Two trains can run at a speed of 54 km/hr and 36 km/hr on parallel tracks. When solving this question we will use the concept of relative speed. First we will calculate the relative speed of the trains in both cases when trains are running in opposite directions and when they move in the same direction. Then we calculate the length of train by using the basic formula of speed-distance relation which is given by $speed = \frac{distance}{time}$ . With the help of given data, find out which train will run faster and which will run slower?

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100m and 150m

100m and 110m

110m and 150m

90m and 110m

answer is A.

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Detailed Solution

On parallel tracks, two trains can travel at speeds of 54 and 36 kilometres per hour, respectively.
We must determine the length of the trains.
Assume that the faster train travels at 54 km/hr and the slower train travels at 36 km/hr.
As stated in the question, trains travelling in opposite directions pass each other in 10 seconds. As a result, the relative speed of the trains will be
⇒54+36 km/hr
⇒90 km/hr
⇒90×

\frac{5}{18}

m/sec
⇒25 m/sec
We have given time to cross each other.
So, the length of train will be

speed = \frac{distance}{time}

Or
⇒length=speed × time
⇒length=25×10
⇒length=250 m
Also, when two trains move in the same direction, a person in the faster train crosses the other train in 30 seconds, according to the question.
We now know that the person in the faster train must have travelled the same distance as the person in the slower train.
As a result, the trains' relative speeds will be
⇒54−36 km/hr
⇒18 km/hr
⇒18×

\frac{5}{18}

m/sec
⇒5 m/sec
Now, the length of the slower train will be

speed = \frac{distance}{time}

Or
⇒length=speed × time
⇒length=5×30
⇒length=150 m
Now, the length of the faster train will be 250−150=100 m
So, we have the length of the trains 100 m and 150 m faster and slower respectively.
Option 1 is the correct answer.

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