People turning twenty in 2015 were born in 1995.
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Given that the year you're looking at is 2010, if you were 20, you would be born in 1990.
1990
It actually depends. If my birthday is in October and I am 20 on April 24, 2009, then I was born in 1988. If my birthday is in January and I am 20 on April 24, 2009, then I was born in 1989. So your answer depends on what month the person is born in.
If you are now (2010) 20 years old then you were born in 1990.
If they have already turned 19 this year (2010) they were born in 1991, if they will be 20 sometime this year they were born in 1990.