does the white colored pc case turns to yellowish color when it gets old?

Newer cases and future cases (especially white ones) have/will have a better manufactured composition of plastic.Most of the time this applies to plastics not metals but unless in a dirty/dusty environment and long period of exposure to the sun (which the radiation makes the discoloring) it will take at least 10-15 years until discoloring may appear. Even when there is smoking in the room or house it can discolor.So unless the case is frequently exposed to sunlight like next to a window or someone is smoking in your house it shouldn't discolor at all.
It also depends on the cases good quality plastics and metal. Check carefully in reviews or before buying the case.
 


another thing that white cases are prone to get dirty easily...well i have a dusty apartment...because its old

 
Then of course i suggest you see for a different approach in colour (without white) or a case with less white appearance. I recommend more darker colours like even grey is fine. If you give me more info i can try to suggest a good case for you.
 


yeah i thot black and white or red and white would be cool but black and red is very common
 
Black also shows dirt (maybe not as easily as white), but it may come down to finish. A flat finish will hide more marks than a glossy one. I have a piano black glossy case and it shows even the slightest fingerprints like mad. Nothing a little windex can't fix but something to consider. Most of the older beige cases yellowed badly because they were all plastic shells and the type of plastic was prone to things like sun bleaching. More modern white cases are often painted metal which makes a huge difference. Plastic yellows as it ages much much faster than white paint does.