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(C) Let the initial quantity of liquid $A$ be $3x$ and liquid $B$ be $2x.$ The total initial quantity is $5x.$When $5$ litres of the mixture is remove

Vedclass · Accepted Answer

$9$

Vedclass · Answer

(C) Let the initial quantity of liquid $A$ be $3x$ and liquid $B$ be $2x.$ The total initial quantity is $5x.$When $5$ litres of the mixture is removed,the amount of $A$ removed is $\frac{3}{5} 	imes 5 = 3$ litres,and the amount of $B$ removed is $\frac{2}{5} 	imes 5 = 2$ litres.Remaining quantity of $A = 3x - 3$.Remaining quantity of $B = 2x - 2$.After adding $5$ litres of liquid $B$,the new quantity of $B = 2x - 2 + 5 = 2x + 3$.The new ratio is given as $2 : 3$,so $\frac{3x - 3}{2x + 3} = \frac{2}{3}$.Cross-multiplying gives: $3(3x - 3) = 2(2x + 3)$.$9x - 9 = 4x + 6$.$5x = 15$,which means $x = 3$.The initial quantity of liquid $A = 3x = 3 	imes 3 = 9$ litres.

$A$ jar contained a mixture of two liquids $A$ and $B$ in the ratio $3 : 2.$ When $5$ litres of the mixture was taken out and $5$ litres of liquid $B$ was poured in the jar,this ratio became $2 : 3.$ The quantity of liquid $A$ contained in the jar initially was (in litres).

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