Well, every studio had their "Music Directors" - and if there wasn't a budget for a new musical score for a particular film, the musical director - who was a composer himself, usually - could "cut and paste" music cues from other scores to weave into a "new" score. For years, I've tried to figure out where the music cues from THE DEVIL BAT (1941) came from. I've never heard them from any previous film, but it appears that David Chudnow had them in his music library of "cues." the sloppier way of doing this was to have a film music editor literally "cut and paste" music tracks together, but the best way - if you had a musical director - was to rework "cues" from older "library" scores and write them into a fairly seamless musical score.
When pressed for time, composers like Has Salter or Frank Skinner or Max Steiner or Erich Wolfgang Korngold might take small pieces from other earlier compositions and weave them into new scores. I suspect that they did this at Fox more often than we might realize! I've heard cues from CHANDU THE MAGICIAN used in CHARLIE CHAN IN EGYPT and THE GORILLA - for example!
Question on CHARLIE CHAN IN EGYPT - are those "reconstructed" main titles for the film? The music seems like a patch job - from the rarely heard "exit music" CHANDU THE MAGICIAN (which is sadly, NOT on the "official" version of the film on DVD - and I suspect - the Blu-Ray version). I've heard that the film was one of the first to make it to TV - was there a problem with the main titles on that film?