Let the present ages of Anup, his father and his son Anuj be x, y and z, respectively.
Given that, the sum of ages of Anup and his father is 100
∴ x+y=100 ..........(1)
Let their new ages after few years be x', y' and z', respectively.
Given that, after those few years, new age of Anup = present age of father = 5 × present age of Anuj
∴ x′=y=5z ............(2)
Also, given that new age of Anuj= 8+present age of Anup
∴ z′=8+x .....(3)
∵ Number of years = New age - present age for each person
∴ Number of years =x′−x=y′−y=z′−z
Taking first and last term we have,
x′−x=z′−z..........(4)
Using equations (1), (2), and (3), we get,
x′=y, x=100−y, z′=8+x=8+100−y=108−y, and z=y5
Substituting these values in equation (4), we get:
⇒y−(100−y)=(108−y)−y5
⇒2y−100=108−y−y5⇒2y+6y5=108+100
⇒16y5=208
⇒16y=208×5
⇒y=65
Now, from equation (1) , x=100−y=100−65=35
And from equation (2), z=y5=655=13
Hence, the present age of Anup is 35 years, that of his father is 65 years and that of his son, Anuj is 13 years.