Aptitude - Problems on Trains - Discussion

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

How - 5 came? Please explain this step.

How this 18/5 come? please explain to me.

How it 18÷5 will become? Please explain.

Here is the solution for this question:

The length of a train is given as 125m (here it is mentioned as m/s), and the speed is given as 5km/hr (here it is mentioned as km/hr).

While converting km/hr into m/s, we are multiplying the speed by 5/18; therefore while converting m/s into km/hr, we have to take the reciprocal of 5/18, that is 18/5. The speed of the train should be calculated in km/hr; therefore, we take 18/5.

How 18/5 came after 25/2? Please answer.

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.

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

18/5 is the direct formula to convert the m/seconds to km/hr.

In this given problem, we can convert the m/sec to km/hr so we use 18/5.

Suppose we have to convert km/hour into m/s.
km/hour = 1000m/hour
i hour = 3600s
km/s = 1000m/3600s = 5/18.

Just reverse it, m/s into km/hour = 18/5, it's an easy way.

@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.