Aptitude - Problems on Trains - Discussion

@Chai.

Why do we have to take the distance 390 when we add this covered by A after x hours and this covered by B after x-1 hours then why we equal it to 390 km?

Here, how will get 110? Please explain.

For equal starting time of two trains (ie 8am, 8am).

Train A cover a distance in one hour = 20km.
So total distance covered by two trains =110-20.
= 90km.
The relative speed of trains =20+25.
= 45kmph.

Two trains are meeting at a time of X hr.
The formula is;
90/X = 45,
X=2,
8am+2 = 10am.

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).

Let x be the meeting distance from A and B.

Then A travels (X/20) hrs and B travels (110-X/25) {time=distance/speed}.
But A stars 1 hour earlier than B.

So;

(X/20)-1 = (110-X)/25.
solving this;
we get X=60kms.

Now
A travels 60 kms at the speed of 20kmph to meet B in the midway of travel.

So now
Time is taken to travel to meet B 60 kms from starting point
A takes+ 60(distance) / 20(speed) = 3 hrs.

From question,

'A' starts to travel at 7 A.M and travels 3 hrs(from final answer) to meet B in the midway of travel.

So the time 'A' and 'B' at meet is [7+3]= 10 A.M.

Let they meet X hrs from the 8 a.m.
Then,
110 * 1000 = 20 * (5/18) * 3600 + 45(5/18) * X.
X=2.
So, time= 8+2 = 10 a.m.

I dint get how x-1 term is used.

Thanks yuvraj.

A----------110---------B 7am

A---------90--------B 8am(Speed of the 1st train is 20 km/h)

A----45----B 9am(relative speed=20+25(45) km/h)

AB 10am

Yuvraj. Cool answer!