A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform.

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 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

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 C

Explanation:

As trains are running in opposite directions so their relative speed will get added
So, Relative speed = 120 +80 = 200 kmph
= 200*(5/18) = 500/9 m/sec

Let the length of other train is x meter then

\begin{aligned}
\frac{x+270}{9} = \frac{500}{9} \\
=> x+270 = 500\\
=> x = 230
\end{aligned}

So the length of the train is 230 meters

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