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      Question

      The speed of the boat exceeds the

      speed of the stream by 66.67%. Determine the speed of the boat in still water. Statement I: The time required for the boat to travel (12d−6)km downstream is the same as the time required to travel (d+18) km upstream. Statement II: The boat can travel 91.2km downstream in 11.4hours.
      A Only I alone is sufficient Correct Answer Incorrect Answer
      B Only II alone is sufficient Correct Answer Incorrect Answer
      C Both I & II are together sufficient Correct Answer Incorrect Answer
      D Either I or II alone is sufficient Correct Answer Incorrect Answer
      E Both I & II together are not sufficient Correct Answer Incorrect Answer

      Solution

      ATQ, Let speed of boat in still water be 'v' & speed of stream be 's' Then, v:s = 5:3  v+s = 8 [downstream speed] & v – s = 2 [upstream speed] From St.I we have Given time is constant, so ratio of speed = ratio of distance covered. D1/D2 = S1/S2 (12-d)/(d+18) = 8/2 So here by determining 'd' we can determine and determine the value of 'd' but still  we do not have the time. So we still cannot determine the speed of boat in still  water. Thus statement I is not sufficient to answer the question. From St.I we have Downstream speed (v+s) = 91.2/11.4 = 8 km/h v +s= 8u = 8 km/h So, v = 5u = 5km/h Thus statement II is sufficient to answer the question

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