P and Q jog along a circular track of 400 m in opposite directions from the same starting point starting together, with speeds 10 m/s and 40 m/s. Whenever they meet, P's speed is doubled and Q's speed is halved. After what time from start, will they meet for the third time?

They run in opposite direction,so their relative velocity is (40+10) m/s =50 m/s.

They will meet for first time after (400/50)= 8 sec.

Now, their speed become (10×2)=20 m/s and (40/2)=20 m/s.

So, now their relative velocity become (20+20)=40 m/s.

So, they will meet for second time after (400/40)=10 sec.

again after meet for third time their speeds will be (20×2)=40 m/s and (20/2)= 10 m/s.

So, relative velocity is= (40+10)=50 m/s.

So, they will meet for third time after (400/50)=8 m/s.

So, total time taken to meet for third time is =(8+10+8)=26 sec.

D is correct choice.