Aptitude - Problems on Trains - Discussion

Second train leaves from B towards A. Many of us got confused that it starts from A towards B.

And we don't have to make it so complicated. We can generalize this question.
first train leaves at 7am.

By 8am it covers 20kms. Remaining distance is 90kms (110-20).
By 9am first train covers 20kms more and second train covers 25kms. Remaining distance is 45kms (90-(20+25)).

At 10am the first train covers another 20kms and second train covers 25kms more. (45-(20+25))=0 kms.

Distance between them is zero. Hence they meet at 10am.

Who ever doesn't understand why they have taken (X-1). Please see the below example.

Length of the track between starting position of train A starts at 7A.M and B Starts at 8A.M is 200 km.

Let's say A train travels with 20 kmph for 5 hours.

Distance covered by train A is = 100 km.

Train B Travels with 25 kmph for 4 hrs.

Distance covered by train B is =100km.

A train => 7+5=12 noon.

B train => 8+4=12 noon.

If we consider 7 as X then 8 should become (X-1) when we compare with the destination time.

Simple solution no formula, no concepts just common sense.

Let us consider first train it's speed is 20 km/hr.

So it covers 20 kms in 1 hour.

Starting from 7 am 1st train second train from 8 am to 9 am.

At 8 am it covers 20 km at 9 am it covers 25 km. 9 am it covers 40 km 10 am it covers 50 km.

10 am === 60 km.

So at 10 am total distance covered by two trains is 60+50=110 km.

Which is the actual distance of separation between two train hence they meet each other so simple.

One more easy method to solve such problems.
Given that distance between two stations is 110km.
First trains speed is 20kmph and starts at 7 am
2nd trains speeed is 25kmph and starts at 8 am.

So at 8 am, the distance covered by first train is 20 kms.
Now remaining distance to cover is (110-20 = 90 km).

The relative speed of both the trains is 20+45 = 45 kms.
So it will take 2 hours to cover 90 km.
Hence the trains will meet after 2 hours from 8am i.e. at 10 am.

Here,

The total distance between them = 110km.
(Making equal starting point)

By the time train B has started, the Train A has already covered 20km (since speed =20km/hr). Both at 8:00am now.
Now the distance between them is;
110-20=90km.

Relative speed= 20+25(since opposite direction) =45km/hr.
To cover 90 km time taken=90/45=2hrs.
2 hrs from 8:00am=10:00am.
(since we have made initial starting point at 8:00am for both the trains).

To solve this we can take a very simple approach.
As we have total distance between them 110 km and A is starting at 7 a.m.
So after 1 hr that is at 8 a.m he will cover 20 km so;
110-20 = 90km.

Now for both the trains we have 90 km and starting at 8 a.m so we can find there crossing time, as they will cross each other
T = d / s(a train ) + s (b train).
T = 90/ (20 + 25),
T = 90/ 45 = 2 hrs,
i.e after 2 hrs so 8 a.m + 2hrs = 10 a.m.

@ANISH MISHRA: Let the speed of the train P be xkm/hr and Q be ykm/hr.

After 6hrs, P would have travelled 6xkm (distance=speed*time) and similarly Q would have travelled 6ykm. Given, the distance between P and Q is 528, Hence,

6x + 6y = 528 -> (i).

Also, given that P having travelled 8km/hr more than Q. So,
x = y + 8 -> (ii).

Solving equation (i) & (ii),

x = 48km/hr (speed of train P).
y = 40km/hr (speed of train Q).

Hai @Poojitha.

x is the time taken, 20 is speed.

So Speed*Time = Distance.

For first train it is 20x. And as the second train started 1 hr later.

The time will be x-1. And distance = 25(x-1).

Since both the trains are yet to cover 110 km.

And travelling in opposite directions to meet each other and we have to calculate the meeting point of time. We have to add them. So,

It is 20x+25(x-1) = 110.

Hope it is clear now.

Your values for the distance travelled by each train are mathematically correct based on their speeds and times.

But from 10:00 a.m. onward, your reasoning ignores that the trains would have already met at 10 a.m.

Because their combined distance = 110 km, which is the total distance between A and B.

So, continuing to add distances after the meeting point doesn't make logical sense in the context of this problem.

60 km as relative speed of both the trains is 100 km/hr and
distance = 100km.

Then time taken to meet = distance/speed(relative).
T = 100/100 = 1 hr

So the trains will meet each other after 1 hour so,
Distance covered by first train in 1 hour = 60km/hr * 1hr = 60 km,
Distance covered by second train in 1 hour = 40km/hr * 1hr = 40 km,
Therefore, the distance from station A where both trains will meet = 60km.