When an alarm goes off, policemen X and Y chase thief T, on foot and on a cycle, respectively, along the same straight road. Initially, the distance between X and Y was 4 times that between T and X. If X runs twice as fast as T and Y rides twice as fast as X, then:

Correct option is B

Concept:
(I) If two objects are moving in same direction and let speed of 1st is x and speed of 2nd is y 
Then Relative Speed between 1st and 2nd  = (x - y) 
(II) Speed = Distance/Time
Solution:
Suppose distance between X and T is 1 Km then distance between X and Y must be 4 Km and distance between Y and T is 5Km.
Now, If speed of T is 1Km/h Then Speed of X is 2Km/h and Speed of Y is 4Km/h 
Now, Relative Speed between Y and T = 4S - S = 3S
And Relative Speed between X and T = 2S - S = S 
Now,  Time Taken by Y to reach T = 5/3 hours
and Time Taken by X to reach T = 1 hour
Clearly, Time Taken by Y is more then Time Taken by X.
Hence, X will catch T first 
Hence, Option (b) is true.