61. The number of books issued to readers from the library is $\frac{1}{16}$ of the number of books on the shelves. After transferring 2000 books from the library to the reading room, the number of books absent from the shelves became $\frac{1}{15}$ of the number of books remaining on the shelves. How many books does the library have?
61. Before transferring books to the reading room, the number of books present in the library was 16 times greater than the number of books issued, which means that the number of issued books (absent from the library) constitutes $\frac{1}{17}$ of the total number of books in the library. After issuing 2000 books (transferring to the reading room), the number of absent books became $\frac{1}{16}$ of the total number of books. Therefore, 2000 books constitute $\frac{1}{16}-\frac{1}{17}=\frac{1}{272}$ of the total number of books. Thus, the library has $2000 \cdot 272=544000$ books.