HELLO!
 
Given, Distance of point A from O is 240m.
Hence, P has to cover a distance of 240m with a speed of 12 m/s.
 
Time taken by P to reach O = Distance/Speed
= 240/12 seconds
= 20 seconds.
 
If B takes lesser time, then B will reach O first.
 
Consider the Triangle OBX (name the adjacent side of OA = BX).
Here, cos 37 = 240/Hypo [Since cos  = Base/Hypotenuse]
cos 37 = 4/5
 
So, 4/5 = 240/h
=>h = 60 x 5m = 300m
 
So, B has to cover a distance of 300 m to reach point O.
 
Intial distance between P and Q is 180m.
Q changes its speed to 15m/s when the distance between them is 120m.
So, when Q changes its speed, it has already travelled 60 m, and has to travel a remaining of 300 – 60 = 240m
 
Q covers first 60m at a speed of 12m/s.
So time taken = 60/12 = 5 seconds.
 
Q covers the next 240m at a speed of 15m/s.
So time taken = 240/15 = 16 seconds.
 
So, total time taken by Q to reach O = 5 + 16 = 21 seconds.
 
Since reaches O in 20 seconds and Q in 21 seconds, P reaches first.
I go for Option (a).