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

Step-by-step explanation:

Let x denotes the age of Demochares .

Time he spent as a boy = $\dfrac{x}{4}$

Time he spent as a youth = $\dfrac{x}{5}$

Time he spent as a man= $\dfrac{x}{3}$

Time he spent in dotage= 13 years

As per given , we have the following equation:

$x=\dfrac{x}{4}+\dfrac{x}{5}+\dfrac{x}{3}+13$

$x=\dfrac{15x+12x+20x}{60}+13$  [Take LCM]

$x=\dfrac{47x}{60}+13$

$x-\dfrac{47x}{60}=13$

$\dfrac{60x-47x}{60}=13$

$\dfrac{13x}{60}=13$

$x=13\times\dfrac{60}{13}=60$

Hence, he is 60 years old.