Let sum invested in both schemes = $$Rs. P$$ Let interest earned in scheme A = $$Rs. 2x$$ In scheme A, time = 2 years and rate = 20% under compound interest. => $$C.I. = P [(1 + frac{R}{100})^T - 1]$$ => $$2x = P [(1 + frac{20}{100})^2 - 1]$$ => $$2x = P [(frac{6}{5})^2 - 1]$$ => $$2x = P (frac{36}{25} - 1) = frac{11 P}{25}$$ => $$x = frac{11 P}{50}$$ -----------(i) Now, in scheme B,  interest earned = $$Rs. x$$ Time = 2 years and rate of interest = $$x \%$$ under simple interest => $$S.I. = frac{P imes R imes T}{100}$$ => $$x = frac{P imes x imes 2}{100}$$ Using, equation(i), we get : => $$frac{11 P}{50} = frac{P imes x}{50}$$ => $$x = 11 \%$$