Question

When i am as old as my father is now, i will be five times as old as my son is now. But then, my son will be eight years older than i am now. The combined ages of my father and myself are 100 years. How old is my son?

Answer 1

My son is 13 years old now.

Step-by-step explanation

Suppose, my age
`=m`, my father's age
`=f` and my son's age
`=s`

When I am as old as my father is now that means after
`(f-m)` years, I will be 5 times as old as my son is now. So, the equation is.....

`m+(f-m)=5s\\ \\ f= 5s ..........................(1)`

And then means after
`(f-m)` years, my son will be 8 years older than I am now. So.....

`s+(f-m)=m+8\\ \\ s+f=2m+8........................(2)`

Substituting equation (1) into equation (2), we will get.....

`s+5s=2m+8\\ \\ 6s=2m+8\\ \\ 3s=m+4\\ \\ m=3s-4 .....................................(3)`

The combined ages of my father and myself are 100 years. So.....

`f+m=100...............................(4)`

Now substituting
`f=5s` and
`m=3s-4` into equation (4), we will get.....

`5s+(3s-4)=100\\ \\ 8s-4=100\\ \\ 8s=104\\ \\ s=(104)/(8)=13`

So, my son's age is 13 years now.