Question

Akhtar plans to cover a rectangular floor of dimensions 9.5 meters and 11.5 meters using tiles. Two types of square shaped tiles are available in the market. A tile with side 1 meter costs Rs. 100 and a tile with side 0.5 meters costs Rs. 30. The tiles can be cut if required. What will be the minimum cost of covering the entire floor with tiles?

Accepted Answer

A. Floor dimensions: $9.5 	ext{ m} 	imes 11.5 	ext{ m}$. Maximum number of $1 	ext{ m} 	imes 1 	ext{ m}$ tiles used without cutting = $9 	imes 11 = 99$ tiles. Remaining area requires $0.5 	ext{ m} 	imes 0.5 	ext{ m}$ tiles: Using 1x1 tiles for $9 	ext{ m} 	imes 11 	ext{ m}$ area = $99 	imes 100 = 9900$. For remaining borders: $9 	ext{ m} 	imes 0.5 	ext{ m} = 4.5$ sq m (requires 18 tiles of 0.5x0.5 = $18 	imes 30 = 540$), $11 	ext{ m} 	imes 0.5 	ext{ m} = 5.5$ sq m (requires 22 tiles of 0.5x0.5 = $22 	imes 30 = 660$), corner $0.5 	imes 0.5$ (1 tile = 30). Total cost = $9900 + 1030 = 10930$.

Cost Optimization: Flooring with Tiles

Explanation

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