Aptitude - Problems on Trains - Discussion

@All

Here they mentioned the relative time of the train to the man is 10 seconds which means the train's length(i.e 125m) has just passed the moving man in 10 seconds,so we need to find the relative speed for the train to the man as mentioned below.

i.e, 125/10 =25/2 m/s as it is in m/s,we need to convert into km/hr
25/2 x 18/5 = 45 km/hr (relative speed between train and man)

Next we need to find the original speed of the train that passes the man's speed with the help of the relative speed between the train and man i.e,45 km/hr(,if the Direction of the man and train is opposite to one another, then do addition, if both man and train running in same direction subtract both )
Here man and train are in the same direction.
So subtract;
Let x be the speed of the train and we know the man's speed as 5 km/hr and the relative speed is 45 km/hr.
Since same direction subtraction,
x = 45+5
x = 50 km/hr (answer)
By checking:
Train's speed =50 km/hr ,,man's speed = 5 km/hr, same direction so do subtraction;
50 -5 = 45 to get the relative speed of both.

125/10 = 12.5,
12.5 * 3.6 = 45,
45 + 5 = 50.

I am not getting this. Anyone, help me to understand this.

How it is 50? please explain to me.

3600sec then, 1sec = 1/3600hr.
1km =1000m then, 1m = 1/1000km.
So,
km/hr to m/s is : 1/1000km bigger divided by 1/3600hr.
So, they put 18/5.

This is the concept of reference of frame.

Train speed is (x)
Let's say A person in a train says that a man(outside of the train(or) beside of train running at a speed of 5 km/ hr) running slow as (x-5)km/hr.

This means if the train speed is 20 km/hr. Then the man's relative speed is as slow as 15 km/hr when compared to train speed.
This relation is mentioned in the mathematical formula as( x-5)km/hr or ( example:20-5 km/hr).
So, the relative speed is;
X - 5 = (120/10)*(18/5)
So x = 50 km/ hr.
*18/5 is used to convert m/s into km/ hr.

How answer is 50 km/hr? Please explain to me.

Sp of man = 5 * 5/18
= 25/18 m/sec.

Let Sp of train be x, then;
x - 25/18 = 125/10
So x = 125/10 + 25/18 = 125/9 m/sec.
So x = 125/9 * 18/5 =50 Km/h.

@All.

Why do we minus the speed of the man moving in the same direction? Please explain to me.

Consider we need to convert m/sec to km/hr..
If we need to convert something from m to km, 1km=1000m. Thus 1m= (1/1000)km
So we multiply the numerator by 1/1000.

Similarly, (denominator part) for a sec to hr, 1hr=3600sec. Thus 1sec=(1/3600)hr.
So we multiply the denominator by 1/3600.

This conversion part becomes 3600/1000 thus simplifying this gives an std form of 18/5.. which is always directly used in converting m/sec conversion to km/hr.. helps in just multiplying this 18/5, instead of separate conversion of numerator and denominator to km and hr separately which is time-consuming..

Similarly, the reciprocal of this is just the vice versa case from km/hr to m/sec just multiply with 5/18.