Demochares has ived a fourth of his life as a boy, a fifth as a youth, a third as a man, and has spend 13 years in his dotage. how old is he?

 60 years

Step-by-step explanation:

Let x denotes the age of Demochares .

Time he spent as a boy =

Time he spent as a youth =

Time he spent as a man=

Time he spent in dotage= 13 years

As per given , we have the following equation:

 [Take LCM]

Hence, he is 60 years old.