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      Question

      A car's speed is 20% faster than that of a bike. The car

      takes 30 minutes longer than the bike to cover 120 km, while the bike covers 80 km. Find the time it takes for an auto rickshaw to travel 154 km, knowing that its speed is the average of the speeds of the car and the bike.
      A 210 minutes Correct Answer Incorrect Answer
      B 180 minutes Correct Answer Incorrect Answer
      C 150 minutes Correct Answer Incorrect Answer
      D 240 minutes Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      Let the speed of bike be 'v' km/h. Speed of car = '1.2v' km/h So, (120/1.2v) - (80/v) = (30/60) Or, (100/v) - (80/v) = (1/2) Or, (20/v) = (1/2) Or, 'v' = 40 Speed of auto = (v + 1.2v) ÷ 2 = 1.1v = 1.1 X 40 = 44 km/h Therefore, required time = (154/44) = 3.5 hours = 3.5 X 60 = 210 minutes 

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