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      Question

      A man rows a boat 36 km upstream and the same distance downstream. The speed of the stream is 3 km/h. It takes him 3 hours more to cover the upstream journey than the downstream journey. What is the time taken by him to row 54 km in still water?

      A 2 hrs Correct Answer Incorrect Answer
      B 11 hrs Correct Answer Incorrect Answer
      C 6 hrs Correct Answer Incorrect Answer
      D 10 hrs Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ, Let speed of boat in still water = v km/h Speed of stream = 3 km/h Upstream speed = v − 3 Downstream speed = v + 3 Given: 36/(v − 3) − 36/(v + 3) = 3 Compute LHS: 36[(v + 3) − (v − 3)] / [(v − 3)(v + 3)] = 36 × 6 / (v² − 9) = 216 / (v² − 9) So, 216 / (v² − 9) = 3 ⇒ v² − 9 = 216/3 = 72 ⇒ v² = 81 ⇒ v = 9 km/h (take positive speed) Time to row 54 km in still water = distance / speed = 54 / 9 = 6 hours

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