Aptitude - Problems on Trains - Discussion

Let speed be x and 2x kmph.

The total relative speed of the two trains = 3xkmph.
3600secs = 3000x.
1sec = 3000x/3600,
8secs=3000x/3600×8,
= 20x/3.
Btp;
20x/3 = 200,
x = 200×3/20,
=30.

Speed of slower train = 30kmph.
The faster train = 30 × 2 = 60kmph.

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.

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.

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.

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.

If x= 25/3, how is 2x= 50/3?

It should have been 50/6. Am I right?

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.

Distance =speed *time,
100+100=speed*8.
200=speed *8,
Speed=200/8,
Speed =25m/s,
Converting m/s into km/h.
25*18/5=90km/h,
As we want twice speed so first find single speed.
1+2 one is the speed of first train and 2 twice a second so combing we get 3 now,
Speed =90/3=30.
Now twice speed is 60km/h.

@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.

When you divide 200/24, you won't get 25/3? So I request you to explain me properly.