Dante's Infernal Puzzle Collection -- 15. Demochares

Denote Demochares's age at death by x.

From the information provided in the question, we know:
(1/4)x + (1/5)x + (1/3)x + 13 = x
(1/4 + 1/5 + 1/3)x + 13 = x
[(15 + 12 + 20)/60]x + 13 = x
(47/60)x + 13 = x
13 = (13/60)x
x = 60

Answer: 60