A man travels form A to B at a speed of x kmph. He then rests at B or x hours. He then travels from B to C at a speed of $2x$ kmph and rests at C for $2x$ hours. He moves further to D at a speed twice as that between B and C. He thus reaches D in 16 hours. If distances A-B, B-C, C-D are all equal to $12$ km. the time for which he rested at B could be:
Total time taken by the man to travel from A to D = 16 hr and total distance traveled = 36 km.
The time that he would have taken had he not rested in between will be (16-x-2x) = (16-3x).
But, this time should be equal to the addition of the times that he takes to travel individual segments. This is given as:
12/x + 12/2x + 12/4x = 21/x
Therefore, 21/x = 16-3x
x = 3 or 7/3
Option A is the Correct Answer.