How to check percentage yields in a given reaction? For a general reaction , if it is asked to predict and not given by theoretically, how would we determine the percentage yield of the products based on their mechanism , stability , path taken for the reaction etc. ?
For example , where my main problem lies is  : 

According to Solomon and Frhyle it is said that chlorine is highly unselective. But in a problem I was asked percentage yields of the two products:


So how do I go about determining the percentage yields in this reaction ?
They are determined experimentally. There isn't any possible way you can determine percentage yield by looking at a reaction (unless there is only 1 possible product).

What the text is trying to explain to you is that when comparing analogous reactions of $\ce{Cl2}$ and $\ce{Br2}$, there will be higher percentage yields of the more highly substituted (and stable) product in the $\ce{Br2}$ reactions. For example, in the reaction between propane and $\ce{Cl2}$, the yields of 1-chloropropane and 2-chloropropane are 45% and 55% respectively. In a reaction between propane and $\ce{Br2}$, the yields of 1-bromopropane and 2-bromopropane are 3% and 97% respectively.

The exact reason for these selectivities has to do with the differences in energies in the transition states for the formation of the free radicals involved in the mechanism for these reactions. If you're interested in learning more you can see for yourself here.