Question

A floor which measures $15m\times 8m$ is to be laid with tiles measuring $50cm\times 25cm$. Find the number of tiles required. Further, if a carpet is laid on the floor so that a space of $1m$ exists between its edges and the edges of the floor, what fraction of the floor is uncovered.

• A. $960$; $\frac{7}{20}$
• B. $940$; $\frac{7}{18}$
• C. $900$; $\frac{7}{20}$
• D. $920$; $\frac{9}{20}$

Answer 1

The correct option is A $960$; $\frac{7}{20}$

We know $50$ cm $=0.5$ m
and $25$ cm $=0.25$ m
Tiles along the length of the room $=$ $\frac{15}{0.5}$ $=$ $30$ tiles
Tiles along the length of the room $=$ $\frac{8}{0.25}$ $=$ $32$ tiles

Total number of tiles required $=$ $30\times 32$ $=$ $960$ tiles

To leave $1$ m between the carpet and wall on all sides, the carpet needs to be $2$ m shorter in each dimension.

Therefore, $(15-2)\times (8-2)$ m
$=(13\times 6)$ m
$=78m^2$

Therefore, the room area is $15\times 8$ $=$ $120m^2$

The carpet area is $78m^2$
The fraction of the area uncovered is
$=$ $\frac{120-78}{120}$

$=$ $\frac{42}{120}$
$=$ $\frac{7}{20}$