Multiple choice

Directions: The question below is followed by two statements numbered I and II. You have to decide whether the data provided in the statements is sufficient to answer the question. What is the difference between the ages of Madhu and Shweta? I. The sum of their ages is 75 years and their ages are in the ratio 3 : 2 or 2 : 3. II. Madhu is 45 years old and the respective ratio of ages of Shweta and Madhu is 2 : 3.

  1. Data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.

  2. Data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.

  3. Data either in statement I alone or in statement II alone is sufficient to answer the question.

  4. Data given in both the statements I and II together is not sufficient to answer the question.

  5. Data given in both the statements I and II together is sufficient to answer the question.
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C Correct answer
Explanation

Statement I provides the sum (75) and the ratio (3:2 or 2:3), allowing us to find the ages (45 and 30) and their difference (15). Statement II provides Madhu's age (45) and the ratio of Shweta to Madhu (2:3), which allows us to find Shweta's age (30) and the difference (15). Both statements independently provide sufficient information.

AI explanation

Statement I provides the sum as 75 and the ratio as 3 to 2, allowing you to find the individual ages of 45 and 30 by dividing 75 by 5 and multiplying by the ratio terms, yielding a difference of 15. Statement II explicitly states Madhu is 45 and the ratio of Shweta to Madhu is 2 to 3, meaning Shweta is 30, which also yields the 15-year difference. Therefore, data in either statement alone is sufficient to answer the question.

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