When 5 children from class A join class B, the number of children in both classes is the same. If 25 children from B, join A, then the number of children in A becomes double the number of children in B. The ratio of the number of children in A to those in B is:

\[\begin{array}{*{20}{c}} {}&{{\text{A}}\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{B}}\,} \\ {{\text{Student}}}&{x - 5 = y + 5} \end{array}\]
$$\eqalign{ & x - y = 10\,.\,.\,.\,.\left( {\text{i}} \right) \cr & x + 25 = 2\left( {y - 25} \right) \cr & x - 2y = - 75\,.\,.\,.\,.\left( {{\text{ii}}} \right) \cr & {\text{Subtract both equation}} \cr & x - y = 10 \cr & x - 2y = - 75 \cr & \underline {\, - \,\,\, + \,\,\,\,\,\,\, + \,\,\,\,\,} \cr & \,\,\,\,\,\,\,\,\,\,y = 85 \cr & x = 95 \cr & x:y = 95:85 = 19:17 \cr} $$