A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is
400 m
450 m
560 m
600 m
Explanation:
Let the length of the first train be $ x $ metres.
| Then, the length of the second train is$ \left(\dfrac{x}{2} \right) $metres. |
| Relative speed = (48 + 42) kmph =$ \left(90 \times\dfrac{5}{18} \right) $m/sec = 25 m/sec. |
| $\therefore \dfrac{[x + (x/2)]}{25} $= 12 or$ \dfrac{3x}{2} $= 300 or $ x $ = 200. |
$\therefore$ Length of first train = 200 m.
Let the length of platform be $ y $ metres.
| Speed of the first train =$ \left(48 \times\dfrac{5}{18} \right) $m/sec =$ \dfrac{40}{3} $m/sec. |
| $\therefore (200 + y ) \times \dfrac{3}{40} $= 45 |
$\Rightarrow 600 + 3 y $ = 1800
$\Rightarrow y $ = 400 m.