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A train, 350 m long, travelling at a speed of 120 kmph crosses a platform in 24 sec. A man going at a certain speed crosses the platform in 3 min. What is the speed of the man?
- a)6 kmph
- b)7 kmph
- c)8 kmph
- d)9 kmph
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A train, 350 m long, travelling at a speed of 120 kmph crosses a plat...
Given:
- Length of the train = 350 m
- Speed of the train = 120 km/hr
- Time taken by the train to cross the platform = 24 sec
- Time taken by the man to cross the platform = 3 min
To find:
The speed of the man
Explanation:
First, let's convert the speed of the train from km/hr to m/s:
- 120 km/hr = (120 * 1000) m/3600 s = 200/3 m/s
Time taken by the train to cross the platform:
- The train covers its own length plus the length of the platform in 24 seconds.
- Let the length of the platform be x meters.
- Therefore, the total distance covered by the train = 350 + x meters.
- The formula for speed is speed = distance/time.
- So, the speed of the train = (350 + x)/24 m/s.
Time taken by the man to cross the platform:
- The man covers his own length plus the length of the platform in 3 minutes.
- Let the speed of the man be y m/s.
- Therefore, the total distance covered by the man = y * 180 meters (3 minutes = 3 * 60 seconds = 180 seconds).
Equating the distances:
Since both the train and the man cover the same distance (length of the platform), we can equate their distances.
- 350 + x = y * 180
Calculating the speed of the man:
- Rearranging the above equation, we get y = (350 + x)/180.
- Substituting the value of x from the equation for the speed of the train, we get y = (350 + (200/3))/180.
- Simplifying the expression, we get y = 9 m/s.
- Converting the speed from m/s to km/hr, we get y = 9 * 18/5 = 162/5 km/hr = 32.4 km/hr.
Therefore, the speed of the man is 32.4 km/hr, which is approximately 32 km/hr. Hence, the correct option is (d) 9 km/hr.
- Length of the train = 350 m
- Speed of the train = 120 km/hr
- Time taken by the train to cross the platform = 24 sec
- Time taken by the man to cross the platform = 3 min
To find:
The speed of the man
Explanation:
First, let's convert the speed of the train from km/hr to m/s:
- 120 km/hr = (120 * 1000) m/3600 s = 200/3 m/s
Time taken by the train to cross the platform:
- The train covers its own length plus the length of the platform in 24 seconds.
- Let the length of the platform be x meters.
- Therefore, the total distance covered by the train = 350 + x meters.
- The formula for speed is speed = distance/time.
- So, the speed of the train = (350 + x)/24 m/s.
Time taken by the man to cross the platform:
- The man covers his own length plus the length of the platform in 3 minutes.
- Let the speed of the man be y m/s.
- Therefore, the total distance covered by the man = y * 180 meters (3 minutes = 3 * 60 seconds = 180 seconds).
Equating the distances:
Since both the train and the man cover the same distance (length of the platform), we can equate their distances.
- 350 + x = y * 180
Calculating the speed of the man:
- Rearranging the above equation, we get y = (350 + x)/180.
- Substituting the value of x from the equation for the speed of the train, we get y = (350 + (200/3))/180.
- Simplifying the expression, we get y = 9 m/s.
- Converting the speed from m/s to km/hr, we get y = 9 * 18/5 = 162/5 km/hr = 32.4 km/hr.
Therefore, the speed of the man is 32.4 km/hr, which is approximately 32 km/hr. Hence, the correct option is (d) 9 km/hr.
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Community Answer
A train, 350 m long, travelling at a speed of 120 kmph crosses a plat...
Let the length of the platform be x m.
Given, length of the train = 350 m
Distance travelled = (x + 350) m
Time taken = 24 s
x + 350 = 800
x = 450
Speed of the man = Distance/Time
Distance = 450 m
Time = 3 × 60 s = 180 s
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A train, 350 m long, travelling at a speed of 120 kmph crosses a platform in 24 sec. A man going at a certain speed crosses the platform in 3 min. What is the speed of the man?a)6 kmphb)7 kmphc)8 kmphd)9 kmphCorrect answer is option 'D'. Can you explain this answer?
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