Why does mixing two solutions decrease the concentration of the solutes? The irreversible liquid reaction
  
  $$\ce{A + B -&gt; C + D}$$
  
  follows an elementary rate law and is carried out
  isothermally in a plug flow reactor (PFR). The volume of the PFR is 500 litres. The concentration of $\ce{A}$ is $\pu{2 mol L-1}$ and concentration of $\ce{B}$ is $\pu{2 mol L-1}$ before mixing. The volumetric flow rate of each stream is $\pu{5 L min-1}.$
  
  The streams are mixed immediately before entering. The reaction rate constant at $\pu{20 °C}$ is $\pu{0.05 L mol-1 min-1}$
  and $E = \pu{20 kcal mol-1}.$ (Note: gas constant $R = \pu{1.987 cal mol-1 K-1})$
  
  Find conversion at $\pu{40 °C}.$


This is what I had:



From the solution given the $c_{\ce{A},0}$ used is $\pu{1 mol L-1}$ which is after mixing. Need some clarification on this. Why is it not $\pu{2 mol L-1}$ before mixing?
Comment turned to answer:

Because it has been mixed. 

Each substance is now in doubled volume, compared to volume before mixing. 

If you had whiskey and if you mixed it with the same volume of soda, it wouldn't have the same strength as before, would it ?