Alcohol and water in two vessels A and B are in the ratio 5 : 3 and 5 : 4 respectively. In what ratio, the liquid of both the vessels be mixed to obtain a new mixture in vessel C in the ratio 7 : 5 ?

According to the question,
$$\eqalign{ & \,\,\,\,\,\,\,\,\,\,\,\,\,{\text{Alcohol}}\,\,\,\,\,\,{\text{Water}} \cr & {\text{Vessel A}}\,\,\,\,\,\,\,\,5\,\,\,\,:\,\,\,\,\,{\text{3}} \cr & {\text{Vessel B}}\,\,\,\,\,\,\,\,5\,\,\,\,{\text{:}}\,\,\,\,\,4 \cr} $$
Now using alligation,