300 rpm => 300 rotations --> 60 secs
1 rotation --> 0.2 secs
Now in one rotation we can scan the entire track. But in double interleaved disk the sectors are not arranged sequentially like 0,1,2,3...7. They are separated by 2 interleaved sectors. And it is given that the scanning should be done in order.
See this :
In one rotation the head moves over 8 sectors which takes 0.2s (i.e. time for 1 rotation).
So for 1 sector it takes 0.2/8 =0.025s. Let us take t=0.025s.
It is given that 1/2 a rotation is needed to place the head over sector 0.
1 rotation as we calculated takes 0.2s. So 1/2 rot will take 0.1s.
Now head is moved to beginning of sector 0.
Recall, Time taken to scan 1 sector is t. So t secs is needed to scan sector 0.
Now we have to move to sector 1. This will require moving past sector no. 3,6 i.e. 2 sector time i.e. 2t. To scan sector 1 another t. So to finish scanning sector 1 we need 3t secs.
Now we have to move to sector 2. This will require moving the head over 4,7 i.e. 2 sectors. Time taken is 2t and to scan sector 2 another t sec. So again 3t to finish scanning sector 2.
Likewise we can see for scanning all the sectors from 1 to 7 it takes 7*3t=21t.
Total time taken = Time taken to position head over sector 0 + time to scan sector 0 + 21t
= 0.1 s + t +21t = 0.1 +22t = 0.1 +22*0.025 = 0.1 +0.55=0.65 s =650ms.