SBI PO – 2015 – 28

Question: A train passes by a stationary man standing on the platform in 7 seconds and passes by the platform completely in 28 seconds. If the length of the platform is 330 meters, what is the length of the train? [एक पैसेंजर प्लेटफार्म पर खड़े एक व्यक्ति को 7 सेकेण्ड में तथा पूरे प्लेटफार्म को वह 28 सेकंड में पार कर लेती है. यदि प्लेटफार्म की लम्बाई 330 मीटर हो; तो ट्रेन की लम्बाई बताएं.]   [Ans. (d)110 m.]

(a) 120 m.     (b) 100 m.    (c) 80 m.     (d) 110 m.   (e) None of these

Detailed  Solution: When a train crosses a man, it means it describes a distance equal to its length in that given time. But, when a train crosses a platform, it means it describes a distance equal to the sum of the length of the train and platform.

First Method: Since here, a train passes by a stationary man standing on the platform in 7 seconds and passes by 

the platform completely in 28 seconds; so the train describes a distance of 330 meter (length of train) in 21 sec (28 - 7). That is, 110 meter in 7 sec, which is the length of the train.

Second Method: Let the length of the train be ‘L’ m.

Since the train crosses a man in 7 sec, so the speed of the train = L/7 m/s

Again, since the train crosses a platform in 28 sec completely, so the speed of the train = (L + 330)/28

So, L/7 = (L + 330)/28, so solving them, we get L = 110 meter Ans.

Third Method: Let the speed of the train be “u” m/s.

Since the train crosses a man in 7 sec, so the length of the train = 7u meter

Again, since the train crosses a platform in 28 sec, so the sum of the length of the train and platform = 28u meter

Therefore, length of the platform = 28u – 7u = 330

Or, 21u = 330, that means, length of the train = 7u = 110 meter Ans.