A train crosses a platform of length 350 m in 12 sec and a man standing on platform in 2 sec. Find the speed of train.a)100 km/hb)126 km/hc)130 km/hd)Nonee)All of the aboveCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Let the length of train be x m.
Since the train crosses the man in 2 sec
Speed of train = x/2 m/s

Also it crosses the platform of length 350 m in 12 sec
So speed of train = (350+x)/12
Equating both the speeds of train ,we get
x/2 = (350+x)/12
x = (350+x)/6
6x = 350+x
5x = 350
x = 70
Thus length of train = 70 m
Now, speed of train = 70/2 = 35 m/s
= 35/1000*3600 = 35/5*18
=126 km/hr

Answer

Given:
Length of platform, L = 350 m
Time taken by train to cross the platform, t1 = 12 s
Time taken by train to cross a man standing on the platform, t2 = 2 s

To find: Speed of train

We know that,
Speed = Distance / Time

Let's first calculate the speed of train when it crosses the platform.

Speed of train when it crosses the platform:
Distance covered by train = Length of train + Length of platform
Distance covered by train = L + 350
Time taken by train to cover this distance = t1
Speed of train = (L + 350) / t1

Now, let's calculate the length of the train.
Length of train = Distance covered by train when it crosses the man - Length of platform
Length of train = L - Distance covered by man in t2 seconds
Length of train = L - (Speed of man × t2)
Length of train = 350 - (Speed of man × 2)

We don't know the speed of man, but we can find it using the fact that he covers the length of the train in 2 seconds.
Speed of man = Length of train / t2
Speed of man = (350 - Speed of man × 2) / 2
Speed of man = 175 - Speed of man
2 × Speed of man = 175
Speed of man = 87.5 m/s

Now we can substitute this value of speed of man in the equation for speed of train when it crosses the platform.

Speed of train = (L + 350) / t1
Speed of train = (350 + L) / 12
Speed of train = (350 + L) / (2 × 6)
Speed of train = (350 + L) / (2 × t2)
Speed of train = (350 + 350 - Speed of man × 2) / (2 × 2)
Speed of train = (700 - 175) / 4
Speed of train = 525 / 4
Speed of train = 131.25 m/s

Therefore, the speed of train is 131.25 m/s or 126 km/h (approx). Hence, option B is the correct answer.

Answer

The correct answer is B as
Let the length of train be x m.
Since the train crosses the man in 2 sec
Speed of train = x/2 m/s
Also it crosses the platform of length 350 m in 12 sec
So speed of train = (350+x)/12
Equating both the speeds of train ,we get
x/2 = (350+x)/12
x = (350+x)/6
6x = 350+x
5x = 350
x = 70
Thus length of train = 70 m
Now, speed of train = 70/2 = 35 m/s
= 35/1000*3600 = 35/5*18
=126 km/hr.

Answer

The correct answer is B as
Let the length of train be x m.
Since the train crosses the man in 2 sec
Speed of train = x/2 m/s
Also it crosses the platform of length 350 m in 12 sec
So speed of train = (350+x)/12
Equating both the speeds of train ,we get
x/2 = (350+x)/12
x = (350+x)/6
6x = 350+x
5x = 350
x = 70
Thus length of train = 70 m
Now, speed of train = 70/2 = 35 m/s
= 35/1000*3600 = 35/5*18
=126 km/hr.

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