A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?

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

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 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:

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

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