NIFT UG 2018 Question Paper with solutions

Let the cost of carpeting per ${\mathit{m}}^2$ be $\mathit{₹}1$.
$\therefore$ Area of the room $=120{\mathit{m}}^2$
Let the breadth of the room be $\mathit{x}\mathit{m}$.
$\therefore$ Length of room $=\frac{120}{\mathit{x}}\mathit{m}$
Cost when breadth is $4\mathit{m}$ less
$=120-20=\mathit{₹}100$
and breadth $=\left(\mathit{x}-4\right)\mathit{m}$
Length $\times$ New breadth $=$ New area
$\therefore \frac{120}{\mathit{x}}\times \left(\mathit{x}-4\right)=100$
$\Rightarrow \frac{6}{\mathit{x}}\left(\mathit{x}-4\right)=5$
$\Rightarrow 6\mathit{x}-24=5\mathit{x}$
$\therefore \mathit{x}=24$
$\therefore$ Width of the room $=24\mathit{m}$