"Aged" vs. "Aging" to describe someone's age
Solution 1:
"AGE"- Be it 'verb' or 'noun' embodies a sense of becoming or being grown up in terms of time from birth or beginning marked by changes may be inward or outward or both applicable to living as well as nonliving.
AGE as noun: Length of time a being or thing existed.
AGE as verb without object: To grow old. (He is ageing rapidly)
AGE as verb with object: to make old. ( Fear aged him)
Ageing/aged : Participle ,gerund / past participle
" Age" embodies this sense of progression or Advancement and its "-ing" form further enhances it and can never mean anything other than conveying something happening or going on. The word-meaning puts a serious limitation on the present participle use of "age" and binds it with the continuing sense only.
So we may write:-
1) Participants aged 20 to 50
2) of the age ranging/spanning from 20 to 50.
AGEING IS A PROCESS , AGED ITS POINTS. If ageing is a flowing stream, aged is to desceibe its innumerable landings
Solution 2:
Why not say "The study included participants between the ages of 20 and 50 years old"?