Concept of Time and Distance [समय और दूरी]-03

Question: 120 meter long train crosses a tunnel of length 80 meters in 20 seconds. Find the time for train to cross a man standing on a platform of length 130 meters? [120 मीटर लम्बी एक रेलगाड़ी, 80 मीटर लम्बी एक नहर को 20 सेकेण्ड में पार कर लेती है. बताइए कि 130 मीटर लम्बे प्लेटफार्म पर खड़े एक व्यक्ति को पार करने में उस ट्रेन को कितना समय लगेगा?]  [Ans. (d) 12 sec]

(a) 24 sec  (b) 42 sec  (c) 22 sec  (d) 12 sec  (e) None of these

Solution:

Detailed Explanation:

Concept: When a train crosses a “platform” (or any object having length along the direction of moving train), then the train describes a distance equal to the sum of the lengths of the train and platform. But, when a train crosses a “man” or an “electric pole”, it describes a distance equal to its length only, because the length (width) of a man or electric pole is taken as zero, as it is negligible, as compared to the length of the train.

One more thing must be remembered that when a train crosses a man standing on a platform, then the length of the platform doesn’t matter, because the train is crossing the man, not the platform.   

Given that a train of length 120 meter crosses a tunnel of length 80 meters in 20 seconds. So, distance is (120+80) meter = 200 meter. Time taken is 20 seconds.

Again, the train is crossing a man standing on a platform of length 130 meters. In this case, length of the platform doesn’t matter. So, the length of train is the distance described, that is, distance is 120 meter only. Time taken is to be determined.

Here, the moving body is only the train, so in crossing a tunnel or a man, the speed is constant. When speed is constant, the distance is proportional to the time taken.

First Method

200 meter ≡ 20 sec

120 meter ≡? = 12 sec Ans.

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Second Method

T₁:T₂ = D₁:D₂ = 200:120 = 5:3

5 ≡ 20 sec

3 ≡? = 12 sec Ans.

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Third Method: As a train of length 120 meter crosses a tunnel of length 80 meters in 20 seconds. So, distance is (120+80) meter = 200 meter. Time taken is 20 seconds.

Speed of the train = (200/20) m/s = 10 m/s

Required Time = 120m/10 sec = 12 sec. Ans. 

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