We know all the years start with 19.  Let's just consider the
last two digits of the year.  For example 1996 will be called just
96 and, say, 1935 would, for instance, be called just 35.

96 - age = birth year

let t = tens digit of the birth year
let u = units digit of the birth year
birth year = 10t + u

1·9·t·u = 9tu = product of digits of birth year = age 

96 - 9tu = 10t + u 

Solve for u

96 - 10t = 9tu + u

96 - 10t = u(9t + 1)

 = u

u = 

We start trying digits for t until we get a digit for u

try t = 0, u =  =  =  = 96, not a digit

try t = 1, u =  =  = , not a digit

try t = 2, u =  =  =  = 4.  Hooray, that's a digit, so we found one answer:

t = 2, u = 4, birth year = 1924, age = 1·9·2·4 = 72, must be the grandfather.
Checking 1996-1924 = 72, so that checks.  

We need another solution for the daughter:

try t = 3, u =  =  = , not a digit.

try t = 4, u =  =  = , not a digit. 
 
try t = 5, u =  =  =  = 1, hooray, another digit.

t = 5, u = 1, birth year = 1951, age = 1·9·5·1 = 45, must be the daughter.
Checking 1996-1951 = 45, so that checks. 

Answer: the grandfather was born in 1924 and was 72 in 1996          
        the daughter was born in 1951 and was 45 in 1996.

Edwin