Aptitude - Problems on Trains - Discussion

Very useful. Thanks for the explanation.

That is nice. Thanks all for the explanation.

Well done, Thanks all for explaining the answer.

Total distance = x.
Time is taken to cross = t.
Speed of both trains = U and V.
Time taken after t seconds to reach Patna = t+9.
Time taken after t seconds to reach Howrah = t+16.

x=(U+V)t-----------(1)
after time t total distance covered by train A.

x=U(t+9)------------(2)
After time t total distance covered by train B.

x=V(t+16)-----------(3)
By solving eq(1) and eq(2).

we get Vt=9U-----------(4)
by solving eq(1) and eq(3).

we get Ut=16V----------(5)
by solving eq(4) and eq(5).

We get U/V=4/3
therefore the ratio is 4:3.

Divide distance into two parts based on the point where they meet.

Let first half of journey took x hrs which is same for both trains.

Total time for train 1 = 9+x.
Total time for train 2 = 16+ x.

Let the speed of the first train(took 9 hrs to complete the second half of its journey) be a

Speed of the second train( took 16 hrs to complete the second half of its journey) be b

The total distance between the cities is 9a+16b.

Now,

Speed = distance/ time.

a = 9a+16b/9+x.
b= 9a+16b/16+x.

eliminate x.
ax= 16 b,
bx = 9a.

16b/a =9a/b.

a/b = 4/3.

Let say the distance between them is d, and it takes time t when both the trains meet each other.

So relative speed = v1+v2.

So t = d/ (v1+v2) -----> (1).

Now for the train 1 distance remains = d - t*v1.
For the train 2 distance remains = d-t*v2.

According to the question, it takes 9 hrs for the first train and 16 hrs for the second train.
So, 9 = (d-t*v1) /v1 and 16 = (d-t*v2) /v2.

Now from the equation 1, d = t*v1+t*v2 substitue above.
So 9 = t*v2/v1 and 16 = t*v1/v2.

Equating t, 9v1/v2 = 16v2/v1 so v1/v2 = 4/3.

Thanks everyone for explaining the answer.

Here we can use the ratio method:
Train 1 ( Howrah to Patna) = A.
Train 2 ( Patna to Howrah) = B/

Ratio of speed = √speed of A/ √speed of B
= √16/√9.
= 4/3.

That is the answer is 4 : 3.

Nice, Thanks all.

Good. Thanks everyone for explaining the answer.