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      Question

      Speed of a car is (v + 3) km/h, which is 10 km/h less

      than that of bike. Time taken by car to cover 84 km is 25% less than the time taken by bike to cover 168 km. Length of a train is (5v + 11) metres. If speed of train is (v - 5) m/s, then find the time taken (in seconds) by train to cross a man standing on a platform of length 420 metres.
      A 6 Correct Answer Incorrect Answer
      B 9 Correct Answer Incorrect Answer
      C 12 Correct Answer Incorrect Answer
      D 10 Correct Answer Incorrect Answer
      E 8 Correct Answer Incorrect Answer

      Solution

      Speed of bike = v + 3 + 10 = (v + 13) km/h 84 ÷ (v + 3) = (3/4) × 168 ÷ (v + 13) Or, 84(v + 13) = 126(v + 3) Or, 84v + 1092 = 126v + 378 Or, 42v = 714 Or, v = 17 Length of train = 5 × 17 + 11 = 96 metres Speed of train = 17 − 5 = 12 m/s Since we need to calculate the time taken by train to cross the man standing on the platform, so the length of the platform will not be considered. Required time = 96 ÷ 12 = 8 seconds

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