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The following questions are accompanied by two statements, I and II. Determine which statement(s) is/are sufficient to answer the question. Vessel A contains a mixture of milk and water. Find the quantity of milk in the initial solution. Statement I: When 25 litres of the mixture is extracted from the vessel three times, then the vessel becomes empty. Statement II: When 15 litres of the mixture is replaced by pure milk two times, then the ratio of milk to water in the final mixture becomes 17:8.

1. Neither statement I nor statement II by itself is sufficient to answer the question.
2. Statement II alone is sufficient to answer the question but statement I alone is not sufficient to answer the question.
3. Either statement I or statement II by itself is sufficient to answer the question.
4. Both the statements taken together are necessary to answer the question, but neither of the statements alone is sufficient to answer the question.

Correct answer: Both the statements taken together are necessary to answer the question, but neither of the statements alone is sufficient to answer the question.

Solution

Statement I alone only tells us that repeated extraction empties the vessel, which is not enough to determine the initial milk quantity. Statement II alone gives the final ratio after replacement, but not the starting amount. Together, they provide enough information to form equations and determine the initial quantity uniquely.

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