A cuboidal water tank contains 216 litres of water. Its depth is $$\frac{1}{3}$$ of its length and breadth is $$\frac{1}{2}$$ of $$\frac{1}{3}$$ of the difference between length and depth. The length of the tank is :

Solution(By Examveda Team)

Let the length of the tank be x dm
Then, depth of the tank = $$\frac{x}{3}$$ dm
Breadth of the tank :
$$\eqalign{ & = \left[ {\frac{1}{2}{\text{ of }}\frac{1}{3}{\text{ of }}\left( {x - \frac{x}{3}} \right)} \right]{\text{dm}} \cr & = \left( {\frac{1}{2} \times \frac{1}{3} \times \frac{{2x}}{3}} \right){\text{dm}} \cr & = \frac{x}{9}\,{\text{dm}} \cr} $$
$$\eqalign{ & \therefore x \times \frac{x}{9} \times \frac{x}{3} = 216 \cr & \Rightarrow {x^3} = 216 \times 27 \cr & \Rightarrow x = 6 \times 3 \cr & \Rightarrow x = 18\,dm \cr} $$