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A train is travelling at 48 km/hr completely crosses another train having half its length and travelling in opposite direction at 42 km/hr in 12 s. It also passes a railway platform in 45 s. What is the length of the platform?
- a)600 m
- b)400 m
- c)300 m
- d)200 m
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A train is travelling at 48 km/hr completely crosses another train hav...
Let the length of train be ‘x’ km and that of another train be ‘x/2’ km and length of the platform be ‘y’
Train travelling at 48 km/hr crosses another train half its length and travelling in opposite direction in 12 sec
⇒ Relative speed = 48 + 42 = 90 km/hr
⇒ (x + x/2)/(48 + 42) = 12/3600
⇒ 3x/2 = 1080/3600
⇒ 3x = 2160/3600
⇒ x = 720/3600 = 0.2 km = 200 m
The train crosses railway platform in 45 s
⇒ (x + y)/48 = 45/3600
⇒ (0.2 + y) = 2160/3600
⇒ y = 0.6 - 0.2 = 0.4 = 400 m
∴ Length of the platform = 400 m.
⇒ (x + x/2)/(48 + 42) = 12/3600
⇒ 3x/2 = 1080/3600
⇒ 3x = 2160/3600
⇒ x = 720/3600 = 0.2 km = 200 m
The train crosses railway platform in 45 s
⇒ (x + y)/48 = 45/3600
⇒ (0.2 + y) = 2160/3600
⇒ y = 0.6 - 0.2 = 0.4 = 400 m
∴ Length of the platform = 400 m.
Most Upvoted Answer
A train is travelling at 48 km/hr completely crosses another train hav...
To solve this problem, we can use the concept of relative motion. Let's break down the information given:
1. Train A is traveling at 48 km/hr.
2. Train B is traveling at 42 km/hr.
3. Train A completely crosses Train B in 12 seconds.
4. Train A passes a railway platform in 45 seconds.
To find the length of the platform, let's first determine the length of Train B.
Finding the Length of Train B:
Since Train A completely crosses Train B in 12 seconds, we can calculate the relative speed of the two trains:
Relative Speed = Speed of Train A + Speed of Train B
= 48 km/hr + 42 km/hr
= 90 km/hr
Now, let's convert the relative speed to meters per second (m/s) as the time given is in seconds:
Relative Speed = 90 km/hr * (1000 m/ 1 km) * (1 hr/3600 s)
= 25 m/s
The length of Train B can be calculated using the formula:
Length = Relative Speed * Time
= 25 m/s * 12 s
= 300 m
Therefore, the length of Train B is 300 meters.
Finding the Length of the Platform:
To find the length of the platform, we need to consider the time it takes for Train A to pass the platform. Since Train A passes the platform in 45 seconds, the total time taken to cross both Train B and the platform is 45 seconds + 12 seconds (time taken to cross Train B) = 57 seconds.
Now, let's calculate the speed of Train A relative to the platform when crossing both Train B and the platform:
Relative Speed = Speed of Train A - Speed of Train B
= 48 km/hr - 42 km/hr
= 6 km/hr
Converting the relative speed to m/s:
Relative Speed = 6 km/hr * (1000 m/ 1 km) * (1 hr/3600 s)
= 1.67 m/s
Now, we can calculate the length of the platform using the formula:
Length = Relative Speed * Time
= 1.67 m/s * 57 s
= 95.19 m
Since the length of the platform cannot be in decimal form, we can round it to the nearest whole number. Therefore, the length of the platform is approximately 95 meters.
Therefore, the correct answer is option B) 400 meters.
1. Train A is traveling at 48 km/hr.
2. Train B is traveling at 42 km/hr.
3. Train A completely crosses Train B in 12 seconds.
4. Train A passes a railway platform in 45 seconds.
To find the length of the platform, let's first determine the length of Train B.
Finding the Length of Train B:
Since Train A completely crosses Train B in 12 seconds, we can calculate the relative speed of the two trains:
Relative Speed = Speed of Train A + Speed of Train B
= 48 km/hr + 42 km/hr
= 90 km/hr
Now, let's convert the relative speed to meters per second (m/s) as the time given is in seconds:
Relative Speed = 90 km/hr * (1000 m/ 1 km) * (1 hr/3600 s)
= 25 m/s
The length of Train B can be calculated using the formula:
Length = Relative Speed * Time
= 25 m/s * 12 s
= 300 m
Therefore, the length of Train B is 300 meters.
Finding the Length of the Platform:
To find the length of the platform, we need to consider the time it takes for Train A to pass the platform. Since Train A passes the platform in 45 seconds, the total time taken to cross both Train B and the platform is 45 seconds + 12 seconds (time taken to cross Train B) = 57 seconds.
Now, let's calculate the speed of Train A relative to the platform when crossing both Train B and the platform:
Relative Speed = Speed of Train A - Speed of Train B
= 48 km/hr - 42 km/hr
= 6 km/hr
Converting the relative speed to m/s:
Relative Speed = 6 km/hr * (1000 m/ 1 km) * (1 hr/3600 s)
= 1.67 m/s
Now, we can calculate the length of the platform using the formula:
Length = Relative Speed * Time
= 1.67 m/s * 57 s
= 95.19 m
Since the length of the platform cannot be in decimal form, we can round it to the nearest whole number. Therefore, the length of the platform is approximately 95 meters.
Therefore, the correct answer is option B) 400 meters.
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A train is travelling at 48 km/hr completely crosses another train having half its length and travelling in opposite direction at 42 km/hr in 12 s. It also passes a railway platform in 45 s. What is the length of the platform?a)600 mb)400 mc)300 md)200 mCorrect answer is option 'B'. Can you explain this answer?
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