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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 $1:1$?

1. $5:6$
2. $4:3$
3. $3 :4$
4. $6:5$

Sir In answer it's showing A but those who already answered showing your ans @.
Is it coming correct now?

Yes @Arjun sir now it's fine.

$\rightarrow$ 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.
by

r u sure? I am getting 31:40 by allegation :(
yass!
Let the required ratio be $x:y$

$\frac{4}{5}x+ \frac{1}{4} y = \frac{1}{5}x +\frac{3}{4}y$

$\implies\frac{3}{5} x = \frac{1}{2}y$

$\implies x:y = \frac{1}{2} : \frac{3}{5} = 5:6$
by

Hi Arjun Sir, could you please explain the LHS and RHS as I am unable to grasp the solution?
As given in Question "to obtain a mixture of A and B in the ratio 1:1" So after  mixing

A : B = 1 : 1

A/B = 1/1

A = B

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