Aptitude - Problems on Trains - Discussion

Consider first train speed v' & other v"

After meeting point v'=(meeting point to patna)/9 = b/9.
v"=(meeting point to howrah)/16 =a/16
v'/v"=[b/a][16/9] ------> (1)
when train start and meet each other
time taken is same ie. T.

v'= (howrah to meeting point)/T = a/T.
v"=(patna to meeting point)/T = b/T.
then from above eq. v'/v"=a/b -----> (2)put in eq. 1.
From eq. 1;
v'/v" = (v"/v')[16/9].
v'^2/v"^2 = 16/9.
v'/v" = 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).

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.

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.

Thanks for explaining @Pandu Ranga.

Thank you so much @Ishita Narula.

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.

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.

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.

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