A floor which measures 15 m x 8 m is to be laid with tiles measuring 50 cm x 25 cm. 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 left uncovered.

Given:

Dimensions of the floor = 15 m x 8 m

Dimensions of the tile = 50 cm x 25 cm = 0.5 m x 0.25 m

Area of floor = l x b

= 15 x 8 m²

= 120 m²

Area of tile = l_tile x b_tile

= 0.5 x 0.25 m²

= 0.125 m²

Let n be the number of tiles.

Area of floor = Area of tile x Number of tiles

⇒ 120 = 0.125 x n

⇒ n = $\dfrac{120}{0.125}$

⇒ n = $\dfrac{120000}{125}$

⇒ n = 960

Now, a carpet is laid on the floor, leaving a space of 1 m between its edges and the edges of the floor.

Length of the carpet = 15 - 1 - 1 m = 13 m

Breadth of the carpet = 8 - 1 - 1 m = 6 m

Area of uncovered floor = Area of floor - Area of carpet

= 15 x 8 - 13 x 6 m²

= 120 - 78 m²

= 42 m²

Fraction of floor left uncovered = $\dfrac{42}{120}$ = $\dfrac{7}{20}$

Hence, the number of tiles needed is 960 and the fraction of the floor left uncovered is $\dfrac{7}{20}$.