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.