How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr

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 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 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 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 B

Explanation:

Speed = 72 km/hour = 72*(5/18) m/sec
= 20 m/sec

Total distance to be covered = 110+132 = 142 meters

Time = Distance/Speed
= 242/20 = 12.1 seconds