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The age of 'E' is thrice the age of 'S'. To find out the difference in their ages, which of the following information is/are sufficient?

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

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


1. Only I
2. Only II
3. Either I and II
4. Both I and II

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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.

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