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 1 m exists between its edges and the edges of the floor, what fraction of the floor is uncovered.

• A. $960;\frac{7}{20}$
• B. $860;\frac{20}{7}$
• C. $760;\frac{7}{13}$
• D. $660;\frac{7}{15}$

Answer 1

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

We know, $50cm=0.5m$ and
$25cm=0.25m$
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 $1m$ between the carpet and wall on all sides, the carpet needs to be $2m$ shorter in each dimension.
Therefore,
$(15-2)m(8-2)m$
$=(13\times 6)m$
$=78m^2$
Therefore, the room area is $15\times 8$ = $120m^2$

The carpet area is $78m^2$
The fraction of the area uncovered =$\frac{120-78}{120}$= $\frac{42}{120}$=$\frac{7}{20}$