In 1940, a correspondent proposed the following question:A man's age at death was one............How old was he in 1900?

Question

In 1940, a correspondent proposed the following question:

A man's age at death was one twenty-ninth of the year of his birth. How old was he in 1900?

Answer 1

52

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It has to be a mutiple of 29 between 1900 and 1940 if we consider he died wihin this interval.
1940/29=66+ so the number is 66*29=1914. 65 or 67 if multiplied by 29 rusults outside of 1900-1940 window.
The man died at the age of 66 years in 1914. He was 66-14=52 years old in 1900.

Answer 2

He was 44 years old.

From the question you know the man died between 1900 and 1940. We also know his age at death (x) is one twenty-ninth of the year of his birth (29x). If you add his age at death to the year he was born you get the year he died (30x). Only one year between 1900 and 1940 is divisible by 30, 1920 (the year he died). The year he was born can now be found: 1920 * (29/30) = 1856. So in 1900 he was (1900 - 1856) = 44 years old.