As revealed in latest chapter,Rin died on 10th of October,
The same day, Naruto born,
Now we all know Kakashi was 26-27 years old at the during part-1, so in short he was 14-15 year old when Naruto born (Naruto was 12-13 year old in Part-1, do math)..Kakashi became Chunnin when he was 6 years younger than Naruto, in short when he was 6-7 year old
Now,in many threads including in
Now 10th October when Rin died was
So he became Jounin 3 years before Rin's death i.e. when he was 10 years old, why 3 years, because 365*3/29.5=37.12(also fraction but with less remainder so can be considered accurate, because of leap year thing, take 365+366+365, it will be accurate) it also proves Kakashi's physical change(growth)->
10 year old Kakashi->
14-15 year old Kakashi->
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it is said that Kakashi promoted to Jounin 13 years before the series started i.e. when he was 13-14 years old, that means there was only one year gap between Kakashi gaiden and nine tails attack on Konoha but Rin died in between this period (Minato was alive and Obito was supposedly dead, and there can't be two October 10's), so in short Kakashi didn't become Jounin at the age of 13-14, now let's say he was 12-13 when he became Jounin,(because we are not exact as we arenot taking birthdays into consideration) that means Rin died when he(Kakashi) was 13-14 year old and on 10th of October..Now 10th October when Rin died was
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, 10th October when Naruto born was also
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, in short we had two full moons in two successive years which is wrong..How?? One year=365 days,365/29.5(minimum difference between two full moons=29.5 days)=12.378(in short fraction,which proves there is remainder and hence no full moon), but it is wrong, as Kishi drew full moon in both the panels, so Kakashi didn't become Jounin at the age of 12-13.(only thing I didn't calculate, or derived from timeline)So he became Jounin 3 years before Rin's death i.e. when he was 10 years old, why 3 years, because 365*3/29.5=37.12(also fraction but with less remainder so can be considered accurate, because of leap year thing, take 365+366+365, it will be accurate) it also proves Kakashi's physical change(growth)->
10 year old Kakashi->
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14-15 year old Kakashi->
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-Conclusion-
Kakashi became jounin at the age of around 10 and not when he was 13 years old..