Aptitude - Problems on Trains - Discussion

Now study the problem carefully the given data is
two trains moving in opposite direction . that means we add them 100+100=200mts

to cross these 200mts it takes 8 secs ok
now, they have asked to find the speed of the faster train if the speed is twice the slower train , this is given in the question.

Now ,

speed=distance/time

speed=200mts/8secs ok
as options are given in km/hr , we have to convert speed to km/hr

So we multiply with 18/5
well (200mts/8secs)*18/5=(200/8)*(18/5)=90km/hr
these is the total speed .

Now they asked us to find the speed of the train twice the other train

Let the speed of first train =xkm/hr

Speed of other train should be twice=2x km/hr

So we have got total speed as 90km/hr
x+2x=90km/hr
3x=90km/hr
x=30km/hr
speed of one train is 30km/hr.

So they asked twice the speed of train

So we get 2x=2*30
=60km/hr
Now if we add 30+60=90km/hr

We got the total speed

The speed of the faster train is 60 km/hr

Let the speed of the slower train be "x" m/s.

Since the faster train is moving twice as fast, its speed is "2x" m/s.
When two trains moving in opposite directions cross each other, their relative speed is the sum of their individual speeds.
So, the relative speed of the two trains is (x + 2x) m/s = 3x m/s.
Distance traveled by each train to cross each other is 100 meters (the sum of their lengths).
Now, we can use the formula: Distance = Speed × Time.

In this case, Distance = 100 meters and Time = 8 seconds.

So, 100 = 3x × 8.
Now, solve for x:
100 = 24x,
x = 100/24,
x = 25/6,
x = 4.1667 m/s (approximately).

So, the speed of the slower train is approximately 4.1667 m/s, and the speed of the faster train is twice that, which is 2 * 4.1667 ≈ 8.3333 m/s.
Therefore, the speed of the faster train is approximately 8.3333 m/s.
Converted to Km/hr is 30Km/hr.

L of train A= 100m.
L of train B= 100m.

Time taken for trains to cross each other= 8s.
Assume the speed of Train A= you.
Assume the speed of Train B= 2u since the rate of one train is twice the speed of the other.
Both trains are running in opposite directions hence, use the formula.
The Time is taken to cross each other= (L of train A + L of train B) / (speed of train A + speed of train B).

Substituting: 8sec= (100m+100m) / (u+2u) ;.
8sec= 200m/3u.
Cross multiply 8sec*3u=200m.
24uSec=200m; Divide both sides by 24Sec.
U= 25m/3Sec or 8. 33333m/sec.

Therefore, the speed of a faster train (i.e train with a speed twice as fast as the other) = 2u= (2*25) /3 or 2*8. 3333= 50/3 m/sec.

Convert the answer to km/hr by dividing the answer by 5/18.

= (50/3) / (5/18) = (50*18) / (3*5) = 60km/hr.

@Mounika.

We supposed the speed of the first train = x.

Nd speed of the faster train which is moving twice as fast the other = 2x (as we have given).

Now, given length of each train = 100m,

Time = 8sec,

Substitute these value in formula.

Time = (distance/speed).

8sec = (100+100/x+2x).

"Here we are adding the values b'coz the trains are in opposite direction with each other, which you can easily understand by reading the formula column. ".

8 = 200m/3x.

By cross multiplication.

24x sec = 200m.

x = 200/24.

x = 25/3 m/sec.

When we convert it into km/hr it becomes.

x = 30km/hr but.

Acc. To question they are asking for faster train which is 2x.

So by putting the value of x in 2x we'll get the correct answer.

2(30km/hr).

Answer = 60 km/hr.

Two train length is 100 m long each.
So, 100 + 100 = 200m.
Cross eachother in 9 sec so to find speed.

Speed = length/time.
Speed here ( one is moving twice as fast as the other).

If one train is x then another should be twice of x so 2x.

They are moving in opposite directions so x + 2x = 3x ( when moving in same direction we substract { u - v} in case of opposite direction { u+v}.

3x = 200m/9 sec * 18/5 (But the answer should be in km/s so we use 18/5).
3x = 90km/hr,
x = 90/3,
x = 60km/hr.

Let;
Speed of slower train (u) = X m/sec.
Speed of faster train(v) = 2X m/sec.

Because the second train is twice as faster the first train.
Each train is 100 m long So
a=100,
b=100.

Two trains are running in the opposite direction, So (u+v).
u+v=x+2x
=3x.

Time = 8sec
a+b/u+v = time
100+100/3x = 8;
200/3x = 8;
X = 25/3 m/sec;
X = 25/3*18/5 km/hr,
= 30 km/hr.

Speed of faster train = 2x.
=2*30.
=60km/hr.

How come 3?

Answer - If speed of slow train is x km/h.

In question the speed of fast train is twice to slow train.

So speed of fast train = 2*(Speed of slow train).

So speed of fast train = 2*(x) = 2x.

If trains are moving in opposite direction then we ADD the Speed. And trains are in same direction then we sub speed.

Here train in same direction so we add the speed of both train.

So x + 2x = 3x.

Here it is said that Relative speed is x + 2x (in opp. Direction).
So if you solved this then you get 30 km/hr but there is a catch the question said "If one is moving twice as fast as the other, then the speed of the faster train is" Currently 30 km/hr are following both train but question said what if faster has 2 X current speed, then calculate the faster train is 2 X 30 km/hr = 60 km/hr.

This is another way.
two trains opposite direction 100m+100m=200m.
200m to cover 8 seconds then,
(200m 8sec
? 3600sec
90000m that means 90k).
3600sec that mean 1 hour to cover 90000m that is 90k/h.
the train speed is 2:1.
total 3 parts.
3parts 90kilometers then,
2parts ?
60k.

"D = ST".

Total distance = 100+100 = 200 m.

Relative speed = s+2s = 3s.

T= 8 sec.

Putting these values.

200 = 3s*8.

S = 200/8*3.

S = 25/3 m/s.

Now be need to calculate speed in terms of km/h.

25/3*18/5 = 30 km/h.

Speed of slower train now speed of faster train is 60 km/h that is just double.