The correct answer is Option 3, which states that the average age of the father and his two sons is 28 years.

Here`s why:

1) The average age of father and elder son is 35 years, meaning the total age of both is 35*2 = 70 years.

2) The average age of father and younger son is 32 years, which means the total age of both is 32*2 = 64 years.

So, if we subtract the total age from scenario 2 from scenario 1, we get the age of the elder son which is 70 - 64 = 6 years.

3) The average age of two sons is 17 years, indicating the total age of both sons is 17*2 = 34 years.

If we subtract the age of the elder son from the total age, we get the age of the younger son which is 34 - 6 = 28 years.

Adding up the age of the elder son, the younger son, and the father (which we obtain from either scenario 1 or scenario 2 by subtracting the elder son`s age or the younger son`s age respectively) yields 70 years. Hence, the average age of the father and his two