## Problem on Trains

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

**Options:**

A. | 400 m |

B. | 450 m |

C. | 560 m |

D. | 600 m |

**Answer: Option A**

Let the length of the first train be *x* metres.

Then, the length of the second train is\(\left(\frac{x}{2}\right)metres.\)

Relative speed = (48 + 42) kmph =\(\left(90\times\frac{5}{18}\right)m/sec = 25m/sec\)

\(\frac{[x+(\frac{x}{2})]}{25}=12 or \frac{3x}{2}=300 . or . x= 200\)

Therefore Length of first train = 200 m.

Let the length of platform be *y* metres.

Speed of the first train = \(\left(48\times\frac{5}{18}\right)m/sec = \frac{40}{3}m/sec\)

\(\therefore\left(200+y\right)\times\frac{3}{40}= 45\)

600 + 3*y* = 1800

*y* = 400 m.

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