A train is moving at a speed of 132 km/hour. If the length of the train is 110 meters, how long will it take to cross a railway platform 165 meters long.

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 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 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 D

Explanation:

Let the length of bridge is X [as always we do :)]
Speed of train is = 45*(5/18) m/sec = 25/2 m/sec
Time = 30 seconds

Total distance = 130+x
We know Speed = distance/time
so,
\begin{aligned}
\frac{130+x}{30} = \frac{25}{2} \\
=> 2(130+x) = 750 \\
x = 245 \text{ meters}
\end{aligned}

So length of the bridge is 245 meters

Answer: Option B

Explanation:

Relative Speed = 60+40 = 100 Kmph
= 100*(5/18) = 250/9 m/sec

Distance to be covered = 140 + 160 = 300 metres

Time = Distance/Speed

\begin{aligned}
Time = 300*\frac{9}{250} \\
= \frac{54}{5} = 10.8\text{ seconds}
\end{aligned}