Aptitude - Problems on Trains - Discussion
Discussion Forum : Problems on Trains - General Questions (Q.No. 31)
31.
Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:
Answer: Option
Explanation:
Let us name the trains as A and B. Then,
(A's speed) : (B's speed) = b : a = 16 : 9 = 4 : 3.
Discussion:
109 comments Page 4 of 11.
Sk.vali said:
1 decade ago
Speed, distance, time.
s1, d, t+9 (s1=d/t+9) ----1.
s2, d, t+16 (s2=d/t+16) ----2.
(s1+s2), d, t (s1+s2=d/t) ----3.
From equation 3.
s1+s2 = d/t.
=> (d/t+9) + (d/t+16) = d/t (from 1&2).
d get cancelled.
Finally by solving we get t = 12.
Now by substituting 't' value in equation 1&2.
We get s1 = d/21.
s2 = d/28.
Therefore ratio s1/s2 = 28/21.
= 4/3.
s1, d, t+9 (s1=d/t+9) ----1.
s2, d, t+16 (s2=d/t+16) ----2.
(s1+s2), d, t (s1+s2=d/t) ----3.
From equation 3.
s1+s2 = d/t.
=> (d/t+9) + (d/t+16) = d/t (from 1&2).
d get cancelled.
Finally by solving we get t = 12.
Now by substituting 't' value in equation 1&2.
We get s1 = d/21.
s2 = d/28.
Therefore ratio s1/s2 = 28/21.
= 4/3.
Lalit said:
1 decade ago
Just think like they all traveled equal time before meeting.
Take that time as T so.
A traveled to the point of meeting in T time while the same was traveled by B in 9 hours after meeting. similar situation for B.
So Considering the ratio of their speed remains constant.
T/16=9/T, This will give value of T as 12.
Now calculate time by each and thus Ratio.
Take that time as T so.
A traveled to the point of meeting in T time while the same was traveled by B in 9 hours after meeting. similar situation for B.
So Considering the ratio of their speed remains constant.
T/16=9/T, This will give value of T as 12.
Now calculate time by each and thus Ratio.
Himanshu said:
1 decade ago
One of the smart way of doing the question is by seeing the options itself. Since the first train reach its destination earliest after meeting the second train, then its speed would be greater than the second train and so as the ratio. In the options given above, only in B the ratio of the first train greater than the second.
Abhishek Raaz said:
8 years ago
Let a be the speed of train A.
b be the speed of train B.
Time taken by train to meet each other = t.
at is distance covered by A in meeting with train B,
bt is distance covered by B in meeting with train A.
A/Q
bt/a = 9 ----> (1)
at/b = 16 ----> (2).
Solving equation (1) and (2) we get,
a/b = 4/3.
b be the speed of train B.
Time taken by train to meet each other = t.
at is distance covered by A in meeting with train B,
bt is distance covered by B in meeting with train A.
A/Q
bt/a = 9 ----> (1)
at/b = 16 ----> (2).
Solving equation (1) and (2) we get,
a/b = 4/3.
Parvatraj said:
1 decade ago
L.C.M of 60,80 and 40 is 240..
so let be 240 is the distace .
then train with 60kmh will take 8 hrs to complete.
and trains with 80 kmh and 40 kmh will take 9 hrs to complete.
so the time difference is (9-8) =1.. so what is required is 4 hrs lap.
so multiply with 4 we will get 240*4 = 960 km ..that is the answer.
so let be 240 is the distace .
then train with 60kmh will take 8 hrs to complete.
and trains with 80 kmh and 40 kmh will take 9 hrs to complete.
so the time difference is (9-8) =1.. so what is required is 4 hrs lap.
so multiply with 4 we will get 240*4 = 960 km ..that is the answer.
Praveen said:
1 decade ago
A train travelled from Delhi to Patna and back in a certain time at the rate of 60kmph. But if the train had travelled from Delhi to Patna at rate of rate 80Kmph. And back from Patna to Delhi at the rate of 40Kmph. It would take two hours Longer. Find the distance between Delhi and Patna?
Detailed solution please.
Detailed solution please.
Adarsh said:
1 decade ago
I understand what you did there abhishek. There is just one Problem. The distance "X" which you are taking for both trains, how do you know it is the same. i.e. They are both travelling at different speeds, so they definitely won't meet at a mid point so there cannot be a single X for both train's distances, right?
Shubham said:
9 years ago
Let Total Distance = D.
If they take t time to cross each other then.
A * t + B * t = D.
Total time taken;
A is t + 9 hrs.
B is t + 6 hrs.
Thus.
A * (t + 9) = D.
B * (t + 16) = D.
A * t + B * t = A * (t + 9).
A * t +B * t = B * (t + 16).
Take t common and divide above two equations to get the answer.
If they take t time to cross each other then.
A * t + B * t = D.
Total time taken;
A is t + 9 hrs.
B is t + 6 hrs.
Thus.
A * (t + 9) = D.
B * (t + 16) = D.
A * t + B * t = A * (t + 9).
A * t +B * t = B * (t + 16).
Take t common and divide above two equations to get the answer.
PS KUMAR said:
7 years ago
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.
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.
NANI said:
1 decade ago
Here in this question, one train had reached in 9 hrs and another one in 16 hrs.The first train reached faster than the second one ,clearly it should have more speed than the second one, as we know that time and speed are inversely proportional and comparing all answers, 4:3 is most optimal.
(1)
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