A train is running with a speed of 60 kmph and its length is 110 metres. Calculate the time by which it will pass a man running opposite with speed of 6 kmph.

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 D

Explanation:

Speed = Distance/time = 300/18 = 50/3 m/sec

Let the length of the platform be x meters
then
$$\begin{aligned} Distance = Speed*Time \\ x+300 = \frac{50}{3}*39 \\ =>3(x+300)= 1950 \\ => x = 350 \text{ meters} \end{aligned}$$

Answer: Option B

Explanation:

Let the speeds of the two trains be x m/sec and y m/sec respectively.

Then, length of the first train = 27x metres,
Length of the second train = 17y metres.
[because distance = speed*time]

$$\begin{aligned} \frac{27x+17y}{x+y} = 23 \\ => 27x + 17y = 23x + 23y \\ => 4x = 6y \\ => \frac{x}{y} = \frac{6}{4} \end{aligned}$$
So ratio of the speeds of train is 3:2

Answer: Option B

Explanation:

Distance covered = 120+120 = 240 m
Time = 12 s

Let the speed of each train = x.
Then relative velocity = x+x = 2x

2x = distance/time = 240/12 = 20 m/s

Speed of each train = x = 20/2 = 10 m/s

= 10*18/5 km/hr = 36 km/hr

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