A train passes two persons cycling in the same direction as the train in 10 sec and 15 sec, where the speeds of the two cyclists are 9 km/hr and 18 km/hr, respectively. Find the length of the train.
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74 m
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73 m
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75 m
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70 m
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None of these
C
Correct answer
Explanation
Let L be the length of the train and v be its speed in m/s. Cyclist speeds: 9 km/hr = 2.5 m/s, 18 km/hr = 5 m/s. Relative speeds: (v - 2.5) and (v - 5). L = 10(v - 2.5) and L = 15(v - 5). 10v - 25 = 15v - 75 => 5v = 50 => v = 10 m/s. L = 10(10 - 2.5) = 75 m.