A train which 360m long takes 36 sec to cross a telegraph pole. How long will it take to cross a 600m long platform?

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

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 of the train = (264 x 5/18) m/sec = 220/3 m/sec
Distance covered in passing the platform = (330+330) m= 660m
Time taken= ( 660 / (220/3) ) sec = (660 x 3/ 220 ) = 9 sec

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

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

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

Then, (x + 480 m) / 24 sec = y ....(i)
and , (x + 720 m) / 36 sec = y ....(ii)

From Eqs (i) and (ii)
(x + 480) / 24 = (x + 900) / 36
? 3x + 1440 = 2x + 1800
? Length of train, x= 360m

We know that, when the trains are moving in the same direction,
Relative speed= Difference between the speed of train

and total distance for crossing each other = Sum of the length of train

Therefore, Relative speed = 72 km/hr - 54 km /hr = 18 km/hr
Relative speed in m/sec = 18 km/hr x 5/18 = 5 m/sec

and Total distance = 200m + 300m = 500m

and Total time taken to cross each other = Total distance in meter/ Relative speed in m/sec

= 500 m / (5 m/sec) = 100 sec

Speed of train in m/sec = (speed of train in km/hr) x 5/18

? speed of train in m/sec = 54 x 5/18 = 15 m/sec

Time taken to cross the tunnel = 2 minutes = 120 sec

Therefore, Total length covered by train in crossing the tunnel = Speed of train x Time taken to cross the tunnel

= 15 m/sec x 120 sec = 1800 m

Now, we know that
Total length covered by train in crossing the tunnel = Length of train + Length of tunnel

Given, Length of train =400m and
Calculated above, Length covered by train in crossing the tunnel = 1800 m

Therefore, Length of tunnel = 1800m- 400m = 1400m