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      Question

      The question given below consists of a question and 3

      statements given below it. You must decide whether the data provided in the statements is sufficient to answer the question. Two boats X and Y started from point P towards point Q. The speed of the stream is 10 km/hr less than the speed of boat Y. The ratio of the speeds of boat X and boat Y in still water is 4:3. Find the distance between P and Q. I. Total time taken by boat X and Y to travel from P to Q is 11 hours. II. Total time taken by boat X and Y from Q to P in upstream is 45 hours. III. Average speed of boat X and Y in still water is 35 km/hr.
      A Only I and II Correct Answer Incorrect Answer
      B Only II and III Correct Answer Incorrect Answer
      C All I, II and III Correct Answer Incorrect Answer
      D Any II together Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ, Let the speed of boat X and Y in still water be 4a km/hr and 3a km/hr respectively. Speed of stream = (3a - 10) km/hr So, Downstream speed of X = 7a - 10 Downstream speed of Y = 6a - 10 Upstream speed of X = a + 10 Upstream speed of Y = 10 From I, d/(7a - 10) + d/(6a - 10) = 11 Not sufficient alone. From II, d/(a + 10) + d/10 = 45 Not sufficient alone. From III, (4a + 3a)/2 = 35 7a/2 = 35 7a = 70 a = 10 Now a is known, but distance is still not directly known. So III alone is not sufficient. Thus, any two statements together are required. Hence, D is correct.

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