Aptitude - Problems on Trains - Discussion

Why we are using 18/5 instead of 5/8 is as follows,
1km = 1000m.
1hr = 3600s.

So 1km/hr = (1000/3600)m/s.
Hence 1km/hr = (5/8)m/s.

Then 5/8 becomes reverse as 8/5 and it will becomes as,

(8/5)km/hr = m/s.

Again you get a doubt that why it converts into m/s because check our problem has 125 m and also they gave 10 seconds.

So (125/10)m/s.

Here the train is crossing a moving object rather than a stationary object like a pole. Then how it is possible to say its relative speed to man is (125/10) m/sec ?

This solution easy to understand:

Convert man speed from km/hr into meter/sec.

5km/hr = 5*1000m/3600sec or 25m/18sec.

Since 18sec = 25meter.

10sec = ? meter.

So it would be 25*10/18 = 125/9 meter.

So man complete 125/9 meter in 10 sec.

Train complete distance in 10 sec = 125 meter (train length) + 125/9 meter of man.

So it would be 10 = 125+125/9 or 10 sec = (1125+125) /9 meter or 10*9 sec=1125+125 meter or 90 sec = 1250 meter or 125 meter/9sec or convert it into km/hr so it be 125m/9s * 18/5 = 50 km/hr.

So train speed is 50 km/hr.

To convert km/hr into m/s it is multiplied by 5/18 or 1000/3600.

And from m/s into km/hr multiplied by 18/5 k done.

Can anyone explain how to find length of train when the train speed and person speed given?

60min -> 5km.

1min->? =>(1*5)/60 = 1/12km.

For 1 second -> (1/12)/60 = 1/720km.

For 10 second ->(1/720)*10 = 1/72km.

It means train covered 1/72km in 10second, then calculate how much distance that train can cover in 60 min(1 hour). Because they've given the choices in km/hr.

=>(1/72)*(60*60)=50km/hr.

Note: Length of the train is not required in the calculation.

Distance covered by man = 5*5/18*10.

= 250/18 Meter.

Total Distance covered by Train = 125+250/18 = 2500/18 Meter.

So Train speed = (2500/18)/10 Meter/Second.

or = 2500/180*18/5 Km/Hr.

= 50 Km/Hr.

You're running at a speed of 5km/hr.
(1 km = 1000 meter and 1hr = 3600 seconds, which will be 1000/3600 = 10/36 = 5/18).
Note : for 1 km/hr.
Therefore 5(given km)*5/18 = 1.39.
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Meanwhile 125m long train crosses you in 10 seconds along with you in same direction.
Then!
125/10 i.e its in the form of (125)m/(10)s.
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So add those two values in the form of m/s, which is 13.89 = a.
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Now question to find speed of the train,since we found in the form of m/s, but the options provided are in the form of KM/HR.
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So to convert M/S to KM/HR :
(a*18/5)=(13.89*3.6).
Gives answer as 50 km/hr.

I solved this question in a different way:

When we solve the questions in which train passes a pole(or a standing man), in that case the distance traveled is equal to the length of the train. in this case,

1. The distance travelled would be = The distance traveled by the train assuming the man was standing+The distance travelled by the moving man in those 10 seconds.

= 0.125km+5*(10/3600).

= 0.139km.

Where,

0.125 is the length of the train in km.

5 is the value of speed of the man i.e. km/h.

10/3600 is the time given but converted in hr.

2. Now the speed.

As we know speed = distance/time.

Above calculated value divided by 10/3600 hr.

= 0.139/(10/3600).

= 0.139/0.00278.

= 50 km/hr.

Man speed 5 km/hr, So man's speed per second (5*5/18) m/s.

After 10 sec, train passes the man, so, man cover distance in 10 sec is :

5*5*10/18 = 13.89m.

So, train covered total distance in 10 sec is :

125 m+13.89 m = 138.89 m.

So, speed of train is :138.89/10 m/s = 13.889*3600/1000 Km/hr = 50 Km/hr.

Friends its a simple logic that if a men travel along the same direction of the train then the train speed is subtracted if it travel in opposite direction then train speed is added.

Hope you understand take this logic in your mind and solve any problem.