In a circular race of 1500 m, A and B start running simultaneously at speeds of 27 km/hr and 45 km/hr from the same point and the same time. After how much time will they meet at the starting point for the first time if they are running in the opposite direction?

Correct option is A

Given:
Track length = 1500 m
A speed = 27 km/hr
B speed = 45 km/hr
They start together from the same point and run in opposite directions.
Formula Used:
Convert speeds to m/min: speed (m/min) = (km/hr × 1000) / 60.
Time for one lap = track length / speed (in m/min).
They will meet at the starting point together when the time is a common multiple of their lap times — so find the least common multiple (LCM) of the lap times.
Solution:
A = 27 km/hr = 27000 m/hr = 27000/60 = 450 m/min.
B = 45 km/hr = 45000 m/hr = 45000/60 = 750 m/min.
Time for one lap (track = 1500 m):
Time_A = 1500 / 450 = 10/3 min = $$3\frac{1}{3} min.$$​​
Time_B = 1500 / 750 = 2 min.
LCM(10,6)/3 = 30/3 = 10 min.
Therefore, they will meet at the starting point together for the first time after 10 minutes.
Exam Hall Method: