Aptitude - Problems on Trains - Discussion

6 = 220 then,
36 = (x+50)*10.
After cross multiple;
6*22 = X + 50.
X = 82.

(220)m
----------------- =6 sec.
((250+5x)/18)m/s
here,m and s are cancelled so x km/hr.

Hi.

I can't get it clearly. Please anyone explain it.

Hi Sundar.

What you said is right we have taken x in terms on km/hr, considering above explanation while converting relative speed we use (x + 50) km/hr both speeds converted into meters/seconds in next step. So final answer will be in m/s how it will be in km/hr?.

But Raj, When we calculate the speed of second Train, then we also convert the time in hour. But in the above question time write it as it is, without any conversion of time.

If we want result in Km/hr then we also need to change the time in hour because both the trains takes 6 seconds to cross each other.

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.

I want to explain clearly for those who have confusio b/w km/h & m/s.
Let take v M/s is the speed of the second train.
Thus formula is
T=220/(v+50*5/18)
after solv. it
we get
v=410/18 in M/s
convert v into km/hr
thus
v=410*18/(18*5)km/hr
then
v=82 km/hr.
I think its very clear now

Nice explanation Sanjay.

Hey the final answer is in m/s its not in km/h can some one clarify my doubt.

@Karthika , see when we take the series 220/5x+250/18=6 than the 18 will go up side and new series came 220*18/5x+250=6 , so here the formula 18/5 km/h is applicable .
I think ur doubt is clear