Aptitude - Problems on Trains - Discussion

To convert m/s to km/hr we use direct formula,
i.e 18/5.
Here,1km/hr = 5/18 m/sec.

To convert a given data from m/sec to km/hr we use 18/5.

l = 125m,
u = 5km/hr,
v = ?
t = 10s.
u - v = 125/10 m/s,
u - v = 25/2 m/s,
u - v = 5*9 km/hr,
u - v = 45km/hr,
5km/hr - v = 45km/hr.
v = 50 km/hr.
Hence, option (B).

How 18/5? Please explain to me.

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.

HERE,
1hr = 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.

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.

According to me, it should be 25/2 × 18/5 = 45.

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.

@All.

Why do we minus the speed of the man moving in the same direction? 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.