The acid and water in two vessels A and B are in the ratio 4 : 3 and 2 : 3. In what ratio should the liquid in both the vessels be mixed to obtain a new mixture in vessel C containing half acid and half water ?

According to the question,
$$\eqalign{ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Acid}}\,\,\,\,\,\,{\text{Water}} \cr & {\text{Vessel A}}\,\,{\text{4}}\,\,\,:\,\,\,\,{\text{3}} \cr & {\text{Vessel B}}\,\,\,2\,\,\,\,{\text{:}}\,\,\,\,\,{\text{3}} \cr} $$
Now using alligation,