Question

The cost of carpeting a room $15m$ long with a carpet of width $75cm$ at $Rs.80$ per metre is $Rs.19200$. Find the width of the room.

Answer 1

Given: Length of the room $=15m$
Width of the carpet $=75cm=\frac{75}{100}m=0.75m$ (since $1m=100cm$)
Let the length of the carpet required for carpeting the room be $xm$.
Cost of the carpet $=Rs.80$ per $m$
$\therefore$ Cost of $xm$ carpet $=Rs.(80\times x)=Rs.80x$
Cost of carpeting the room $=Rs.19200$
Therefore, $80x=19200$
$\Rightarrow x=\frac{19200}{80}=240$
Thus, the length of the carpet required for carpeting the room is $240m$.
Area of the carpet required for carpeting the room $=$ Length of the carpet $\times$ Width of the carpet $=(240\times 0.75)m^2=180m^2$
Let the width of the room be $bm$.
Area to be carpeted $=15m\times bm=15b{m}^2$
$\therefore 15b{m}^2=180m^2$
$b=\frac{180}{15}m=12m$
Hence, the width of the room is $12m$.