# Problems on Ages – Data Sufficiency 2

Directions to Solve

Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.

1.
 What is Arun’s present age? I. Five years ago, Arun’s age was double that of his son’s age at that time. II. Present ages of Arun and his son are in the ratio of 11 : 6 respectively. III. Five years hence, the respective ratio of Arun’s age and his son’s age will become 12 : 7.
 A. Only I and II B. Only II and III C. Only I and III D. Any two of the three E. None of these

Explanation:

II. Let the present ages of Arun and his son be 11x and 6x years respectively.

I. 5 years ago, Arun’s age = 2 x His son’s age.

III. 5 years hence, Clearly, any two of the above will give Arun’s present age. Correct answer is (D).

2.
 What is Ravi’s present age? I. The present age of Ravi is half of that of his father. II. After 5 years, the ratio of Ravi’s age to that of his father’s age will be 6 : 11. III. Ravi is 5 years younger than his brother.
 A. I and II only B. II and III only C. I and III only D. All I, II and III E. Even with all the three statements answer cannot be determined.

Explanation:

I. Let Ravi’s present age be x years. Then, his father’s present age = 2x years.

II. After 5 years, III. Ravi is younger than his brother.

From I and II, we get This gives x, the answer.

Thus, I and II together give the answer. Clearly, III is redundant. Correct answer is (A).

3.
 What is the present age of Tanya? I. The ratio between the present ages of Tanya and her brother Rahul is 3 : 4 respectively. II. After 5 years the ratio between the ages of Tanya and Rahul will be 4 : 5. III. Rahul is 5 years older than Tanya.
 A. I and II only B. II and III only C. I and III only D. All I, II and III E. Any two of the three

Explanation:

I. Let the present ages of Tanya and Rahul be 3x years and 4x years.

II. After 5 years, (Tanya’s age) : (Rahul’s age) = 4 : 5.

III. (Rahul’s age) = (Tanya’s age) + 5.

From I and II, we get This gives x. Tanya’s age = 3x can be found. Thus, I and II give the answer.

From I and III, we get 4x = 3x + 5. This gives x. Tanya’s age = 3x can be found. Thus, I and III give the answer.

From III : Let Tanya’s present age be t years.

Then Rahul’s present age = (t + 5) years.

Thus, from II and III, we get : This gives t.

Thus, II and III give the answer. Correct answer is (E).

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