A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length.

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 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 calculate answer in seconds, so first convert speed into meter/sec.

we know 1 km/hr = 1*(5/18) m/sec
So, Speed = 132* (5/18) = 110/3 m/sec

Distance need to be covered in passing the platform =
Length of train + length of platform = 110 + 165
= 275 meters

Time = Distance/Speed

$$\begin{aligned} => Time = 275* \frac{3}{110} = \frac{15}{2} \\ = 7.5 seconds \end{aligned}$$

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 C

Explanation:

First convert speed from km/hr to m/sec

So, Speed = 72*(5/18) = 20 m/sec
Time = 26 seconds

Let the length of the train be x meters.
We know, Distance = Speed*Time.
[you can remember this formula as remembering DUST = D*ST... Distance=Speed*Time]

x+250 = 20*26
=> x = 270 meters

So length of the goods train is 270 meter