Would you mind...

Hi everyone,

Regarding the following exchange--

A: Hi, Pete. I’m going away for a few days, and I was wondering if you’d mind feeding my cat while I’m away.
B: Yeah, sure. No problem.

I know that going by a strict literal reading of the question/statement that B's reply should be "No, I don't mind" -- but would you guys agree that, idiomatically and following the normal conventions of conversation, B's reply of "Yeah, sure. No Problem" is pretty natural and unambiguous?

Thanks in advance

TT