Let Anup's age be A and Anup's father's age = F. Then A + F = 100.

Father's age F = 100 - A.

When Anup is as old as his father, his age will be (100 - A).

Difference between Anup's age now and then = (100 - A) - A = (100 - 2A).

Hence Anup will reach his father's age after (100 - 2A) years.

Anuj's age now = (1/5) of Anup's age when his age equals his father's age = (100 - A)/5.

Anuj's age when Anup attains his father's age,i.e., after (100 - 2A) Years = [(100 - A)/5] + (100 - 2A).

This age is 8 years more than Anup's age now,i.e., 8 more than A = A + 8.

Hence [(100 - A)/5] + (100 - 2A) = A + 8

Solving, Anup's age A = 35, Anup's father's age F = 65, Anuj's age = (100 - 35)/5 = 13.