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A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is ?
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- 72 meters
- 54 meters
- 50 meters
- 45 meters
Correct Option: C
Let the length of the train be L km and its speed by y km/hr
Then , speed of train relative to first man = (y - 2) km/hr
Speed of train relative to second man = (y - 4) km/hr
∵ L / (y - 2) = 9 /(60 x 60)
and L / (y - 4) = 10/ (60 x 60)
∴ 9y - 18 = 3600 x L ...(1)
and 10y - 40 = 36000 x L ... (2)
So, 9y - 18 = 10y - 40
⇒ y = 22
∵ L/ (22 - 2) = 9/ 3600
∴ L = (20 x 9) / 3600 = 1/20 km = (1/20) x 1000 = 50 m.
