The sum of the ages of Anup and his father is 100.

Solution:

Let Anup's age be $x$ years.

Therefore, his father's age will be $(100-\mathrm{x})$ years.

When Anup is as old as his father after $(100-2 \mathrm{x})$ years,

Anuj's age $=\left(\frac{100-\mathrm{x}}{5}+100-2 \mathrm{x}\right)$ years $=\frac{600-11 \mathrm{x}}{5}$ years.

Again, when Anup is as old as his father,

Let Anup's age be $x$ years.

Therefore, his father's age will be $(100-\mathrm{x})$ years.

When Anup is as old as his father after $(100-2 \mathrm{x})$ years,

Anuj's age $=\left(\frac{100-\mathrm{x}}{5}+100-2 \mathrm{x}\right)$ years $=\frac{600-11 \mathrm{x}}{5}$ years.

Again, when Anup is as old as his father,

Anuj's age $=\mathrm{x}+8$.

Now,

$\frac{600-11 \mathrm{x}}{5}=\mathrm{x}+8$

or $600-11 \mathrm{x}=5 \mathrm{x}+40$

or $16 \mathrm{x}=560$

or $\mathrm{x}=35$.

Thus, Anup's age $=35$ years

Anup's f ather's age $=100-\mathrm{x}=100-35=65$ years

Anuj's age $=\mathrm{x}+8=35+8=43$ years