Two planes move along a circle of circumference 1.2 km with constant speeds. When they move in different directions, they meet every 15 seconds and when they move in the same direction, one plane overtakes the other every 60 seconds. Find the speed of the slower plane.

The sum of speeds would be 0.8 m/s (relative speed in opposite direction).
Also if we go by option (B) the speeds will be 0.03 and 0.05 m/s respectively.
At this speed the overlapping would occur in every 60 second.

Alternate :
Let their speeds be x m/sec and y m/sec respectively.
Then,
$$\eqalign{ & \frac{{1200}}{{x + y}} = 15 \cr & \Rightarrow x + y = 80.....(i) \cr} $$
And,
$$\eqalign{ & \frac{{1200}}{{x - y}} = 60 \cr & \Rightarrow x - y = 20.....(ii) \cr} $$
Adding (i) and (ii), we get :
2x = 100 or x = 50
Putting x = 50 in (i), we get : y = 30
Hence, speed of slower plane :
= 30 m/sec
= 0.03 km/sec