Solved the problem of keeping fit (6,3)
I believe the answer is:
worked out
'keeping fit' is the definition.
The answer and definition are not the same part of speech. However, adjectives and past participle verbs can occasionally define each other.
'solved the problem' is the wordplay.
'solved' becomes 'worked' ('work' can be a synonym of 'solve').
'the problem' becomes 'out' (I can't explain this - if you can you should believe this answer much more).
'worked'+'out'='WORKED OUT'
'of' acts as a link.
Can you help me to learn more?
(Other definitions for worked out that I've seen before include "Went training" , "planned" .)