The sum of the age of a father and his son is 100 years now.  5 years ago their age was in the ratio of 2 : 1.  The ratio of the age of father and son after 10 years will be:

5 : 3

Age of father and son 5 years ago = 100 - 2 × 5 = 90

    F   :    S

    2   :    1           [3R = 90 ⇒ 1R = \(\frac{90}{3}\) = 30]

  ×30     ×30

   60       30     (age 5 years ago)

   +5      +5      (at present)

  +10     +10    (after 10 years)

   75       45

    5    :    3

Now,

Required ratio = F  :  S = 5  :  3