Option 1: We cannot ascertain that `A is older than B` because it may be that A and B are of the same age.

Option 2: `B and D are of the same age` cannot be concluded because nothing relates B to D in terms of age in the given statements.

Option 3: `D is older than C` can be one of the possibilities but not a definite conclusion because C and D can also be of the same age as stated in the II statement; thus, we cannot draw this conclusion definitely.

Option 4: `A is older than C` is the correct answer. Here`s why - Given that `B is older than C` (from Statement III), and from Statement I, there are two possibilities; either A and B are of the same age, or A is older than B. In both scenarios, A is definitely older than C. Therefore, we can draw this conclusion from the given statements.