Aptitude - Problems on Trains - Discussion

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.

Consider we need to convert m/sec to km/hr..
If we need to convert something from m to km, 1km=1000m. Thus 1m= (1/1000)km
So we multiply the numerator by 1/1000.

Similarly, (denominator part) for a sec to hr, 1hr=3600sec. Thus 1sec=(1/3600)hr.
So we multiply the denominator by 1/3600.

This conversion part becomes 3600/1000 thus simplifying this gives an std form of 18/5.. which is always directly used in converting m/sec conversion to km/hr.. helps in just multiplying this 18/5, instead of separate conversion of numerator and denominator to km and hr separately which is time-consuming..

Similarly, the reciprocal of this is just the vice versa case from km/hr to m/sec just multiply with 5/18.

Your running at a speed of 5km/hr
(1km=1000 meter and 1hr=3600seconds,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 diretion.
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

Dear Friends,
Understand the question:
Train speed relative to man (X-Y) = ?
X is Train speed.
Y is Man speed (given as 5 km/hr).

We have length(distance) train passes = 125m.
Train passed in time = 10 seconds.

Hence, speed = distance/time.
speed = 125/10 meters/seconds.
Speed = 25/2 m/s.

Let's convert m/s to km/hr.

****Remember While conversion of km/hr to m/s, multiply with 5/18 or 0.277.
Similarly, conversion m/s to km/hr, multiply with 18/5 or 3.6.
(these are not blind values, we can get if we calculate)****

= 25/2 X 18/5 km/hr.
= 45 km/hr.

Let's see,
Train speed relative to man.
X-Y = ?
X-Y = 45 km/hr.
as we know Y = 5 km/hr.
X-5 = 45.
X = 45+5 = 50 km/hr.

The only thing to remember is that when objects are moving in the same direction,then relative speed is equal to subtraction of their respective speeds and when the objects are moving in opposite direction,then relative speed is equal to addition of their respective speeds.

Therefore, here v1 = 5 km/h, v2=?, t=10sec => 10/3600 hr.,
Distance = 125 mt => 125/1000 kms.

Now we know, Speed=distance/time.
or we can say, Relative speed = distance/time.

Since here relative speed= v2-v1 (objects moving in same direction).
Therefore, v2-5=125/1000 whole divided by 10/3600.

or, v2-5=125/1000 * 3600/10, on solving we get,
v2-5= 45 => v2 = 45+5 => V2=50 Km/hr.

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.

HEY NEERAJA.

Distance = Time*Speed 125 = 10*Speed.

Distance/Time = Speed 125/10 = (25/2) m/s = Speed.

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Answer should be in km/hr so convert m/s.

Km = 1000 m and hr = 3600 s.

M = km/1000 and s = hr/3600.

M/s = (3600/1000) km/hr.

M/s = (18/5) km/hr.

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The condition was speed = (25/2) m/s.

= (25/2)(18/5) km/hr.

= 45 km/hr.

The speed was relative to man so we have taken time in consideration of man.

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See further in in view answer.

Relative speed of any two object say x km/h and why km/h moving in the same direction would always be (x-y) km/h.

Here the speed of the train is related to the man.

Hence relative speed = 125/10 m/s = 25/2 m/s.

The speed of the man is 5 km/h. When you convert it for m/s the speed will be (5x5/18) m/s = 25/18 m/s.

We know that relative speed,

R.S = (x-y) m/s or km/h.

Here x (unknown) , y= 25/18 m/s and R.S = 25/2 m/s.

Substituting we get,

X = (25/2)+(25/18).
X = 250/18 m/s (or) (250/18) x (18/5) km/h.

So X = 50 km/h.

Therefore the speed of the train will be 50 km/h. Hope you got it!.

DONT WORRY FRIENDS ITS VERY SIMPLE

instead of going for a new formula.we can simply get the answer by using the standard formula.i,e

t=(a+b)/(u-v)
u can see this formula from the general formulas of this exercise.
where
t-time taken by the train to cross the man=10 sec;

a-length of the train=125meters;
b=0(because the train is supposed to cross a person);
u=speed of the train(you are supposed to find out);
v=speed of the man who is running=5km/hr=5*(5/18)=25/18m/sec;

by substituting the values in the above equation you can get the value..

Step 1:

The relative speed of the train concerning man = Distance/Time =125m/10sec= 12.5m/s.

Step 2: Convert the answer of "step 1" from m/s to km/hr..
To convert it into km/hr multiply it with 18/5.
12.5 * 18/5 = 45km/hr.

Step 3:
Train as well as the man both are moving in the same direction so we will have to subtract the speed of train(x) from the speed of the man(5).
(Note: If the train and man both are moving in opposite directions then add both of their values (x+5) ).

Relative speed = (x-5)km/hr
45km/hr = (x-5),
x=50 km/hr.