Question
Speed of a car is (v + 2) km/h, which is 8 km/h less
than that of bike. Time taken by car to cover 96 km is 20% less than the time taken by bike to cover 150 km. Length of a train is (5v + 12) metres. If speed of train is (v - 3) m/s, then find the time taken (in seconds) by train to cross a man standing on a platform of length 540 metres.Solution
Speed of bike = v + 2 + 8 = (v + 10) km/h 96 ÷ (v + 2) = (4/5) × 150 ÷ (v + 10) Or, 96 (v + 10) = 120 (v + 2) Or, 96v + 960 = 120v + 240 Or, 24v = 720 Or, v = 30 Length of train = 5 × 30 + 12 = 162 metres Speed of train = 30 − 3 = 27 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 = 162 ÷ 27 = 6 seconds
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