Eevee Badge Question

Say you started off with an eevee, and it got to its 25th post to get the normal type badge, but by the 35th post it evolved into a different type. Would the silver badge still be the normal type, or would it change to the new type?

((I use eevee since that's the only one i can think of that changed its type completely @_@))

That would change the badge.
But of course, you could always just RP with another normal type to get a higher rank for the swift badge.
Fortunately, there's not many pokemon that change their type completely, and most of them go dual if they do.