Arjun and Bhim can run a full round around a circular track in 4 minut

Question)
Arjun and Bhim can run a full round around a circular track in 4 minutes and 7 minute respectively. If they start simultaneously, after how much time will they meet together at a point diametrically opposite form the starting point?

Solution)
Time taken by A = 4 min & that by B = 7 min
To avoid complicated calculations, we can assume the length of the track as 28 meters (LCM of 4 and 7)
[note: you may also take it as 28k meters]
Thus, speeds of A and B = 7 meters/min and 4 meters/min

Same direction:
Speed ratio = 7 : 4 (lowest form)
Thus, number of meeting points = 7 - 4 = 3
Each gap (length) between meeting points = 28/3 meters
Thus, the meetings are: 28/3 meters from starting point; 56/3 meters from starting point and the starting point itself

Opposite direction:
Speed ratio = 7 : 4 (lowest form)
Thus, number of meeting points = 7 + 4 = 11
Each gap (length) between meeting points = 28/11 meters
Thus, the meetings are: 28/11 meters from starting point; 56/11 meters from starting point and so on.

Thus, there would never be any meeting diagonally opposite to the starting point
Answer E



Alternate approach:
Let they meet at a point diametrically opposite. For that, let A cover x laps and B cover y laps.
We have already assumed the lap length as 28 meters
Thus, equating the time taken by A and B, we have:
(28x + 14)/7 = (28y + 14)/4
=> 4x + 2 = 7y + 3.5
=> 4x - 7y = 1.5

However, x and y are integers, hence the above is not possible
Thus, answer is E