Aptitude - Problems on Trains - Discussion

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.

Why are getting the square root. Can anyone explain to me?

Solving the eqns..
D=(v1+v2)t ---------> 1
D=(t+9)v1---------> 2
D=(t+16)v2---------> 3.

Putting the value of t from eq 1 in eq 2 & 3 then taking all the term having D on one side and then taking ratio of eq.2 & 3.

And we will get v1/v2=√16/√9= 4/3.

The correct answer is 4/3 because in the question both trains meets with each other before the now covered their remaining distance in 9hr and 16hrs respectively.

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.

Thank you so much @Ishita Narula.

Thanks for explaining @Pandu Ranga.

The above explanations are not correct. For example,

2 trains at station A&B. It starts at the same time at 8 AM in the morning. Train A speed is 100km/hr&train B speed is 150km/hr. Then they will meet after 4 hrs. If the total distance is 1000km.

After meeting, B takes 9hrs (TOTAL 13hrs) to complete its journey and A takes 16hrs (TOTAL 20HRS) to complete its journey. So the speeds of both trains decreasing to 50 km/hr &76.92km/hr. So equations 2&3 are not correct.

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.

Let us take both trains to meet after time t.

And the speed of train A and B as x and y.

So now whatever distance covered by train A in time t is covered by train B in 16 hours.
So x*t = y*16 --> eq(1)

Similarly whatever distance covered by train B in time t is covered by train A in 9 hours.
so y*t = x*4 --> eq(2).

From eq(1) and eq(2),
We get (x^2 / y^2) =( 16/4).