Aptitude - Problems on Trains - Discussion

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?

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.

I didn't understand, please anyone explain me to get it.

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.