Given in question:-
size of data generated by the application layer is 200 KB
fraction of header in the channel is 20%
let the size of the header is H Bytes.
Now remember
the fraction of header in the channel is NH/(NH + M)
and the fraction of data in the channel is M/(NH + M)
where, N = No of layers
M = Message size
H = Header size
So, fraction of header in the channel is 20% = 0.2
N = 10, M = 200, H = header size which we have to find,
Now, 0.2 = 10*H / (10 * H + 200*10^3)
0.2 * 10 * H + 0.2 * 200 * 10^3 = 10^H
2H + 40 * 10 ^3 = 10H
40 * 10 ^3 = 8H
H = 5 * 10^3
or H = 5KB.
Hence header size is equal to 5KB