Aptitude - Problems on Trains - Discussion

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

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.

Let the train meet after time t at point O and train from Howrah to Patna travels X1 distance with speed v1 and train from Patna travels X2 distance with speed v2 to reach O.
X2=9 *v1 ; X1= 16*v2
and X1 = t*v1 ; X2= t*v2.
From above equations
16* V2^2=9*V1^2,
V1/V2=4/3.

Howrah(A) ------------------------- Patna(B).

Let, distance between Howrah and Patna be x; S1 = speed of 1st train from A to B; S2 = speed of 2nd train from B to A.

Let, after t hours both trains meet each other.

So, distance covered by 1st train in t hours = S1 * t = distance covered by 2nd train after he meets the 1st train and goes towards station A.

So, S1 * t = S2 * 16 Or, S1/S2 = 16/t--> (I)

Again, distance covered by 2nd train in t hours = S2 * t = distance covered by 1st train after he meets the 2nd train and goes towards station B.

So, S2 * t = S1 * 9 Or, S1/S2 = t/9--> (II)
From equations (I) and (II), we get,
16/t = t/9
=> t^2 = 9*16 = 144
=>t = 12 hours ( as t is time hence -12 is neglected).

Hence, ratio of speeds,
S1/S2 = 12/9 = 4/3 (putting t=12 in equation(II)).
Or, S1 : S2 = 4 : 3.

The initial answers were lengthy.

Now since both are departing at same time,
1 step d1/d2=v1*t/v2*t=v1/v2,
2nd step d1/d2=v2*16/v1*9,
And on equating both we get the required solution.

Here we need to find the ratio of the speed of the trains for which trains have travelled.

Distance D is same for both. So the ratio of speed,
=> S1:S2,
=> D/a:D/b,
=>1/a:1/b
=>b:a.

As per your answer 4:3.

Take A= 40 kmph,
and B= 30 kmph,
So now distance travelled by A = 40*9= 360km,
Distance by B = 30*16 = 480 km.

Is these two distance are same.

Two get the ratio of the speed of trains simply flip the ratio of the time(speed and time are inversely proportional to each other). i.e, 16:9.

Otherwise to get your answer 4:3 simply replace 9 with 12 in question.
16:12 ==== 4:3.

I think answer for this question will be 3:4.

Thanks for the explaining the answer @Ishita Narula.

Let the trains name as 1 and 2.
Let the time taken to meet be t.

Train1with speed S1 took 9hrs which took time "t" for train2 .(S1*9 = S2* t)
Similarly, train2 with speed S2 took 16hrs which took time "t" for train1(S1*t = S2*16).
Equating t from both equations we get the answer.