Aptitude - Problems on Trains - Discussion

Given:

Length of the train = 125 m.
Speed of the man = 5 km/hr.
Time taken to pass the man = 10 seconds.

First, we need to convert the speed of the man from kilometres per hour to meters per second:
5 km hr=5×1000 m3600 s=50003600≈1.39 m s.
5 km hr=5×3600 s1000 m​=36005000​≈1.39 m s.

Next, we calculate the speed of the train using the formula:
Speed=DistanceTime.
Speed=TimeDistance​.

The distance in this case is equal to the length of the train (125 m), and it passes the man in 10 seconds:
Speed of train relative to man =125 m10 s=12.5 m s.
Speed of train relative to man =10 s125 m​=12.5 m s.

Since this is the relative speed (train's speed minus man's speed), we can express it as:
Speed of train − Speed of man = 12.5 m s.
Speed of train − Speed of man =12.5 m s.

Substituting in the man's speed:
Speed of train−1.39 m s=12.5 m s
Speed of train−1.39 m s=12.5 m s.

Now, solving for the speed of the train:
Speed of train=12.5+1.39=13.89 m s
Speed of train=12.5+1.39=13.89 m s

Finally, converting this back to kilometres per hour:
13.89 m s=13.89×36001000=50 km hr
13.89 m s=13.89×10003600​=50 km hr.

Therefore, the speed of the train is 50 km/hr.

hai!frinds,.
in this above problem they given speed of the one object.
we know that if the two objectives are move in the same direction then the formula is"(A-B)"(assume A is one objective and B is another objective).so,nw we know one objective speed(taken as B speed we know),that is subtutited in above.

then s=(A-5).(here it is the speed of the train)
1.in the problem train(objective) speed is given in the form of seconds,so convert the seconds into the km/hr.because of the one objective speed is give in the form of km/hr and also answer is given in the form of km/hr.
2.while the conversion we have to follow the following,
i)if we covert m/sec inti km/hr then multiplis with"8/15"
ii)if we convert km/hr into the m/sec then multiplies with "15/8"
3.we know the formula for speed is
"speed=Distance/Time"(s=D/T)
s=125/10 m/sec [here 125 is the distance,and 10 is the speed of the objective]
the conversion
s=125/10*(18/5)km/hr
=45.
4.in starting we initialse the speed(s)=A-5
then subtuted that speed in the above,
A-5=45
A=50.
therefore the speed of the train(another objective) is "A=50".

@All

Here they mentioned the relative time of the train to the man is 10 seconds which means the train's length(i.e 125m) has just passed the moving man in 10 seconds,so we need to find the relative speed for the train to the man as mentioned below.

i.e, 125/10 =25/2 m/s as it is in m/s,we need to convert into km/hr
25/2 x 18/5 = 45 km/hr (relative speed between train and man)

Next we need to find the original speed of the train that passes the man's speed with the help of the relative speed between the train and man i.e,45 km/hr(,if the Direction of the man and train is opposite to one another, then do addition, if both man and train running in same direction subtract both )
Here man and train are in the same direction.
So subtract;
Let x be the speed of the train and we know the man's speed as 5 km/hr and the relative speed is 45 km/hr.
Since same direction subtraction,
x = 45+5
x = 50 km/hr (answer)
By checking:
Train's speed =50 km/hr ,,man's speed = 5 km/hr, same direction so do subtraction;
50 -5 = 45 to get the relative speed of both.

So in the above problem let us consider that the speed of the person is 5 km\hr .

Leave the 5 as it is and then convert the km\hr into m\s
that means 1 km=1000m
and 60min=3600sec

Now when actually converted 3600\1000 that would give u the two zero gets cut and remains is 36\10 that would give u after dividing each by 2 i.e 18\5which means
(18m\5s)1.FRACTION

Now the major calculation,
Two object over here is Train and the Man consider them as A and B
where A is the Train as we have to find the speed of the train
then B is the speed of the Man is 5
so we get A-5

We had 125m the length of train time 10 seconds
already these are in meters and in seconds no need to convert them so 125m\10s u get (25m\2sec) 2.FRACTION

Now, finally get the first fraction and the second fraction together i.e (18\5)*(25\2)u get 45 as answer when u calculate
then A-5=45 ,when u move the negative -5 to this side of the equals too sign it converts to positive giving u A=45+5

i.e 50 so A=50 and A is the speed of train!!hope u'll understood!!take care!!

