Aptitude - Problems on Trains - Discussion

How does 660 comes in last step?

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

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

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.

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.

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

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

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.

Formula : T=(x+y)/(u+v).

Where,
x,y -- Distance.
u,v -- Speed.

6 = (108+112)/((50*5/8)+V).

6v+250/3 = 220.

Therefore, v = 205/9 m/sec.

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

Given,

Speed of first train = 50km/hr (after convert it into m/s it becomes 125/9m/s).

Speed of second train = ?

Length of first train = 108m.

Length of second train = 112m.

Now, lets take the speed of second train be x m/s.

So by speed formula i.e.

Speed = distance/time keeping the values in this formula we'll get,

125/9+x = 108+112/6 (here we are adding these value b'coz they are moving in opposite direction).

By taking lcm of 9 on L.H.S it becomes,

(125+9x)/9 = 220/6.

By cross multiplication.

6 (125+9x) =220*9.

750+54x = 1980.

54x = 1980-750.

54x = 1230.

x = 1230/54.

x = 205/9 m/s.

But now we've to convert it into km/hr so.

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

After cancellation it become.

Answer: 82 km/hr.

Total distance = 108+112 = 220 m.

Time = 6s.

Relative speed = distance/time = 220/6 m/s = 110/3 m/s.

= (110/3)x(18/5) km/hr = 132 km/hr.

=> 50 + speed of second train = 132 km/hr.

=> Speed of second train = 132-50 = 82 km/hr.