Aptitude - Problems on Trains - Discussion

Easiest method is,

220*18 = 6(250+5x).

Multiply by 6(250+5x) you get 1500+30x.

3960 = 1500+30x.

Subtract the value of 3960-1500 = 2460.

Then divide by this form,
2460/30 = 82 kmph

108+112=220.

220/6 is the relative speed per sec.

(220/6)*(18/5)=132 is the relative speed per hour.

Speed of the 2nd train is 132-50 = 82kmph.

Total distance of the 2 trains are 220 (108+112) :first don't change anything. Just change the speed 50 km/hr into m/sec.

If we change speed 50 ino m/sec then it will be 125/9. The equation becomes.

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

We get x=410/18 m/sec.

Now convert to km/hr we get x= (410/18) (18/5).

X=82.

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.

Here we assumed speed of second train as 'x' km/hr which is in km/hr,okay

then in problem it is converted in to m/sec as 'x*(5%18)' okay and

finally we got answer in terms of 'x' whose units are km/hr as

x=82 km/hr,

which can be in m/sec as

x*(5%18) = 82*(5%18) m/sec

In the equation all the units meter, second get cancelled so the remaining is x only, whose units is km/hr as we have choosen at beginning of the problem. Hence the result is in km/hr.

@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

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

Nice explanation Sanjay.

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