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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?

- $210$ and $140$
- $162.5$ and $187.5$
- $245$ and $130$
- $175$ and $200$

Migrated from GO Mechanical 3 years ago by Arjun

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Best answer

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.

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.