What are their ages in years?

Let G, S, and F represent the ages in years of the grandson, the son, and the father, respectively. Since a year has 365 days, or 52 weeks, or 12 months, the problem can be represented by three equations with three unknowns:

365 G = 52 S (The grandson is about as many days old as the son is in weeks)
12 G = F (The grandson is approximately as many months old as the father is in years)
G + S + F = 120 (The ages of the grandson, the son, and the father add up to 120 years)

Because the grandson’s age is G = F/12, the son’s age can be represented in terms of F by substituting:

S = (365/52)×G
S = (365/52)×(F/12)
The third equation can now be represented with only the father’s age as an unknown:

F/12 + (365/52)×(F/12) + F = 120

Multiplying by 12, we get: 

F + (365/52)×F + 12 F = 120×12
20 F = 1440
F = 72
G = F/12 = 6
S = (365/52)×6 = 42

The father is 72, the son is 42, and the grandson is 6 years old.
You may have noticed that the statement of the problem is somewhat ambiguous: “The grandson is approximately as many months old as the father is in years” indicates that there may be some variance. A year really has 365 1/4 days instead of 365, and 52 weeks times 7 days gives only 364 days in a year. These inconsistencies produce fractional results that need to be rounded.

Doing the division in the following equation:
F + (365/52)×F + 12 F = 120×12

produces 20.019 F = 1440, which is rounded to 20 F = 1440