A train is 100 meter long and is running at the speed of 30 km per hour. Find the time it will take to pass a man standing at a crossing.

Answer: Option D

Explanation:

Speed = Distance/time = 300/18 = 50/3 m/sec

Let the length of the platform be x meters
then
\begin{aligned}
Distance = Speed*Time \\
x+300 = \frac{50}{3}*39 \\
=>3(x+300)= 1950 \\
=> x = 350 \text{ meters}
\end{aligned}

Answer: Option C

Explanation:

As trains are running in opposite directions so their relative speed will get added
So, Relative speed = 120 +80 = 200 kmph
= 200*(5/18) = 500/9 m/sec

Let the length of other train is x meter then

\begin{aligned}
\frac{x+270}{9} = \frac{500}{9} \\
=> x+270 = 500\\
=> x = 230
\end{aligned}

So the length of the train is 230 meters

Answer: Option A

Explanation:

As Trains are moving in same direction,
So, Relative Speed = 40-20 = 20 kmph
= 20*(5/18) = 50/9 m/sec

Length of Train= Speed * Time

\begin{aligned}
Length = \frac{50}{9}*5 \\
= \frac{250}{9} \\
=27\frac{7}{9}
\end{aligned}

Answer: Option B

Explanation:

Speed = 72 km/hour = 72*(5/18) m/sec
= 20 m/sec

Total distance to be covered = 110+132 = 142 meters

Time = Distance/Speed
= 242/20 = 12.1 seconds

Answer: Option C

Explanation:

Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds

Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s

Distance = Speed*Time
\begin{aligned}
=> 800+x = \frac{65}{3}*60 \\
=> 800+x = 20*65 = 1300 \\
=> x = 1300 - 800 = 500 \\
\end{aligned}

So the length of the tunnel is 500 meters.

[If you want to calculate it practically, then please have your copy and pen and take a ride of Kalka to Shimla toy train in north India. It has many tunnels on the way :) ]