19 Hobbit chapters + 62 LotR chapters = 81 chapters.
The Hobbit and LotR are basically what make up the Red Book; the rest of the information (appendices, etc.) are held in different books:
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But annexed to [The Red Book]and preserved with it, probably in a single red case, were the three large volumes, bound in red leather, that Bilbo game to him as a parting gift. To these four volumes there was addedin Westmarch a fifth containing commentaries, genealogies, and various other matter concertning the hobbit members of the Fellowship.
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