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 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:

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 B

Explanation:

As we need to calculate answer in seconds, so first convert speed into meter/sec.

we know 1 km/hr = 1*(5/18) m/sec
So, Speed = 132* (5/18) = 110/3 m/sec

Distance need to be covered in passing the platform =
Length of train + length of platform = 110 + 165
= 275 meters

Time = Distance/Speed

$$\begin{aligned} => Time = 275* \frac{3}{110} = \frac{15}{2} \\ = 7.5 seconds \end{aligned}$$

Answer: Option C

Explanation:

Let the length of the train is x meter and Speed of the train is y meter/second
Then x/y = 15 [because distance/speed = time]
=> y = 15/x

$$\begin{aligned} => \frac{x+100}{25} = \frac{x}{15} \\ x = 150 \text{ meters} \end{aligned}$$

So length of the train is 150 meters