Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is ?

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:

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 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 A

Explanation:

As Trains are moving in same direction,
So, Relative Speed = 40-20 = 20 kmph
= 20*(5/18) = 50/9 m/sec

Length of Train= Speed * Time

\begin{aligned}
Length = \frac{50}{9}*5 \\
= \frac{250}{9} \\
=27\frac{7}{9}
\end{aligned}