A train is 100 meter long and is running at the speed of 30 km per hour. Find the time it will take to pass a man standing at a crossing.

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 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:

First convert speed into m/sec

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

Time = Distance/speed
= 100/40 = 2.5 seconds

Answer: Option B

Explanation:

Relative Speed = 60+40 = 100 kmph
= 100*(5/18) = 250/9 m/sec

Distance = 140+160 = 300 meters

Time = Distance/Speed

$$\begin{aligned} 300*\frac{9}{250} = \frac{54}{5} \\ = 10.8 \text{ seconds} \end{aligned}$$

So the time trains will take to cross each other will be 10.8 seconds

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