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      Question

      I: A car travels from town P to town Q at a speed of 60

      km/h, and returns from Q to P at a speed of 90 km/h. The total time taken for the entire journey (P → Q → P) is 5 hours. II: The car’s fuel consumption per kilometre is the same in both directions. What is the distance between P and Q (in km)?
      A 120 km Correct Answer Incorrect Answer
      B 180 km Correct Answer Incorrect Answer
      C 200 km Correct Answer Incorrect Answer
      D 165 km Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      Let distance between P and Q be d km. Time from P to Q = d/60 hours Time from Q to P = d/90 hours Total time = d/60 + d/90 = 5 LCM of 60 and 90 is 180: d/60 = 3d/180 d/90 = 2d/180 So: (3d + 2d) / 180 = 5 5d / 180 = 5 Multiply both sides by 180: 5d = 900 d = 900 ÷ 5 = 180 km So the distance between P and Q is 180 km.

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