When you add the People Search Box Web Part to your page, the layout looks fine.
People Search Box
The problem arises when you click on the Search Options link.
People Search Box Layout Problem
As you can see, the property box is shown with a transparent background and the labels are almost unreadable.
Solution
To solve this problem, you could add the following CSS styles to your custom stylesheet or inside the master page itself.
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.psrch-OptionsContainer {
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font-size: 8pt;
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height: 130px;
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margin-top: 20px;
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width: 355px;
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}
Result
People Search Box With CSS Fix
Source: Fix: People Search Box Has Layout Problems When Used Outside a Search Center
Aryan Nava 
i am experiencing the same problem as you show above in my test farm that has a customized master page and style sheet, but not in my farm that has not been customized. The ootb farm works fine because it includes a background image in the psrc-optionscontainer class as well as a few other properties. I can’t figure out why thes properties are not showing up in my test envrironments style sheet. It looks like you are havnig the same problem, i think your suggestion is on the right track but there is something else going on that is causing our problems. please let me know if you have any thoughts on this and i’ll let you know what i find.
Yes your correct. I developed custom search box to resolve this problem. If you want let me know.