SSC CHSL 15 Nov 2015 Shift 2 Paper

Let length of rectangular base = 3x cm and breadth = 2x cm
Surface area of rectangular prism = $2\left(\mathit{l}\mathit{b}+\mathit{b}\mathit{h}+\mathit{h}\mathit{l}\right)$
⇒ $2[\left(3\mathit{x}\times 2\mathit{x}\right)+\left(2\mathit{x}\times 12\right)$ $+\left(12\times 3\mathit{x}\right)]=288$
⇒ $6{\mathit{x}}^2+24\mathit{x}+36\mathit{x}$ $=\frac{288}{2}=144$
⇒ ${\mathit{x}}^2+10\mathit{x}-24=0$
⇒ ${\mathit{x}}^2+12\mathit{x}-2\mathit{x}-24=0$
⇒ $\mathit{x}\left(\mathit{x}+12\right)-2\left(\mathit{x}+12\right)=0$
⇒ $\left(\mathit{x}-2\right)\left(\mathit{x}+12\right)=0$
⇒ $\mathit{x}=-12,2$
∵ x cannot be negative ⇒ x = 2
Thus, length = 3 × 2 = 6 cm and breadth = 4 cm
∴ Volume = $\mathit{l}\mathit{b}\mathit{h}$
= $6\times 4\times 12=288\mathit{c}{\mathit{m}}^3$