A container contains two liquids A and B in the ratio 7 : 5. When 9 litres of mixture are drawn off and the container is filled with B, the ratio of A and B becomes 1 : 1. How many litres of liquid A was in the container initially = ?

Answer: Option C

Quantity of A in mixture 7x and B in Mixture in 5x
Quantity of A in Mixture left after 9 liter Drawn = $$\left(7x-\frac{7}{12}\times 9\right)=\left(7x-\frac{21}{4}\right)$$     liters
Quantity of B in Mixture left after 9 liter Drawn = $$\left(7x-\frac{5}{12}\times 9\right)=\left(7x-\frac{15}{4}\right)$$     liters
$$\begin{array}{rl}& \therefore \frac{\left(7x-\frac{21}{4}\right)}{\left(5x-\frac{15}{4}\right)+9}=\frac{1}{1}\\ & \Rightarrow \frac{28x-21}{20x+21}=1\\ & \Rightarrow 28x-21=20x+21\\ & \Rightarrow x=\frac{42}{8}=\frac{21}{4}\end{array}$$

∴Quantity of A in mixture = $$7x$$
$$=7\times \frac{21}{4}=\frac{147}{4}=36\frac{3}{4}$$     liter.