Aptitude - Problems on Trains - Discussion

l=125m;
s=5*5/18;
t=10s;
l=t*s;
s=t/l;
s=125/10;
s=12.5*18/5;
the man was also going same direction so,
s=45+5;
s=50;

Let the speed of the train is 'x'
Length=125m
Speed=10s
--> as per "Length of the train = speed X time"
--> 125m = 10s.x
--> x=(125m/10s) X (360/360)=(360 X 125m)/3600s
--> =45000m/3600s = 45km/1hr

As the above value is relative with the speed of man whose speed of running is 5km/1hr also to be added for the exact speed of the train.

There fore..
-->exact speed of the train is = (45km/1hr)+(5km/1hr)=50km/1hr

I believe its simple and right answer.

Let relative velocity of train with respect to man be vtm,actual velocity of train Be vt and velocity of man be vm.
We know that vtm=vt-vm,
But from problem vtm is =length of train/time taken
=(125*18/5)/10
=45 km/hr.

From above actual speed of train is,vt=vtm+vm

=45+5=50 km/hr.

A train of length 110mtr travelling at a speed of 80km/hr. Find the time taken by that train to overtake a train having length 130mtr travelling at a speed of 62km/hr?

@Preethi.

Relative speed u-v = 80-62= 18km/hr=(18* 5/18)= 5 m/s.

Total length a+b = 110+130= 240 m.

Time to overtake = (a+b)/(u-v)[see formula 9 from formula section]

= 240/5

= 48 sec.

Am I correct?

How we come to know that the speed 5km\hr is the speed of the man because it is not given in the question?

@Diksha.

A train 125 m long passes a man, running at 5 km/hr in the same direction means the , in between man and running is for confusing you it should be taken as 125 m long train passes a man running at 5 km/hr.

Why we are using 18/5 instead of 5/8 is as follows,
1km = 1000m.
1hr = 3600s.

So 1km/hr = (1000/3600)m/s.
Hence 1km/hr = (5/8)m/s.

Then 5/8 becomes reverse as 8/5 and it will becomes as,

(8/5)km/hr = m/s.

Again you get a doubt that why it converts into m/s because check our problem has 125 m and also they gave 10 seconds.

So (125/10)m/s.

Here the train is crossing a moving object rather than a stationary object like a pole. Then how it is possible to say its relative speed to man is (125/10) m/sec ?

This solution easy to understand:

Convert man speed from km/hr into meter/sec.

5km/hr = 5*1000m/3600sec or 25m/18sec.

Since 18sec = 25meter.

10sec = ? meter.

So it would be 25*10/18 = 125/9 meter.

So man complete 125/9 meter in 10 sec.

Train complete distance in 10 sec = 125 meter (train length) + 125/9 meter of man.

So it would be 10 = 125+125/9 or 10 sec = (1125+125) /9 meter or 10*9 sec=1125+125 meter or 90 sec = 1250 meter or 125 meter/9sec or convert it into km/hr so it be 125m/9s * 18/5 = 50 km/hr.

So train speed is 50 km/hr.

To convert km/hr into m/s it is multiplied by 5/18 or 1000/3600.

And from m/s into km/hr multiplied by 18/5 k done.