Greek Anthology Book XIV: Metrodorus: 127

Arithmetical Epigram of Metrodorus

 * Demochares lived for a quarter of his whole life as a boy,
 * for a fifth part of it a young man,
 * and for a third as a man,
 * and when he reached grey old age he lived thirteen years more on the threshold of eld.

Solution
Let $n$ be the age in years of Demochares at his death.


 * $\dfrac n 4$ was spent as a boy


 * $\dfrac n 5$ was spent as a young man


 * $\dfrac n 3$ was spent as a man


 * $13$ more years were spent as an old man.

We have:

So Demochares lived for $60$ years, of which:


 * $15$ years were spent as a boy


 * $12$ years were spent as a young man


 * $20$ years were spent as a man

and as we know:


 * $13$ more years were spent as an old man.