The correct answer is option 2 - II only.

To understand why, let`s break down both statements:

I. The sum of the number of persons who take either tea or coffee or both is four times the number of persons who take both coffee and tea.

This statement is incorrect. From the data given in the question, we don`t have information to validate this assertion. There`s no given relationship in the question that would imply that the total number of persons who take tea, coffee or both is four times the number of persons who take both.

II. The sum of the number of persons who take only coffee and those who take only tea is twice the number of persons who take both tea and coffee.

This statement is correct. The question tells us that the number of persons who take coffee is twice the number of persons who take only tea and the number of persons who take tea is twice the number of persons who take only coffee. Therefore, the sum of people who take only coffee and those who take only tea would logically be twice the number of persons who take both tea and coffee.

Hence option 2 (II only) is the correct answer.