ANSWER
Find out the how old was we when he died.
To proof
Let us assume that the age of the Adam be x
As given
Adam lived a quarter of his life as a boy as fifth as a young man, a third in middle-age and 13 years in retirement.

L.C.M of denominator i.e ( 4,5,3) =60
than the equation becomes
60x = 15x + 12x +20x +780
60x - 47x = 780
13x = 780

x = 60 years
therefore the Adam age when he died is 60 years.
Hence proved