Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: 2005 · Marks: · Difficulty:
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
Answer
Answer (as printed): C
Explanation
Let the length of the tank be $x \mathrm{dm}$. Then, depth of the tank $=\frac{x}{3} \mathrm{dm}$. Breadth of the tank $$\begin{aligned} & =\left[\frac{1}{2} \text { of } \frac{1}{3} \text { of }\left(x-\frac{x}{3}\right)\right] \mathrm{dm}=\left(\frac{1}{2} \times \frac{1}{3} \times \frac{2 x}{3}\right) \mathrm{dm}=\frac{x}{9} \mathrm{dm} . \\ & \therefore x \times \frac{x}{9} \times \frac{x}{3}=216 \Rightarrow x^{3}=216 \times 27 \Rightarrow x=6 \times 3=18 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.