Multiple choice

Passage

Directions: The question below is followed by three statements labelled I, II and III. You have to consider the information in all the three statements and decide which of the statements is/are necessary to answer the question. Indicate your answer accordingly.

What is Suchitra's present age? I. Suchitra's present age is double the age of her son. II. Ratio of the present ages of Suchitra and her mother is 2 : 3. III. Four years hence, the ratio of Suchitra's age to that of her son will be 24 : 13.

  1. Both I and III

  2. Both I and II

  3. All I, II and III

  4. Only II or III

  5. None of these
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A Correct answer
Explanation

Let S be Suchitra's age and s be her son's age. Statement I gives S = 2s. Statement III gives (S+4)/(s+4) = 24/13. With two variables and two independent equations, we can solve for S. Statement II is irrelevant as it introduces a third person (mother) without linking to the son.

AI explanation

Let Suchitra's present age be S and her son's age be Y. Statement I provides the equation S = 2Y. Statement III provides the equation (S + 4) divided by (Y + 4) equals 24 divided by 13. Substituting the first equation into the second gives (2Y + 4) divided by (Y + 4) equals 24 divided by 13, which simplifies to 26Y + 52 = 24Y + 96. Solving for Y gives 2Y = 44, making the son 22 years old and Suchitra 44 years old. Therefore, statements I and III together are necessary to find the answer, while statement II is insufficient.

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