Two rods, one of aluminum and the other made of steel, having initial length \[{{l}_{1}}\] and \[{{l}_{2}}\] are connected together to form a single rod of length \[{{l}_{1}}+{{l}_{2}}\]. The coefficients of linear expansion for aluminum and steel are \[{{\alpha }_{a}}\] and \[{{\alpha }_{s}}\] respectively. If the length of each rod increases by the same amount when their temperature are raised by \[{{t}^{o}}C\], then find the ratio \[\frac{{{l}_{1}}}{({{l}_{1}}+{{l}_{2}})}\] [IIT-JEE (Screening) 2003]

• A. \[\frac{{{\alpha }_{s}}}{{{\alpha }_{a}}}\]
• B. \[\frac{{{\alpha }_{a}}}{{{\alpha }_{s}}}\]
• C. \[\frac{{{\alpha }_{s}}}{({{\alpha }_{a}}+{{\alpha }_{s}})}\]
• D. \[\frac{{{\alpha }_{a}}}{({{\alpha }_{a}}+{{\alpha }_{s}})}\]