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?
Explanation:
Consider the diagram below:
Area of a 1 × 1 tile = 1 cm2
Total area of A = 9 × 11 = 99 cm2 ∴ Number of 1 × 1 tiles required to cover A = 99/1 = 99 tiles.
Total Area of B + C = 9 × 0.5 + 11 × 0.5 = 20 × 0.5 = 10 cm2 ∴ Number of 1 × 1 tiles required to cover B and C = 10/1 = 10 tiles.
Now the remaining area i.e., D = 0.5 × 0.5 = 0.25 cm2
It would be better to but a 0.5 × 0.5 tile to cover D.
∴ The minimum cost of covering entire floor with tiles
= (99 + 10) × 100 + 1 × 30 = 10930
Hence, option (a).
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