TS ICET 23 May 2018 Shift 2 Paper

Let the sides of three metal cubes be 3x, 4x and5x respectively.
Let the side of the single cube formed be a.
Length of the diagonal of the cube $\mathit{a}\sqrt{3}=48\sqrt{3}$
$\Rightarrow \mathit{a}=48$ meters
Given the three cubes are melted and made into a single cube.
⇒ Volume of three cubes = Volume of cube
$\Rightarrow {\left(3\mathit{x}\right)}^3+{\left(4\mathit{x}\right)}^3+{\left(5\mathit{x}\right)}^3={\mathit{a}}^3$
$\Rightarrow 27{\mathit{x}}^3+64{\mathit{x}}^3+125{\mathit{x}}^3={48}^3$
$\Rightarrow 216{\mathit{x}}^3={48}^3\Rightarrow \mathit{x}=8$
Required answer, the side of the smallest cube
$=3\mathit{x}=3\times 8=24$m