Hannah has 16 books.
50% of these books are paperback books.
She gives 7 of her paperback books to a charity shop.
She buys 1 new paperback book.
What percentage of the books she has now are paperbacks?
Initially, Hannah has 16 x 50/100 = <<16*50/100=8>>8 paperback books.
After giving 7 paperback books, she has 8 - 7 = <<8-7=1>>1 paperback book left.
Then Hannah has a total of 16 - 7 + 1 = <<16-7+1=10>>10 books.
Therefore, 1/10 x 100% = <<1/10*100=10>>10% of the books Hannah has now are paperbacks. Answer: \boxed{10}.