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1. 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 :

A. 2 dm

B. 6 dm

C. 18 dm

D. 72 dm

Solution:

Let the length of the tank be x dm
Then, depth of the tank =

\frac{x}{3}

dm
Breadth of the tank :

\begin{aligned} = [\frac{1}{2} of \frac{1}{3} of (x - \frac{x}{3})] dm \\ = (\frac{1}{2} \times \frac{1}{3} \times \frac{2 x}{3}) dm \\ = \frac{x}{9} dm \end{aligned}

\begin{aligned} ∴ x \times \frac{x}{9} \times \frac{x}{3} = 216 \\ \Rightarrow x^{3} = 216 \times 27 \\ \Rightarrow x = 6 \times 3 \\ \Rightarrow x = 18 d m \end{aligned}

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