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Problems on Ages - General Aptitude

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.
Q1:

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

ANS:E - Any two of the three

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 3x + 5 = 4 . This gives x.
4x + 5 5
 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 : t = 4 . This gives t.
t + 5 5
Thus, II and III give the answer.  Correct answer is (E).