can 2 gateways exist in same network?

Yep. That's the correct way. The IP addresses are also correct. One of your unspecified Linksys routers acts normally as an ethernet router. The other unspecified Linksys wireless router is actually acting as an "access point", where the router and DHCP server features are disabled. This is a good arrangement as it allows the ethernet router to sit on the floor where all the cables come together, while the wireless box can sit high on a bookshelf where it has a better view of the coverage area.

Thanks for the confirmation...

kevd