imc

Let $k$ be the number of knights: then the number of red knights is $\frac{2}{7}k$ and the number of blue knights is $\frac{5}{7}k$. Let $b$ be the fraction of blue knights that are magical - then $2b$ is the fraction of red knights that are magical. Thus we can write the equation $b\cdot \frac{5}{7}k+2b\cdot \frac{2}{7}k=\frac{k}{6}⟹\frac{5}{7}b+\frac{4}{7}b=\frac{1}{6}$ $⟹\frac{9}{7}b=\frac{1}{6}⟹b=\frac{7}{54}$ We want to find the fraction of red knights that are magical, which is $2b=\frac{7}{27}=\boxed{\frac{7}{27}}$