Q57. A rectangular floor measures 4 m in length and 2.2m in breadth. Tiles of size 140 cm by 60 cm have to be laid such that the tiles do not overlap. A tile can be placed in any orientation so long as its edges are parallel to the edges of the floor. What is the maximum number of tiles that can be accommodated on the floor?

The floor dimensions are 4 m = 400 cm in length and 2.2 m = 220 cm in breadth. The tiles are 140 cm by 60 cm. We need to find the maximum number of tiles that can be accommodated, considering both orientations.

Consider placing tiles with their 140 cm side along the 400 cm length and 60 cm side along the 220 cm breadth: - Along length: 400 cm / 140 cm = 2 tiles (280 cm used). Remaining length = 120 cm.

- Along breadth: 220 cm / 60 cm = 3 tiles (180 cm used). Remaining breadth = 40 cm. This initial placement covers 2 × 3 = 6 tiles. The remaining area is a 120 cm × 220 cm strip and a 400 cm × 40 cm strip.

Let's focus on the 120 cm × 220 cm strip. In this area, we can place tiles with their 60 cm side along the 120 cm length (120/60 = 2 tiles) and their 140 cm side along the 220 cm breadth (220/140 = 1 tile).

This fits 2 × 1 = 2 more tiles. Total tiles = 6 + 2 = 8 tiles. Other arrangements or trying to fit into the 400 cm × 40 cm strip will not yield more tiles. For example, if we place tiles with 60 cm side along 400 cm length (400/60 = 6 tiles) and 140 cm side along 220 cm breadth (220/140 = 1 tile), we get 6 tiles, with a remaining 40 cm × 220 cm area where no full tile can fit.

Thus, the maximum number of tiles is 8. This question tests practical application of mensuration and optimization, requiring careful consideration of orientations and remaining space, a challenging aspect of CSAT.