The length of a hall is 18 m and its width is 13.5 m. Find the least number of square tiles, each of side 25 cm, required to cover the floor of the hall,

(i) without leaving any margin.

(ii) leaving a margin of width 1.5 m all around.

In each case, find the cost of the tiles required at the rate of ₹ 6 per tile.

(i) Given:

Length of the floor = 18 m

Breadth of the floor = 13.5 m

As we know, the area of the floor = length x breadth

= 18 x 13.5 m²

= 243 m²

Side of the square tile = 25 cm

= $\dfrac{25}{100}$ m

= $\dfrac{1}{4}$ m

As we know, the area of a tile = side²

= $\Big(\dfrac{1}{4}\Big)$² m²

= $\dfrac{1}{16}$ m²

Area of square tiles x Number of tiles = Area of the floor

⇒ Number of tiles = $\dfrac{\text{Area of the floor}}{\text{Area of square tiles}}$

⇒ Number of tiles = $\dfrac{243}{\dfrac{1}{16}}$

⇒ Number of tiles = 243 x 16

⇒ Number of tiles = 3,888

Rate per tile = ₹ 6 per tile

Total cost = ₹ 3,888 x 6

= ₹ 23,328

Hence, the number of tiles is 3,888 and the cost of the tiles is ₹ 23,328.

(ii) Width of the margin on each side = 1.5 m

Length of the inner floor = 18 m - 1.5 m - 1.5 m

= 18 - 3 m

= 15 m

Breadth of the inner floor = 13.5 m - 1.5 m - 1.5 m

= 13.5 - 3 m

= 10.5 m

As we know, the area of the floor = length x breadth

= 15 x 10.5 m²

= 157.5 m²

Side of the square tile = 25 cm

= $\dfrac{25}{100}$ m

= $\dfrac{1}{4}$ m

As we know, the area of a tile = side²

= $\Big(\dfrac{1}{4}\Big)$² m²

= $\dfrac{1}{16}$ m²

Area of square tiles x Number of tiles = Area of the floor

⇒ Number of tiles = $\dfrac{\text{Area of the floor}}{\text{Area of square tiles}}$

⇒ Number of tiles = $\dfrac{157.5}{\dfrac{1}{16}}$

⇒ Number of tiles = 157.5 x 16

⇒ Number of tiles = 2,520

Rate of tiles = ₹ 6 per tile

Total cost = ₹ 2,520 x 6

= ₹ 15,120

Hence, the number of tiles is 2,520 and the cost of the tiles is ₹ 15,120.