Question

The sum of ages of anup and father is 100. When anup is as old as his father now, he will be 5 time as old as his son anuj now. Anuj will be 8 years older than anup is now , when anup is as old as his father. What are their ages now?

Answer 1

Let the ages of Anup be A
                       Anup's Father be F
                       Anup's Son be S

Equation 1   The sum of ages of Anup and Father is 100
                   A+F=100
Equation 2  When Anup is as old as his father now, He will be 5 Times As old as this son Anuj (5S)
                    F=5S
Equation 3  Anuj(S) will be 8 years older, than Anup(A) , when Anup is as old as his father(F).
                   8+A=S+(F-A)

Now substitute F=5s in eq 3
                  8+A=S+(5S-A)
                  8+2A=6S
                 A=(6S-8)/2
now substitute A in eq 1
                 (6S-8)/2 + 5S =100
                  6S-8+10S=200
                      16S=208
                          S=13
HENCE F= 5S
            F=65
            A= 100-F
            A=100-65
            A=35

Thus the ages of Anup is 35
                         Anup's Father 65
                         Anup's son Anuj 13 at Present