Valakinek (expressed in whole years) age at death was the 31st part of their birth year. How old was this person in 1930?
I. solution: Let's assume that in 1930, the person was $x$ years old. If they died at the age of $y$, then according to the problem,

$$
31 y + x = 1930
$$

from which

$$
y = \frac{1930 - x}{31} = 62 + \frac{8 - x}{31}
$$

where $0 < x < y$, and $8 - x$ is divisible by 31. Only $x = 39$ satisfies this, because if we choose 8 for $x$, the person would still be alive, and if we choose 70 or a larger value, it would imply that they died before 1930. The problem statement excludes both possibilities.

II. solution: If someone's age ($y$ years) is the 31st part of their birth year, then their age is the 32nd part of their death year. According to the problem, the death occurred between 1930 and 1957, so

$$
1930 < 32 y < 1957
$$

which means

$$
60 \frac{5}{16} < y < 61 \frac{5}{32}
$$

from which

$$
y = 61
$$

Thus, the birth year is $31 \cdot 61 = 1891$, and in 1930, the person was 39 years old.

László Fejes (Makó, József A. g. I. o. t.)