Aptitude - Problems on Trains - Discussion

Let me explain in details.

First train length, a = 108m.
Its speed, u = 50 km/hr = 50*5/18 m/sec= 125/9 m/sec.

Second train length,b = 112m.
Let, its speed, v = x m/sec.
Each other crosses in 6 sec.

So, we have, t= ((a+b)/(u+v)).
6= ((108+112)/((125/9)+x)).

(125/9)+x = 220/6.
x = (220/6)-(125/9)= 205/9 m/sec.

Converting in km/hr.

(205/9)*(18/5) = 82 km/hr.

Well I have a doubt, how did you get 5/18? Sorry if it is a stupid question!

I would like to bring this error to your notice that it is 82 m/s and not 82 km/hr.

Hai I have another option.

D = 220.
S = 50 kmph.
T = 6.
Other speed = x.

So speed = (x+50)*5/18.

T = D/S. Find T subtract 50 that's answer = 82 kmph.

Let me explain in detail.

Let the speed of second train be xkm/hr.

Therefore, relative speed = (50+x)km/hr (since it is opposite direction the speeds should be added). Then no need to confuse yourself by converting the speed to m/s.

Take it as it is, so as to get our answer in km/hr (as the given options are in km/hr). Now just convert the distances 108m & 112m into km/hr.

So add the distances & then convert it.

D = 108+112 = 220m = (220 x 18/5) = 792km/hr.

So now distance is in km/hr.

T = D/S.
6 = 792/(x+50).
6x+300 = 792.

Therefore x = 82km/hr.

(108+112)/6 = 50 + x.
(220/6)*(18/5) = 50 + x.

132 = 50 + x.
x = 82 Km/hr.

How does 660 comes in last step?

Yes answer is correct but checking through reverse process.

Let x = 82 km/h and we have find time to cross each other. Then then the answer will come 6 sec. So it is correct.

Relative speed = x+50 km/hr.

6 = 220/(x+50)*(5/18).

5/3 = 220/(x+50).

x+50 = 132.

x = 82 m/sec.

Please explain, how km/hr.

And one more method.

6/3600= (220*10^-3)/(x+50).

x+50 = 600*0.22.

x = 142-50.

x = 92 km/hr.

Now I am totally confused. Please help.

Distance = (220/1000) km {Want to convert meter into kilometer).

Time = (6/3600) seconds {Second into hours - one hour has 3600 seconds}.

Distance/Time = Speed.

= (220/1000)/(6/3600) = x+50 km {Opposite speed should be added).

Now without converting, follow normally:

220/6*3600 = (50+x) speed (If goes 220 m within 6 seconds, what is the distance per hour or 3600 seconds).

132000 m per hour = (50+x).

So, 132 kilometer = (50+x).

x = 132-50 = 82.