Correct Option (D)
The dimensions of the rectangular floor are given as 4 m in length and 2.2 m in breadth. Converting these to centimeters, the length is 400 cm and the breadth is 220 cm.
The tiles measure 140 cm by 60 cm. The problem requires determining the maximum number of these tiles that can be laid on the floor without overlapping, with their edges parallel to the floor's edges, and allowing for either orientation (140x60 cm or 60x140 cm).
Calculating the total area of the floor (400 cm × 220 cm = 88000 cm²) and the area of a single tile (140 cm × 60 cm = 8400 cm²) and then dividing the floor area by the tile area (88000 / 8400 ≈ 10.47) does not directly provide the solution. This is because the tiles must fit perfectly without cutting, and the remaining space after placing tiles may not be large enough to accommodate additional full tiles.
Through an optimal arrangement that considers both possible orientations of the tiles and efficient space utilization, it is determined that a maximum of 9 tiles can be accommodated on the floor. This involves strategic placement to minimize unusable leftover space.
Incorrect Options:
Options A (6), B (7), and C (8) represent quantities of tiles that are less than the maximum number that can be accommodated. While these numbers of tiles can certainly be placed on the floor, they do not represent the most efficient or maximum possible arrangement. Various straightforward tiling patterns might yield 6 or 8 tiles, but further optimization of tile placement, including considering both orientations, allows for a greater number of tiles to be fitted, up to 9.