Two liquids $A$ and $B$ are in the ratio $4:1$ in container $1$ and in container $2,$ they are in the ratio $1:3.$ In what ratio should the contents of the two containers be mixed so as to obtain a mixture of $A$ and $B$ in the ratio $1:1$?

$\rightarrow$ In ${\color{Red} {container\ 1}}$ liquids $A$ and $B$ are in the ratio $4:1$ i.e. $\frac{4}{5}$ part is Liquid $A$ and $\frac{1}{5}$ part is Liquid $B$

$\rightarrow$ In ${\color{Blue} {container\ 2}}$ liquids $A$ and $B$ are in the ratio $1:3$ i.e. $\frac{1}{4}$ part is Liquid $A$ and $\frac{3}{4}$ part is Liquid $B$

Option $A.$

$\rightarrow$ It says that $5$ parts from ${\color{Red} {container\ 1}}$ and $6$ parts from ${\color{Blue} {container\ 2}}$ should be mixed.

$\rightarrow$ Then amount of ${\color{Red} A}:{\color{Red} B}$ taken from ${\color{Red} {container\ 1}}$ = ${\color{Red} {5*\frac{4}{5}:5*\frac{1}{5}}}$ = ${\color{Red} 4}:{\color{Red} 1}$

$\rightarrow$ Then amount of ${\color{Blue} {A:B} }$ taken from ${\color{Blue} {container\ 2}}$ = ${\color{Blue} {6*\frac{1}{4}:6*\frac{3}{4} = 1.5:4.5}}$

$\rightarrow$ So ratio of $A:B$ in the final Mixture = $({\color{Blue}4}+{\color{Red}{1.5}}):({\color{Blue}1}+{\color{Red}{4.5}})$ = $5.5:5.5$ = $1:1$

$\therefore$ Option $A.$ $5:6$ is the correct answer.