A train speeds past a pole in 15 seconds and a platform 100 meter long in 25 seconds. What is length of the train ?

Answer: Option A

Explanation:

Speed = 60*(5/18) m/sec = 50/3 m/sec

Length of Train(Distance) = Speed * Time

\begin{aligned}
= \frac{50}{3}*9 = 150 meter
\end{aligned}

Answer: Option C

Explanation:

Speed = 45 Km/hr = 45*(5/18) m/sec
= 25/2 m/sec
Total distance = 360+140 = 500 meter

Time = Distance/speed
\begin{aligned}
= 500*\frac{2}{25} = 40 seconds
\end{aligned}

Answer: Option D

Explanation:

First convert speed into m/sec

Speed = 144*(5/18) = 40 m/sec

Time = Distance/speed
= 100/40 = 2.5 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 :) ]

Answer: Option B

Explanation:

Distance covered = 120+120 = 240 m
Time = 12 s

Let the speed of each train = x.
Then relative velocity = x+x = 2x

2x = distance/time = 240/12 = 20 m/s

Speed of each train = x = 20/2 = 10 m/s

= 10*18/5 km/hr = 36 km/hr