Question : On parallel tracks, two trains of equal length are moving at speeds of 46 and 36 kilometres per hour in the same direction. In 36 seconds, the quicker the train overtakes the slower one. The length of each train is:
Option 1: 60 metres
Option 2: 50 metres
Option 3: 56 metres
Option 4: 52 metres
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Correct Answer: 50 metres
Solution :
Let the length of the trains be $x$ metre each.
So, the distance to be covered = 2$x$
Now the trains are running in the same direction.
So, their relative speed = (46 − 36) kilometres per hour
= 10 kilometres per hour
= $\frac{10\times{5}}{18}$ metres per second
= $\frac{25}{9}$ metres per second
So, the time taken by the trains to cover 2$x$ metre distance = $\frac{2x}{\frac{25}{9}}$ seconds
By the given conditions,
$2x = {\frac{25}{9}}× 36$ seconds
$\therefore x = 50$ metres
So, the length of each train is 50 metres.
Hence, the correct answer is 50 metres.
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