Question
Speed of a car is (v + 4) km/h, which is 9 km/h less
than that of bike. Time taken by car to cover 108 km is 20% less than the time taken by bike to cover 162 km. Length of a train is (10v + 10) metres. If speed of train is (v - 6) m/s, then find the time taken (in seconds) by train to cross a man standing on a platform of length 480 metres.Solution
Speed of bike = v + 4 + 9 = (v + 13) km/h
108 ÷ (v + 4) = (4/5) × 162 ÷ (v + 13)
Or, 108(v + 13) × 5 = 4 × 162(v + 4)
Or, 540(v + 13) = 648(v + 4)
Or, 540v + 7020 = 648v + 2592
Or, 108v = 4428
Or, v = 41
Length of train = 10 × 41 + 10 = 420 metres
Speed of train = 41 − 6 = 35 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 = 420 ÷ 35 = 12 seconds
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