Length of train is 130 meters and speed of train is 45 km/hour. This train can pass a bridge in 30 seconds, then find the length of the bridge.

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 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 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 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:

Speed of train relative to jogger = (45-9) = 36 kmph
= 36*(5/18) = 10 m/sec

Distance to cover = 240 + 120 = 360 metres

Time = Distance/Speed
So,
\begin{align}
Time = \frac{360}{10} = 36 \text{ Seconds}
\end{align}