I would say early 20s. Katy Manning herself was just 23 when her final story, "The Green Death", was aired around June 1973.
Ms. Manning will also be making a return to her Jo Grant role in the new season of "The Sarah Jane Adventures", alongside Sarah and the Eleventh Doctor.
As with most companions, the show never gave a definitive answer.
If you're asking how old she's supposed to be now, in her upcoming Sarah Jane Adventures episode, it's probably somewhere in her late 50s. We don't know whether "The Green Death" was supposed to take place in 1973, 1978, or 1980 (see the article on the UNIT dating controversy for details). And we don't know whether Sarah Jane Smith, her replacement, played by 25-year-old Elisabeth Sladen, was supposed to be 22, 27, or 29.
However, we do know that Sarah Jane Smith is 58 right now (born in May 1951), and Elisabeth Sladen is 62 (born in February 1948), and Katy Manning is 60 (born October 1949).
So, if we assume Jo Grant was a couple years younger than Sarah Jane Smith or so, then she's somewhere near 56.