Tiling a Square Floor — Count of 50 cm Tiles: A square room of side 10 m is to be fully tiled with square tiles of side 50 cm. What is the smallest number of tiles needed?
Aptitude
Area
Difficulty: Easy
Choose an option
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A200
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B300
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C400
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D500
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E600
Answer
Correct Answer: 400
Explanation
Introduction / Context:Counting tiles requires dividing the floor area by the area of one tile, keeping units consistent. Here, dimensions mix metres and centimetres, so converting to the same unit avoids mistakes.
Given Data / Assumptions:
- Room: square, side = 10 m
- Tile: square, side = 50 cm = 0.5 m
- No wastage assumed; exact tiling
Concept / Approach:Room area = 10 * 10 = 100 m^2. Tile area = 0.5 * 0.5 = 0.25 m^2. Number of tiles = 100 / 0.25 = 400. This is a simple area division once units are aligned in metres.
Step-by-Step Solution:
Convert tile side: 50 cm = 0.5 m.Room area = 10^2 = 100 m^2.Tile area = 0.5^2 = 0.25 m^2.Tiles needed = 100 / 0.25 = 400.Verification / Alternative check:
Alternatively, along each side we place 10 / 0.5 = 20 tiles; total tiles = 20 * 20 = 400.Why Other Options Are Wrong:
- 200 and 300 undercount; 500 and 600 overcount.
Common Pitfalls:
- Leaving tile side in centimetres and mixing units.
Final Answer:400.