A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform.

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

Answer: Option D

Explanation:

Speed of train relative to jogger = (45-9) = 36 kmph
= 36*(5/18) = 10 m/sec

Distance to cover = 240 + 120 = 360 metres

Time = Distance/Speed
So,
$$\begin{align} Time = \frac{360}{10} = 36 \text{ Seconds} \end{align}$$

Answer: Option C

Explanation:

From the given question,
we will first calculate the speed of train relative to man,
=> ( 60 + 6 ) = 66 km/hr ( we added 6 because man is running opposite )
Convert it in metre/second
$$\begin{aligned} = 66 \times\frac{5}{18} \\ = \frac{55}{3} m/sec\\ \text{Time it will take to pass man }\\ = 110 \times \frac{3}{55} \\ = 6 \text{ seconds} \end{aligned}$$

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:

First person speed = 2*(5/18) = 5/9 m/sec
Second person speed = 4*(5/18) = 10/9 m/sec

Let the length of train is x metre and speed is y m/sec

then,
$$\begin{aligned} \frac{x}{y-\frac{5}{9}} = 9 \\ => 9y-5 = x \\ => 9y-x = 5 .....(i) \\ Also, \\ \frac{x}{y-\frac{10}{9}} = 10 \\ 90y-9x = 100 .....(ii)\\ \text{from (i) and (ii), we get,} \\ x=50 \end{aligned}$$
So length of train is 50 metre