Answer: 60 years
Step-by-step explanation:
Let x denotes the age of Demochares .
Time he spent as a boy = [tex]\dfrac{x}{4}[/tex]
Time he spent as a youth = [tex]\dfrac{x}{5}[/tex]
Time he spent as a man= [tex]\dfrac{x}{3}[/tex]
Time he spent in dotage= 13 years
As per given , we have the following equation:
[tex]x=\dfrac{x}{4}+\dfrac{x}{5}+\dfrac{x}{3}+13[/tex]
[tex]x=\dfrac{15x+12x+20x}{60}+13[/tex] [Take LCM]
[tex]x=\dfrac{47x}{60}+13[/tex]
[tex]x-\dfrac{47x}{60}=13[/tex]
[tex]\dfrac{60x-47x}{60}=13[/tex]
[tex]\dfrac{13x}{60}=13[/tex]
[tex]x=13\times\dfrac{60}{13}=60[/tex]
Hence, he is 60 years old.
