Man whose death age was a 29th of his birth year

A man's age when he died was exactly one twenty-ninth of the year he was born. He was alive for his birthday in 1900 and died before 1945. What age did he reach on his 1900 birthday?

$44$. If he died aged $x$, he was born in $29x$ and died in $30x$. The only multiple of $30$ after 1900 and before 1945 is 1920, so $x=64$ and he was born in 1856, making him $44$ in 1900.