In The Lord of the Rings: The Fellowship of the Ring, 17 years pass before Frodo leaves Hobbiton after Bilbo’s birthday party.
Bilbo’s elaborate 111th birthday celebration opens the film’s story in the Shire. He leaves the party using the One Ring, while Frodo remains behind with the Ring in Bag End. The narrative then jumps forward before Gandalf returns to explain what the Ring really is and why Frodo must leave.
This time span comes from Tolkien’s chronology and is reflected in the film’s opening setup. It is easy to miss because the movie moves quickly from Bilbo’s departure to Gandalf’s investigation and Frodo’s journey. The 17-year gap also explains why Gandalf’s discovery is not immediate after the party.
A common mix-up is to answer with Bilbo’s age at the party, 111, or Frodo’s age when he leaves. The question concerns elapsed time, not either character’s age. Frodo is 33 when Bilbo’s party takes place and 50 when he sets out in the book’s chronology.