Detective Fix is pursuing Phileas Fogg around the world in an attempt to arrest him for robbing a bank—Fogg has absolutely no clue this is happening throughout the entire trip, so this is a huge example of dramatic irony. Even more ironic is that Passepartout eventually finds out, too, but still Fogg has no idea.
The Early Arrival (Situational Irony)
Fogg has meticulously planned every aspect of this voyage around the world. He is extremely organized and prepared for everything that comes their way. Because of this, it is extremely ironic that he failed to realize they would gain a day traveling eastward, and he had no idea that they arrived early when they made it back to London.
Passepartout's Suspicions (Dramatic Irony)
In the middle of the journey, Passepartout comes to the conclusion that Detective Fix is actually a member of the Reform Club, sent to monitor Fogg's progress along the world to see if he actually completes the task. This is an example of dramatic irony as well, since readers know that this is not true and that Fix is really a detective out to arrest Passepartout's master.
Passepartout's New Job (Dramatic Irony)
Early on in the novel, after Passepartout has just been introduced, he announces that he has come to work for Fogg "in the hope of living with him a tranquil life" (pg. 3), which is ironic since tranquil is the last thing Passepartout's life will be as he serves Fogg and gets dragged on a madcap journey around the world.
Around the World in 80 Days Questions and Answers
The Question and Answer section for Around the World in 80 Days is a great
resource to ask questions, find answers, and discuss the novel.