The sum of the ages of Anup and his father is 100. When Anup is as old as his father now, he will be five times as old as his son anuj is now. Anuj will be eight years older than Anup is now, when anup is as old as his father. What are their ages now?

The sum of the ages of Anup and his father is 100. When Anup is as old as his father now, he will be five times as old as his son anuj is now. Anuj will be eight years older than Anup is now, when anup is as old as his father. What are their ages now?

Sol :

Let Anup's present age be x years.
His father's present age = 100 - x.
Therefore, Anup's present age = (100-x)/5 years.

Anup becomes as old as his father is now after (100-2x) years.

Therefore after 100-2x years, we have anup's age = {(100-x)/5 (100-2x)} =(600-11x)/5.

It is given that after 100-2x years, Anuj is 8 years older than his father Anup is now.

Therefore, (600-11x)/5 = x + 8. 
     ==>     600 - 11x    = 5x + 40.
     ==>          600 - 40 =  5x + 11x.
    ==>            560       =  16x
    ==>                     x  =  560/16  = 35.

Hence , Anup's present age be 35 years
His father's present age = 100 - 35 = 65