The main question is :
A tank contains 729 litres of pure acid (Capacity of tank is 729 litres). 3$x$ litres of acid is removed and replaced by water. The two liquids are thoroughly mixed, and 3$x$ litres of solution is withdrawn and replaced by water. This process is repeated for six times. If finally the volume of press avoid left on the tank is 64 litres (rest is water), find $\sqrt{x}$.
My approach :
% of water after step 1 = $\frac{100x}{243}$
Therefore, amount of water in $3x$ litre removed solution = $\frac{3x*100x}{243}$ = $\frac{100x^2}{81}$
Therefore, amount of acid removed = $3x-\frac{100x^2}{81}$
I'm trying to form a pattern but I cannot proceed further. Please help.