Re: A train with 120 wagons crosses Ram who is going in the same direction
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08 Dec 2019, 04:53
The answer is B: 3576 seconds.
EXPLANATION:
First, we have to assume that the horse moves with the same speed. Otherwise, this question can't be solved, as there would be an extra variable to consider with less equations.
Now, let the speed of horse be y, and the speed of train be x.
Now, using relative speed formula:
\( (X-Y)*36= (X+Y)*24 \)
This is because, train is moving towards shyam, who is moving towards train. Hence, their combined speed is X + Y. Similarly, train is moving away from Ram, who is moving in the same direction as the train. So combined speed is X - Y.
Since the distance covered by Shyam would be the same that would be covered by Ram, we calculate the distance covered by Ram in 36 seconds as \( speed*time \) which is \( (X-Y)*36 \), and the distance covered by Shyam in 24 seconds as \( (X+Y)*24 \). Equating both, we get the equation.
Solving them, we get:
\( X = 5Y \)
This means, speed of the train is 1/5th of speed of horse. This relationship gives us following idea:
For L distance covered by Train, Horse would cover L/5 (as Distance = Speed*Time, assuming time as constant, distance would vary by speed directly).
Also, if train covers something in 30 minutes, the horse would take 150 minutes (as Distance = Speed*Time, assuming distance constant, time would vary inversely)
So if the train takes 30 minutes of the time that it starts overtaking Ram before it starts overtaking the Shyam coming from the opposite direction, each horse would take 150 minutes.
Now, let's assume the length of the train as L. This L, is the same distance, that the train has to cover WHEN IT STARTS overtaking Ram, and BEFORE IT STARTS overtaking shyam.
Understand this, by the time train covers this L distance, 30 minutes would have passed (given in the question). This means, in these 30 minutes, the horse in which Ram is riding would also have moved towards Shyam. By how much? We go to our earlier relationship of X = 5Y.
Since we know the speed is 5 times, so Ram WOULD HAVE MOVED L/5 distance, BEFORE TRAIN STARTS OVERTAKING SHYAM.
This means, the remaining distance is 4L/5.
Now, to cover L distance, horse uses 150 minutes (as train uses 30 minutes).
So, to cover 4L/5 distance, horse would use 120 minutes.
This is given for both horses. So for each individual horse (or to get midpoint of their meeting), we would get 120/2 = 60 minutes.
Now, we are not done yet. By the time train was overtaking shyam, shyam moved for 24 seconds. This means we have to subtract 24 seconds from 60*60 = 3600 seconds.
Hence, the final answer would be 3600 - 24 = 3576.
To sum up, following line of thought is followed:
A) First, we get relationship between speed of train (x) and speed of horse (y), which is x = 5y. This is done by equating their relative distance covered (which is same).
B) Then, once we know their relationship between speed, we get the relationship between time and distance.
C) Now, we assume L is the distance train moves in 30 minutes, which is when it STARTS overtaking Ram, and BEFORE it starts overtaking Shyam.
D) For this L distance that is covered by the train in 30 minutes, L/5 distance is covered by the horse in 150 minutes. So we calculate the time taken by the horse for the leftover distance (4L/5), which comes to 120 minutes.
E) Since we need midpoint for each horse, we get 60 minutes the distance to be covered by EACH horse.
F) We also subtract the additional 24 seconds covered by Shyam when the train was overtaking Shyam.
G) So we get final value as 3600 - 24 = 3576!