If we have given two same url with different anchor text on a page. Whether Google will give importance to both anchor text Or either of them, if so which one?
Same important provide by the Google for the website. But also give priority by that website your website have received back links.
I am not sure if this experiment holds true in your case. Some time back Rand from Seomoz published an experiment to test the value to anchor texts. He used 2 different anchor texts to point at the same URL. What he found out was that the website ranked for the first anchor text used on the link page. This outcome leads us to believe that if you have multiple anchor text point to the same URL, the anchor text used first will be used for ranking purposes. I think the same would apply in our case.
Ya, Google will give importance to both of them but your overall weightage will be reduced. Means if you give link to your site from single anchor text than you'll get more weightage from it to your website. And if you try to get backlinks to your site with two different anchor text than weightage to your website from backlinks will be reduced.