Speed of a goods train is 72 km/hr. This train crosses a 250 meter platform in 26 seconds. Then find the length of goods train.

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

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 C

Explanation:

Relative Speed = 63-3 = 60 Km/hr
= 60 *(5/18) = 50/3 m/sec

Time taken to pass the man will ne
\begin{aligned}
500*\frac{3}{50} = 30 \text{ seconds}
\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 B

Explanation:

As we need to get answer in seconds, so never forget to convert speed into meter per second.

Speed = 30 km/hr = 30* 5/18 m/sec
= 25/3 m/sec

Distance = length of train = 100 meter

Required time =
\begin{aligned}
\frac{Distance}{Speed} \\
= \frac{100}{\frac{25}{3}} \\
= 100* \frac{3}{25} = 12 sec \\
\end{aligned}