A train is moving at a speed of 132 km/hour. If the length of the train is 110 meters, how long will it take to cross a railway platform 165 meters long.

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

Answer: Option C

Explanation:

Let the length of each train is x meter
Distance will be x+x = 2x

Relative Speed = 46-36 = 10 km/hr
= 10*(5/18) = 25/9 m/sec

Distance = Speed*Time

$$\begin{aligned} 2x = \frac{25}{9}*36 \\ 2x = 100 \\ => x = 50 \end{aligned}$$
So length of both the trains are 50 meters

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 D

Explanation:

Let the length of bridge is X [as always we do :)]
Speed of train is = 45*(5/18) m/sec = 25/2 m/sec
Time = 30 seconds

Total distance = 130+x
We know Speed = distance/time
so,
$$\begin{aligned} \frac{130+x}{30} = \frac{25}{2} \\ => 2(130+x) = 750 \\ x = 245 \text{ meters} \end{aligned}$$

So length of the bridge is 245 meters