Aptitude - Problems on Trains - Discussion

Friends best answer is here.

Let train from Howrah to Patna (thp) speed is a kmph.

Let train from Patna to Howrah (tph) speed is b kmph.

Total distance from h to p = 9a+16b.

Train starts simultaneously, hence when both train meets then both spend same time while travel some distance.

Thp<------------16b----><-------9a----->tph.

Time through thp = Time through tph.

16b/a = 9a/b.

Hence, a/b = 4/3.

@Ishita Narula is correct. See her explanation.

Ishita Narula is absolutely right, no more debates on this.

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.

@Ishita Narula.

Thanks for your clear explanation.

Thank you @Ishita Narula.

Thanks a lot @Sourav Sinha.

Best answer, thanks a lot @Chunky Kumar.

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.

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.