How old was Timothy when he met Paul?

Many Scholars believe he must of been in his thirties.

Here is a quote from a commentary

"The Word youth in the ancient Greek was "Used of grown-up military age, extending to the 40th year" (Lock, cited in Earle). It seems that Timothy was about 30 years old at this time; but Paul was around 70, so youth is a relative thing."

The link is below.

Ref: http://www.blueletterbible.org/cgi-bin/comm_read.pl?book=1Ti&chapter=4&verse=12&Comm=Comm%2Fdavid_guzik%2Fsg%2F1Ti_4.html%230%26*David+Guzik%26&Select.x=17&Select.y=6

Most scholars believe this, and it makes sense from what we know of Jewish culture, anyone under thirty would still be studying under a rabbi. The Age of 30 years old is when most rabbi's would start their ministry and be able to Teach others.