Aptitude - Problems on Trains - Discussion

Ratio of time of A and B =9:16.

Then the ratio of distance is the reverse of the ratio of time because when the time of A is less than B to cover a distance than the speed of A is greater than B so the ratio of the speed of A:B=16:9.

Simply A:B=4:3.

Time to meet the train t=(t1 * t2)^1/2.

Where t1=time take by 1 train to reach at the other ends just after using two train and similarly t2.

Thank you

Let a be the speed of train A.
b be the speed of train B.

Time taken by train to meet each other = t.
at is distance covered by A in meeting with train B,
bt is distance covered by B in meeting with train A.
A/Q
bt/a = 9 ----> (1)
at/b = 16 ----> (2).

Solving equation (1) and (2) we get,
a/b = 4/3.

Lets assume that:

1. They meet at time t.
2. total distance between trains before they start is d.
3. when they meet, one of the trains having speed "v1" has travelled "d1" distance. Hence other train having speed "v2" must have "d-d1" distance traveled.

Explanation:

Using the formula, distance=speed * time.
d1=v1*t -----> (1) for train 1.
d-d1=v2*t -----> (2) for train 2.

By using (1)and (2).
v1/v2=d1/(d-d1) -----> (3).

Now, the second train takes t+16 hours to cover "d" distance and other train take t+9 hours for the same distance.

So,

d=v1*(t+9)-----> (4).
d=v2*(t+16)-----> (5).

For result (4),

d=t*v1+9*v1.
Replacing t*v1 by the result (1).

Then we get,
d=d1+9v1-----> (6).

For result (5),
d=t*v2+16*v2.

Replacing t*v2 by the result (2).
Then we get,
d=d-d1+16*v2-----> (7).

From (6) and (7) we can write,
9v1/16v2 = (d-d1)/(d1)-----> (8).

From (8) and (3) we write that,
9v1/16v2=v2/v1.

Hence:
v1*v1/v2*v2=16/9.
v1/v2=sqrt(16/9).
v1/v2=4/3.

Let speed of train from Howrah to Patna = u.
And speed of train from Patna to Howrah= v.

Now let they meet at a distance x from Howrah and y from Patna after time t.

So t= (x/u ) = (y/ v)
=> x/y = u/v ----------------------------(1)

Now we are given that y/u = 9 --------(A)
and x/v =16 ----------------(B)

Divide B by A. We will get, (x/y) * (u/v ) = 16/9.

From equation (1), replace x/y by u/v,
= > (u/v)2 = 16/9
= > u/v = 4/3.

Best answer, thanks a lot @Chunky Kumar.

Thanks a lot @Sourav Sinha.

Thank you @Ishita Narula.

@Ishita Narula.

Thanks for your clear explanation.

Let Total Distance = D.

If they take t time to cross each other then.

A * t + B * t = D.

Total time taken;

A is t + 9 hrs.
B is t + 6 hrs.

Thus.

A * (t + 9) = D.
B * (t + 16) = D.

A * t + B * t = A * (t + 9).
A * t +B * t = B * (t + 16).

Take t common and divide above two equations to get the answer.