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

1. $25$
2. $10$
3. $20$
4. $21$

Ans is option (D)

Let there be $x$ ltr. of solution initially.

$\therefore$  Initial volume of A and B respectively: $\frac{7}{12}\times x, \frac{5}{12}x$  ltr.

Now, $9$ ltr. of solution is removed and the same volume of B is poured in the can.

$\therefore$  Volume of B removed from the can $=(\frac{\frac{5}{12}\times x \times 9}{x})=3.75$  ltr.

After pouring $9$ ltr. of B again, the volume of B in the can now  $=\frac{9}{16}\times x$  ltr

$\therefore$  $(\frac{5}{12}\times x)-3.75+9=(\frac{9}{16}\times x)$   $\Rightarrow$   $x=36$ ltr

$\therefore$   Volume of A in the can initially $=\frac{7}{12}\times 36=21$  ltr

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