Question

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?

Answer 1

Answer: 60 years

Explanation:

Let x denotes the age of Demochares .

Time he spent as a boy =
`(x)/(4)`

Time he spent as a youth =
`(x)/(5)`

Time he spent as a man=
`(x)/(3)`

Time he spent in dotage= 13 years

As per given , we have the following equation:

`x=(x)/(4)+(x)/(5)+(x)/(3)+13`

`x=(15x+12x+20x)/(60)+13` [Take LCM]

`x=(47x)/(60)+13`

`x-(47x)/(60)=13`

`(60x-47x)/(60)=13`

`(13x)/(60)=13`

`x=13*(60)/(13)=60`

Hence, he is 60 years old.