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 = ?

Solution(By Examveda Team)

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
$$\eqalign{ & \therefore \frac{{\left( {7x - \frac{{21}}{4}} \right)}}{{\left( {5x - \frac{{15}}{4}} \right) + 9}} = \frac{1}{1} \cr & \Rightarrow \frac{{28x - 21}}{{20x + 21}} = 1 \cr & \Rightarrow 28x - 21 = 20x + 21 \cr & \Rightarrow x = \frac{{42}}{8} = \frac{{21}}{4} \cr} $$

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