A and B start from the same point and travel in the same direction round a circular track 3 km in circumference. If their speed be 200 and 150 metres a minute, when will they first together again at the starting point?

Time taken by A in one round = 3000 / 200 = 15 min.
Time taken by B in one round = 3000 / 150 = 20 min
L.C.M. of 15 min and 20 min = 60 min = 1 hr.
Hence, they will meet first together at the starting point after 1 hour.
2nd Method to solve this
Let us assume after T minutes both A and B will meet first time together at starting points.
According to question,
Distance covered by A in T minutes = 200 x T = 200T
Distance covered by B in T minutes = 150 x T = 150T
200T - 150T = 3000 As we know (3 KM = 3000 meters)
⇒ 50T = 3000
⇒ 5T = 300
⇒ T = 300/5 = 60 Minutes.
As we know ( 60 minutes = 1 hours)
⇒ T = 1 Hours