Which one is more common?

[ARMION+]

Two similar sentences, which of them is more common nowadays?

A person can do his or her work.

A person can do their work.

[Casiopea]

Two similar sentences, which of them is more common nowadays?

A person can do his or her work.
A person can do their work.

I'm not sure which is 'more common', but the former is definitely the more preferred in terms of traditional grammar. In academic circles both are preferred. There are professors who prefer 'their' and professors who prefer the more traditional his or her/her or his. If you're writing a paper, either check with your teacher first or use the traditional form.

All the best, :D