Aptitude - Problems on Trains - Discussion

To find the length of each train, you can use the relative speed formula:

Relative Speed = Speed of Faster Train - Speed of Slower Train.
Relative Speed = (46 km/hr - 36 km/hr) = 10 km/hr.
Now, you need to convert the relative speed to meters per second (m/s) because the time is given in seconds:
1 km/hr = 5/18 m/s.

So, 10 km/hr = (10 * 5/18) m/s = (50/18) m/s = (25/9) m/s (approximately)
Now, you can use the formula for distance:
Distance = Speed x Time.
Distance = (25/9) m/s x 36 seconds = (25/9) x 36 meters,
Distance = 100 meters (approximately).
Since the faster train passes the slower train in 36 seconds, the length of each train is 100 meters.

When the two trains start running with different speed, the speeder train will get ahead of the slower train at some time.

With both the train running, it is hard to find the distance after which the speeder train completely pass the slower train.

To make it easy, find the relative speed of the train. It is 4km/hr. It can be said that when the slower train speed is 0km/hr, the speeder train speed is 4 km/hr.

Assume the slower train stops or consider it as a platform, then the speeder train cross the slower train in 36 seconds @ 4km/hr. Here the total distance covered is length of speeder train and the platform (slower train)

Have a good day.

Sir, I am having some difficulties to solve a question. Some confusion is there. I need your help sir. The question is-.

Two trains are running at 40km/hr and 20 km/ hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 sec. What is the length of the fast train?

Sir the formulas is a+b/u-v.

Where a and b lengths and u and v are speeds.

My question is that: why we are not taking both the lengths. In solution, only fast train lengths is taking. Why sir. A/c to formula both the lengths are necessary.

Let us suppose there is only a single train whose speed is (46-36)1OKM/H i.e 25/9 m/s ..

Now it takes 36 seconds to cover a certain distance.. so the distance would be {(25/9)*36} i.e 100 m.. therefore the distance covered by one train is 100m in 36 sec by the speed of 25/9m/s .


Now consider the question, there are two trains and their length is same..

So Train T1(46 KM/H) whose speed is higher than Train T2(36 KM/H) will cover 100m(Length of T1 and T2) that is 2L..(Suppose length of both trains is L)
therefore 2L=100
and L=50m

got my point?

The length of the train is equal.

So let it x.

Then applying the formula.

a + b/u - v = Time taken by the faster train passes the lower train.

x + x/46 - 36 = 36.

The speed of trains are in km/hr. So it have to convert in m/sec.

Firstly it subtract.

Because fraction value will come. So it difficult to multiply.

It's either subtract before or after.

Then, 46 - 36 = 10 km/hr.

10 * 5/18 = 25/9.

The answer will come 2x/25/9 = 36.

Then the 9 goes to multiply denominator.

9*2x/25 = 36.

Then for easy calculation 2x/25 = 36/9.

x = 50.

The correct answer is 100 mts. We can take the length of only one train as answer as both the trains started at the same point and time. The faster train has just to cover its length only to cross the slower train. The formula is:

((46-36)kmph*5/18)*36=50/18*36=100mts.

------------- Added by Author -----------------------------------
This answer is wrong. We have to read the question very carefully, there is no information like "started at the same time and same point".
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I have a doubt, hear if two trains are same length and same direction in that faster train speed 10km/h more then slower train in this case the faster train speed only 10km/h only and it crossed in slower train in 36 seconds that means faster train speed more then (25/9) m/s.

And they mentioned faster train takes 36sec to cross the slower train that means.

According to formula length = speed * time.

(25/9) * 36 = 200m.

The actual length of the train = 200m.

I think none of the above option is the answer.

In the above problem it is given that the lengths of two trains are equal.

according to theory if both trains are moving in same directions then the lenghts will be subtracted but this is the case that both lenghts are different but in the above problem the lenghts are equal in this case we have to add lengths without regarding their directions so lenght is 2x

but as the trains are moving in same directions their relative speeds must be subtracted

so (46-36)*5/18
2x/(50/18)=36
2x=36*(50/18)
x=50m

Length of the trains be x & 2x because after 36 second the faster train is going to pass the slower train. At that time faster train covers 460m and slower train covers 360m. The difference is 100m. This difference is between faster train's front edge and slower train's back edge.

Then it involves the distance of both the trains, hence we need to divide 100m by 2 (because in the question they've given as both the trains of equal length) to get the length of the train.

The simple math is, 46km/1h - 36km/1h= 10km/1h. Now; it can be converted into meter/second that is 10km*1000m/3600sec. 10000m/3600s= 2.778m/1sec.


Now, for the difference of 2.778 meter/1sec the faster train cross the slower train in 36 sec. So, the distance the faster train cross 36sec * 2.778 meter= 100 meters.
This 100 meters distance/way is the length of two trains (faster&slower).
As if, two trains' length is same. So, one train's length is; 100/2= 50 meters.