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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

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