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    Question

    The question consists of two statements numbered "l and II" given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.

    Determine the time taken by a pipe R to empty a water

    tank. Statement I: Pipe P and pipe Q can fill a water tank in 6 hours and 8 hours, respectively. If all pipes P, Q, and R are opened together, the time taken by all three pipes to fill the water tank is 120/23 hours. Statement II: Pipe P can fill the water tank in 6 hours, and the ratio of the efficiencies of pipes Q and R is 2:1.
    A The data in both statements I and II together are necessary to answer the question. Correct Answer Incorrect Answer
    B The data given in both statements I and II together are not sufficient to answer the question. Correct Answer Incorrect Answer
    C The data either in statement I alone or in statement II alone are sufficient to answer the question. Correct Answer Incorrect Answer
    D The data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question. Correct Answer Incorrect Answer
    E The data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question. Correct Answer Incorrect Answer

    Solution

    ATQ, Statement I: Let, the total capacity of tank be 120 units. Efficiency of P = 120/6 = 20 units/hr Efficiency of Q = 120/8 = 15 units/hr Let, the efficiency of R be 'a' units/hr. So, 120/23 = 120/(20 + 15 – a) Or, 120/23 = 120/(35 – a) Or, a = 12 Time taken by pipe R to empty the water tank = 120/12 = 10 hours So, data in statement I alone is sufficient to answer the question. Statement I: We cannot determine the relation between pipes P, Q and R. So, data in statement II alone is not sufficient to answer the question.

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