Here DMA is using cycle stealing mode to transfer data to memory. In cycle stealing mode 1 Byte is transferred in each cycle.
Device transfers 16 kb in 1 sec
=> 1 kb in (1/16 ) sec
now 1 kb = 1000 Bytes
so 1000 B in 0.0625 sec
=> 1 B in ( 0.0625 / 1000 ) sec = 0.0000625 sec , 1 sec = 106 =1000000 μs
That means Device transfers 1 Byte in 62.5 μs.
Memory operation transfers 1 MB in 1 sec
=> 106 B in 1 sec
=> 1 B in (1/106) secs = (1/106 )* 106 μs = 1 μs
so memory transfer rate is 1 Byte in 1 μ second. ( same as above calculation as processor fetch at 1MB / s ).
To fetch 1 Byte data processor needs 1 Microseconds
% time cpu is idle is for 1 cycle , while DMA is transferring data
so cpu time is 1 μs and total transfer time is 62.5 μs
%CPU idle time = 1/(62.5) * 100 = 0.016 * 100 = 1.60 %