A bag initially contains red marbles and blue marbles only, with more blue than red. Red marbles are added to the bag until only $\frac{1}{3}$ of the marbles in the bag are blue. Then yellow marbles are added to the bag until only $\frac{1}{5}$ of the marbles in the bag are blue. Finally, the number of blue marbles in the bag is doubled. What fraction of the marbles now in the bag are blue?
$\mathrm{(A) \ } \frac{1}{5} \qquad \mathrm{(B) \ } \frac{1}{4} \qquad \mathrm{(C) \ } \frac{1}{3} \qquad \mathrm{(D) \ } \frac{2}{5} \qquad \mathrm{(E) \ } \frac{1}{2}$
We can ignore most of the problem statement. The only important information is that immediately before the last step blue marbles formed $\frac{1}{5}$ of the marbles in the bag. This means that there were $x$ blue and $4x$ other marbles, for some $x$. When we double the number of blue marbles, there will be $2x$ blue and $4x$ other marbles, hence blue marbles now form $\boxed{\mathrm{(C)\ }\frac{1}{3}}$ of all marbles in the bag.