Yesterday I couldn't write. Today I hoped to write about basic geometric concepts. But today also I am very busy and I haven't enough time to write a long topic.

So we can have a small puzzle today. This is an ancient problem dating back to about 310 A.D.
Demochares had one-fourth of his life as a boy, one-fifth as a youth , one-third as a man, and has spent 13 years in his dotage. How old was Demochares?


Another problem of this kind:
A stone weights one Kilogram and half of its weight. What is the actual weight of the stone?

Solutions:
First Question
Let x be Demochares's age.
Then, x/4+x/5+x/3+13=x
ie 47x/ 60+13=60
==>47x/60=47
==>x=60
So, Demochares was 60 years.

Second Question
2 kilogram