Correct Answer - Option 2 : 89.4%

__Concept:__

The total transmitted power for an AM system is given by:

\({P_t} = {P_c}\left( {1 + \frac{{{μ^2}}}{2}} \right)\)

Pc = Carrier Power

μ = Modulation Index

The above expression can be expanded to get:

\({P_t} = {P_c} + P_c\frac{{{μ^2}}}{2}\)

The total power is the sum of the carrier power and the sideband power, i.e.

\({P_s} = P_c\frac{{{μ^2}}}{2}\)

__Calculation__:

Given: Pc = 1000 W and P_{s} = 200W

\({P_s} = P_c\frac{{{μ^2}}}{2}\)

\(μ^2=\frac{800}{1000}\)

μ = 0.8944

% Modulation = 89.44%