I take this kind of approach :

College years normally starts from 16 upwards. In US, normally it is 18 I think. So, since the question asks that his age by now is equal to the sum of the digits as he was born. We can eliminate the year 2000 and up. Because the highest possible sum of numbers is 11 (year 2009).

And by looking, the year 1990's and up should be the year Bertie was born because the ages on those bracket are from 17 - 27 (year 2000 and 1990) - The possible years a college student's age. All we need to do now is to find a year that has the sum of the digits equal to the difference on today year (2017).

By trial and error (I would recommend this method since there are only 11 possible trials). We can find out that the year 1994 best fits the criteria given by the problem. Take a look at this :

1994 = 1 + 9 + 9 + 4 = 23

2017 - 1994 = 23.