Since the man is running in the same direction as the train, the distance covered by the train relative to the man is indeed the sum of the distance travelled by the man and the length of the train.

Let's recalculate:

Step 1: Calculate the distance travelled by the man in 10 seconds
Distance traveled by man (d_m) = Speed of man × Time = 1.39 m/s × 10 s = 13.9 m.

Step 2: Calculate the total distance covered by the train relative to the man
Total distance (d_t) = Length of train + Distance traveled by man = 125 m + 13.9 m = 138.9 m.

Step 3: Calculate the relative speed of the train concerning the man
Relative speed (v_r) = Total distance / Time = 138.9 m/10 s = 13.89 m/s

Step 4: Convert the relative speed to kilometres per hour.
Relative speed (v_r) = 13.89 m/s × (3600s/1000 m) = 50 km/hr.

Step 5: Calculate the speed of the train.
Speed of the train (v_t) = Relative speed + Speed of the man = 50 km/hr + 5 km/hr = 55 km/hr.

The correct answer is:
55 km/hr.

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 = 1000m and hr = 3600s
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.
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According to the question,

Trains length = 125m (distance).
Speed = 10sec,
Mans speed = 5km/hr.

The km the train hasn't travelled is not been given so take it as = X km/hr.
Man moves in the same direction = 5km/hr .

When two bodies are moving in the same direction then you will have to subtract it. If the person is moving on the opposite side he feels the train is moving faster hence u got to add But here it's on the same direction.

So, it's (x-5)km/hr.
When you want to convert kilometre into metres multiply with 5/18
So , (x-5) 5/18 ---> (1) i.e time

Time =distance/speed.
= 125/10 --> (2).

Therefore,
Time = distance/speed.
(X-5) 5/18 = 125/10,
(X-5)5/18 = 25/2,
(X-5) = 25/2 * 18/5 (simple cancellation).
(X-5) = 45,
X= 45+ 5,
X= 50.

Hi friends,the problem is very simple.Think in this way.Assume that the man is not moving(standing like a pole),now findout the speed of the train using the data.
LENGTH OF THE TRAIN=125m.
TIME TAKEN BY THE TRAIN TO CROSS THE MAN(assume standing)=10sec
w k t velocity=distance(length of the train)/time.
v=(125/10)m/s
v=(25/2)m/s
convert m/s into km/hr
v=(25/2)* (3600/1000) or (25/2)*(18/5)
v=45 km/hr
45 km/hr is the train speed if the person is standig(not moving).
But in the problem person is moving and that to he is moving in the same direction in which train going,so that's y add the speed of the man to the speed of the train then we will got the correct answer.
speed of the train+speed of the man=45+5=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.

Train moves with speed 125m/10 sec,.. So need to convert it as KM/ Hr ,..To convert 125m to KM we have to divide it with 1000 so it is 125/1000 and to convert 10 sec to hrs we have to divide it with 3600 so it is 10/3600.
Then it becomes (125/1000)Km/(10/3600)hr.
So we can change it to (125/1000)*(3600/10)..
It is (5/40)*(360) = (360*5)/40 = 180/4 = 45 Km/Hr.

.. Now we have got the speed in 1 Hour ie 45 Km..

As the man is travelling at 5 Km/Hr.. In that 1 Hr he already travelled 5 Km's.. So the train speed should be 45+5 Km's to cross that person in that 1 Hr.. Now answer is 50 Km/Hr.. I hope it is clear,... Take a paper a write exactly what i have given above,.. I am sure u guys will like it..