a) 21 liters
b) 23 liters
c) 24 liters
d) 27 liters

Answer: a
Explanation: Suppose the can initially contains 7x and 5x litres of mixtures A and B respectively. When 9 litres of mixture are drawn off, quantity of A in mixture left:
$$\eqalign{ & = \left[ {7x – {\frac{7}{{12}}} \times 9} \right]\, \text{litres} \cr & = \left[ {7x – {\frac{{21}}{4}} } \right]\,{\text{litres}} \cr & {\text{Similarly quantity of B in mixture left}}, \cr & = \left[ {5x – {\frac{5}{{12}}} \times 9} \right]\, \text{litres} \cr & = \left[ {5x – {\frac{{15}}{4}} } \right]\,{\text{litres}} \cr & \therefore \,{\text{ratio becomes}}, \cr & \frac{{ {7x – {\frac{{21}}{4}} } }}{{ {\left(5x – {\frac{{15}}{4}}\right)+9 } }} = \frac{7}{9} \cr & \frac{{ {28x – 21} }}{{ {20x + 21} }} = \frac{7}{9} \cr & {252x – 189} = 140x + 147 \cr & 112x = 336 \cr & x = 3 \cr & {\text{So the can contained}}, \cr & = 7 \times x \cr & = 7 \times 3 \cr & = 21\,{\text{litres of A initially}}{\text{.}} \cr} $$