A train overtake two persons walking along a railway track. The first one walks at 4.5 km/h and the other one walks at 5.4 km/h. The train needs 8.4 s and 8.5 s respectively , to overtake them. What is the speed of the train, if both the persons are walking in the same direction as the train?

66 kkm/h
72 km/h
78 km/h
81 km/h

Correct Answer: 81 km/h

Explanation:

Speed of the person = 4 km/h = 4.5 x (5/18) = m/s = 5/4 m/s = 1.25 m/s
Speed of 2nd person = 5.4 km/h = 5.4 x (5/18) m/s = 3/2 m/s = 1.5 m/s
Let speed of train be x m/s.
Then, (x - 1.25) x 8.4 = (x - 1.5) x 8.5
⇒ 8.4x - 10.5 = 8.5x - 12.75
⇒ 0.1x = 2.25
⇒ x = 22.5
∴ Speed of the train = 225 x (18/5 ) = 81 km/h .

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