On January $1,2010,$ Jack deposited $$1000$ intp Bank X to earn interest at the rate of j per annum compounded semiannually. On January $1,2013,$ he transferred his account to Bank Y to ea interest at the rate of $k$ per annum compounded quarterly. On January $1,2018,$ the balance at Bank $Y$ was $$2094\mathrm{.}54.$ If Jack could have earned interest at the rate of $k$ per annum compound quarterly from January $1,2010,$ through January $1,2018,$ his balance would have been $$2575\mathrm{.}08.$ Calculate the ratio $\frac{k}{j}.$

$\frac{k}{j}=,(Simplify$ your answer.$)$