While 60 makes sense in the US, Europe wants 50 (because they use PAL, with 25 fps). In this case, since film has always been done in 24 fps, 48 was chosen for compatibility with that (and cinema projectors).
Frame rate conversion has always been strange though, to make 24fps content 30fps they perform something called 'telecining'. This mixes up different rows of frames to get the new frames. For PAL, they actually just speed up the video (and audio) to 25fps; so shows actually go for less time.
For modern TVs, the screen usually has a rather high refresh rate (60+ Hz). So it can show older framerates (24, 25, 30) quite well by timing frames across multiple refreshes of the screen. These newer framerates can cause trouble, but to compensate you even have some 120 Hz TVs showing up. A lot of modern TVs even have some form of motion compensation, to add new frames into the video. The techniques used for this try to make an approximation of between frames, and usually look 'too smooth', due to the motion blur not being correct.
Frame rate conversion has always been strange though, to make 24fps content 30fps they perform something called 'telecining'. This mixes up different rows of frames to get the new frames. For PAL, they actually just speed up the video (and audio) to 25fps; so shows actually go for less time.
For modern TVs, the screen usually has a rather high refresh rate (60+ Hz). So it can show older framerates (24, 25, 30) quite well by timing frames across multiple refreshes of the screen. These newer framerates can cause trouble, but to compensate you even have some 120 Hz TVs showing up. A lot of modern TVs even have some form of motion compensation, to add new frames into the video. The techniques used for this try to make an approximation of between frames, and usually look 'too smooth', due to the motion blur not being correct.