I had the same problem with my Samsung tab 3, 10.1.
All kinds of advice was given to me : change the battery, change the cable inside, dump the tablet etc. etc. The authorised Samsung service centre was of no help.
Finally, on a hunch, I changed to a good quality charging cable (Belkin). I did not change the battery or adapter.
And now, lo and behold, it is charging fine - 100% in 3 hours.!
Nat