Correct Answer - Option 3 : Either I and II

Age of S = x

Age of E = 3x

Statement I. After five years the ratio of their ages would be 5 ∶ 9.

After 5 years,

Age of S = x + 5

Age of E = 3x + 5

Age of S / Age of E = x + 5 / 3x + 5 = 5 / 9 .... (i)

From the equation (i), we can find the value of x.

And from there, we can find the age of E and S and so does the difference.

Thus, statement I alone is sufficient to answer the question.

Statement II: Before ten years, the ratio of their ages was 3 ∶ 1.

Before 10 years,

Age of S = x - 10

Age of E = 3x - 10

Age of S / Age of E = x - 10 / 3x - 10 = 3 / 1 .... (ii)

From the equation (ii), we can find the value of x.

And from there, we can find the age of E and S and so does the difference.

Thus, statement II alone is sufficient to answer the question.

Hence, **Either I or II **is correct.