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> most DVDs were encoded 480p and 24 fps

Only in NTSC regions. PAL region DVDs are generally 576p and 25 fps.

Since films are shot at 24fps, how were they converted to 25?

> Since films are shot at 24fps, how were they converted to 25?

Sped up by 4% to make them 25fps. The audio is supposed to be pitch-corrected, but some poorly done conversions did not do that.

Does that mean one of the frames is duplicated every second?

No. If you increase the speed of 24 fps video 4%, it becomes 25 fps. Frame count does not change, frames are just shorter.

Yes. Imagine that you had a fast-forward button that changed the time per frame from 41.7ms to 40ms. This is what a cinema-to-PAL conversion does.

It's a bit weird in the sense that everything is sped up and faster than normal. In the other hand, it's super simple and does not introduce the even weirder judder that a cinema-to-NTSC (telecine) conversion would do.

Personally I think it's easier to get used to everything being slightly faster but unmodified otherwise than to having additional frames being inserted and the resulting judder in all motion.

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