Each question below is followed by two statements I and II. You have to determine whether the data given in the statements are sufficient for answering the question. You should use the data and your knowledge of mathematics to choose the best possible answer. The present age of A is 2/5 of the present age of B then what are their ages. Statement I: After 10 years, the ratio of their ages will become 4 : 7 Statement II: 4 years ago, the ratio of their ages was 2 : 7

Each question below is followed by two statements I and II. You have to determine whether the data given in the statements are sufficient for answering the question. You should use the data and your knowledge of mathematics to choose the best possible answer. The present age of A is 2/5 of the present age of B then what are their ages. Statement I: After 10 years, the ratio of their ages will become 4 : 7 Statement II: 4 years ago, the ratio of their ages was 2 : 7 Correct Answer <p>If the data either in statement I alone or in statement II alone is sufficient to answer the question.</p>

Calculation:

Let the ages of A and B be 2x and 5x respectively.

From statement I

Ages of A and B after 10 years will be (2x + 10) years and (5x + 10) years respectively.

Then, (2x + 10)/(5x + 10) = 4/7

⇒ 14x + 70 = 20x + 40

⇒ 20x – 14x = 70 – 40

⇒ 6x = 30

⇒ x = 5

A’s present age = 2 × 5

⇒ 10 years

B’s present age = 5 × 5

⇒ 25 years

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

From statement II

Ages of A and B 4 years ago were (2x – 4) years and (5x – 4) years respectively.

Then, (2x – 4)/(5x – 4) = 2/7

⇒ 14x – 28 = 10x – 8

⇒ 14x – 10x = 28 – 8

⇒ 4x = 20

⇒ x = 5

A’s present age = 2 × 5

⇒ 10 years

B’s present age = 5 × 5

⇒ 25 years

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

∴ Either statement I alone or statement II alone is sufficient to answer the question.

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