I have used about 110 template files (tpl.php) in my theme, will that slow my drupal site?
more template files == consume Server performance.
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Say you override the default page.tpl.php with your own in your theme folder, and compare this to the case of using the default. In both cases, one page.tpl.php is being evaluated during the page render process - either the default template or yours. Even if you do not override the template, Drupal must search the theme folder to check if an override exists. Of course, if you have a lot of complex logic in your override the page will render more slowly, but that is not due to the overriding itself.
Creating custom templates with hook_theme might slow things down, though.
In general, caching will do more to speed up your site since it bypasses page rendering altogether.