well.. what i understood is you need inner div’s width to be responsive with respect to outer div…. correct?
case 1: if you want the inner div’s width to be responsive continuously when you resize the browser….
specify your inner div’s width in percentage… as shown below
case 2: if you want the inner div’s width responsive only after when outer div’s width equals inner div’s width.. then you may have to go with media queries… as below
if this is not the way you need it… then i think we will have to go for JS