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      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. 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.
      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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