I forgot who but someone did the math and his age of death is 22 years old, he became Hokage for only a year.It makes sense since Shikaku(who is from Minato's generation) was also father of Choji at that moment and he was 25 during the Kyubi's attack. So just that tell us that he couldn't have been older than 25. Minato who was considered as genius, i don't see why he couldn't have been even younger