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From the time the front of a train enters a platform, it takes $25$ seconds for the back of the train to leave the platform, while traveling at a constant speed of $54$ km/h. At the same speed, it takes $14$ seconds to pass a man running at $9$ km/h in the same direction as the train. What is the length of the train and that of the platform in meters, respectively?

1. $210$ and $140$
2. $162.5$ and $187.5$
3. $245$ and $130$
4. $175$ and $200$
Migrated from GO Mechanical 3 years ago by Arjun

Speed of train$=54$ km/h
Speed of man $=9$ km/h
Relative speed of train $=54-9=45$ km/h

Time taken by the train to pass the men $=14$ sec

Distance Traveled = Length of train $=$ Relative Speed $\times$ Time
Length of train $=45\times 14 \times \frac{1}{3600} km =175\;m$

Time for traveling the length of the train and length of platform $=25$ sec
Distance traveled $=$ Length of Train $+$ Length of Platform $=$ Speed of train $\times$ Time
$\qquad\qquad=54\times 25 \times \frac{1}{3600} km=375\;m$
Therefore, length of platform  $=375-175=200\;m$

So, (D) is the correct answer.

Train and Running Man

$S_{relative}=\dfrac{D_{train}}{Time}$

$\dfrac{45\times 1000m}{3600sec}=\dfrac{D_{train}}{14sec}$

$D_{train}=175m$

Train and Platform

$S=\dfrac{D_{train}+D_{platform}}{Time}$

$\dfrac{54\times 1000m}{3600sec}=\dfrac{175+D_{paltform}}{25sec}$

$D_{paltform}=200m$

$Ans:D$

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