A bucket contains a mixture of two liquids A & B in the proportion 5 : 3. If 16 litres of the mixture is replaced by 16 litres of liquid B, then the ratio of the two liquids becomes 3 : 5. How much of the liquid B was there in the bucket?

Answer: Option E

Let bucket contains 5x and 3x of liquids A and B respectively.
When 16 litres of mixture are drawn off, quantity of A in mixture left:
$$\begin{array}{rl}& 5x-\frac{5}{8}\times 16=5x-10\\ & \text{Similarly quantity of B in mixture left},\\ & 3x-\frac{3}{8}\times 16=3x-6\\ & \text{Now the ratio becomes,}\\ & \frac{5x-10}{3x-6}=\frac{3}{5}\\ & \Rightarrow 25x-50=9x-18\\ & \Rightarrow 16x=32\\ & \Rightarrow x=2\\ & \text{So, quantity of liquid B initially},\\ & =3\times 2=6\text{litres}\end{array}$$