A train is running at the speed of 264 Km/hr. If the length of the train is 330m, then how long will it take to cross a platform which is 330m long?

Speed of the train = (60 x 5/18) m/sec = 50/3 m/sec
Distance covered in passing the standing person = 200m
Required time taken= =200/(50/3) = 200 x (3/50) = 12 sec

Relative speed, when the trains are running in the opposite direction = Sum of the speed

Therefore, Relative speed = 36 km/hr +72 km/hr = 90 km/hr
Relative speed in m/sec = 90 km/hr x 5/18= 25 m/sec

Distance covered = sum of the lengths of the train = 200 m+ 300 m = 500m
Therefore, time taken = 500m / 25 m/sec = 20 sec

Let the length of train be x meter and speed be y m/sec

Therefore, time taken to cross the pole = x/y sec

and time taken to cross the platform = ( Length of train + Length of platform) / speed of train

Therefore x/y = 10
And, (x+200) / y = 20
? 10y + 200 = 20 y
? speed of train, y = 20 m/sec
And length of rain = x = 10y = 200m

Speed in km/ hour =200

Speed in m/sec = 200 x 5/18 = 500/9 m/sec = 55.55 m/sec

Let the speed of first lady be (v + 2)km/h and speed of second lady will be v km/h.
Total distance = 24 km

For first lady, Speed = Distance/Time
v + 2 = 24/t ...(i)

Let time taken by first lady to cover distance of 24 km be t h.
Then, time taken by second lady to cover same distance will be(t + 1)h.
For second lady, Speed =Distance/time
v = 24/(t + 1) ...(ii)

Form Eqs.(i) and (ii), we get
24/t - 2 = 24/(t + 1)
? (24 - 2t)/t = 24/(t + 1)
? (24 - 2t)(t + 1) = 24t
? 24t - 2t² + 24 - 2t = 24t
? 2t² + 2t - 24 = 0
? t² + t - 12 = 0
? t² + 4t - 3t - 12 = 0
? t(t + 4) -3(t + 4) = 0
? (t - 3)(t + 4) = 0
? t = 3, -4
? t = 3 (t ?- 4)
? The distance travelled by the first lady in one hour
= 24/t = 24/3 = 8 km
And distance travelled by the second lady in one hour
= 24/t + 1
= 24/3 + 1 = 6 km

Length of train = 264 m

Time taken to cross the pole = 12 sec

Speed of the train, in m/sec = Length of the train/ Time taken to cross the pole

Therefore, speed in m/sec= (264 / 12) m/sec = 22 m /sec

Calculating speed in km/ hour = (22 m/sec ) x 18/5 = 396/5 km/hr = 79.2 km/ hour

Speed in m/sec = 36 km/hr x 5/18 = 10m/sec

Distance covered by train in crossing the bridge = Speed of train in m/sec x time in sec = 10 m/sec x 30 sec = 300 m

Now, we know that
Distance covered by train in crossing the bridge= Length of train + Length of bridge

Therefore, Length of bridge = 300m - 200m = 100m

Speed of train in m/sec = 360m / 36 sec = 10 m/sec

Distance covered by train in crossing the platform = Length of train + Length of Platform = 360m + 240m = 600m

Therefore, Time taken to cover this distance = 600m /(10 m/sec)
= 60 sec

Speed of train in m/sec = 72 km/hr x 5/18 = 20 m/sec

Distance covered in meter = Time taken in crossing the platform in sec x speed in meter = 30 sec x 20 m/sec = 600m

Now, we know , Distance covered by train in crossing the platform = Length of train + Length of Platform
Therefore, length of the train = 600m - 400m = 200m

Speed in m/sec = 36km/hr x (5/18) = 10 m/sec

Given, Time taken by train to cross the platform = 2 min = 120 sec

Therefore, the distance covered by train in crossing the platform = 10 m/sec x 120 sec = 1200 m

Now, distance covered by train in crossing the platform = Length of train + Length of Platform

Given, Length of train = Length of Platform = x

Therefore, 2x = 1200
so, x = Length of train = 1200/2 = 600 m