the replies. This helps.
The two companies are not competitors at all. So that should be okay.
Also I don't mean to do this to cheat any company. Its just that I plan to announce my resignation on Friday from one company. And start work following Monday with the new company. So if the first company takes 2-3 days to react to the whole thing, it may mean that for those 2-3 days I am employed at both place.
Thats all.

