Aptitude - Problems on Trains - Discussion

Here is the simplest form that you can understand.
Since the two train travel in opp directions, add both speeds. the speed of one train is given, let the speed of another train be x.
Speed=x+50 km/hr.
The relative distance = 108 + 112 = 220 m.
Time = 6 seconds.

Speed = distance/time.
x+50 = 220/6 m/s
x+50 = 110/3 *18/5(to convert m/s to km/hr ,since the answer required in km/hr)
x+50 = 132,
x = 82 km/hr.

@All.

First, we are assumed as X in km/hr, but we are applying the formula convert into M/S it is applicable for RELATIVE SPEED=(X+50).

It is not applicable for Assuming X, so the final answer is in KM/H.

The answer 82 is in m/s. We want to convert it into km/hr, because in first step we convert speed into m/s by multiplying 5/18.

Can we convert 50 km/hr into m/s and add the speed of other trains as they are in opposite directions?

Can anyone explain me?

@Ambika.

Good explanation. Thanks.

Given :
(length of 1st train) L1 = 108 m.
(length of 2nd train) L2 = 112 m.
(speed of 1st train) S1 = 50 KMPH = 50* 5/18 = 250/18.

(time taken to cross each other)T = 6 s.

Solution :
T = (L1 + L2 ) / (S1 + S2).

6 = 220 / ( 250/18 + S2).
(taking the right side denominator to left).

6( 250/18 + S2) = 220.
(multiplying 6 inside).

250/3 + 6 S2 = 220.
6 S2 = 220 - 250/3.
6 S2 = (660-250)/3
S2 = 410/18
( to convert this to KMPH - multiply by 18/5 )

S2 = 410/18 * 18/5
S2 = 82 KMPH

Hi Raj,

Please note that

At the first step we are taking the speed of the second train be x KM/HR.

At final step we are finding the value of 'x'.

So, the answer is 'x' km/hr.

Thats why the answer is in km/hr.

The answer is 82 km/h is correct. They have shown calculation for relative speed in wrong way.

Speed for 1st train is 50 km/h after conversion it will be 250/18 m/s.
And suppose speed for the second train in x m/s.
Relative speed will be (125 +9x)/9 m/s.

Then,
(125+9x)/9 = 108+112/6.
750+54x = 1980.
54x = 1230.
x = 22.78 m/s.

After conversion to km/h.
22.78x18/5= 82 km/h. Approx.

I believe this how they should have done.

If everything is converted into m/s then the answer will also be 82m/s not 82 km/hr.

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.