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A coolie standing on a railway platform observe that a train going in one direction takes 4 second to pass him. Another train of same length going in opposite direction takes 5 seconds to pass him. The time taken (in seconds) by two train to cross each other will be:

A coolie standing on a railway platform observe that a train going in one direction takes 4 second to pass him. Another train of same length going in opposite direction takes 5 seconds to pass him. The time taken (in seconds) by two train to cross each other will be: Correct Answer $$\frac{{40}}{9}$$ seconds

Let length of each train be X m, then
$$\eqalign{ & {S_1} = \frac{X}{4}\,{\text{and}} \cr & {S_2} = \frac{X}{5} \cr & {\text{Required time to cross each other,}} \cr & = {\frac{{2X}}{{ { {\frac{X}{4}} + {\frac{X}{5}} } }}} \cr & = \frac{{40}}{9}{\text{seconds}} \cr} $$

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