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(C) Let the initial quantity of liquid $A$ be $7x$ and liquid $B$ be $5x$ litres.Total initial quantity $= 7x + 5x = 12x$ litres.When $9$ litres of mi

Vedclass · Accepted Answer

$21$

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(C) Let the initial quantity of liquid $A$ be $7x$ and liquid $B$ be $5x$ litres.Total initial quantity $= 7x + 5x = 12x$ litres.When $9$ litres of mixture are drawn off,the amount of $A$ removed is $\frac{7}{12} 	imes 9 = \frac{21}{4}$ litres,and the amount of $B$ removed is $\frac{5}{12} 	imes 9 = \frac{15}{4}$ litres.Remaining quantity of $A = 7x - \frac{21}{4}$ litres.Remaining quantity of $B = 5x - \frac{15}{4}$ litres.After adding $9$ litres of liquid $B$,the new quantity of $B = 5x - \frac{15}{4} + 9 = 5x + \frac{21}{4}$ litres.The new ratio is $7:9$,so:$\frac{7x - 21/4}{5x + 21/4} = \frac{7}{9}$$9(7x - 5.25) = 7(5x + 5.25)$$63x - 47.25 = 35x + 36.75$$28x = 84$$x = 3$Initial quantity of $A = 7x = 7 	imes 3 = 21$ litres.

$A$ can contains a mixture of two liquids $A$ and $B$ in the ratio $7:5$. When $9$ litres of mixture are drawn off and the can is filled with the same amount of liquid $B$,the ratio of $A$ and $B$ becomes $7:9$. How many litres of liquid $A$ was contained by the can initially?

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