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### Discussion :: Problems on Trains

1. 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:

2.  A. 45 m B. 50 m C. 54 m D. 72 m

Explanation :

2kmph = $$(2\times\frac{5}{18})m/sec = (\frac{5}{9})m/sec$$

4kmph = $$(4\times\frac{5}{18})m/sec = (\frac{10}{9})m/sec$$

Let the length of the train be x metres and its speed by y m/sec.

Then, $$\left(\frac{X}{Y-\frac{5}{9}}\right)=9$$ and  $$\left(\frac{X}{Y-\frac{10}{9}}\right)=10$$

9y - 5 = x and 10(9y - 10) = 9x

On solving, we get: x = 50.

Length of the train is 50 m

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