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Q.

A mason has to fit a bathroom with square marble tiles of the largest possible size. The size of the bathroom is 10 ft. by 8 ft. What would be the size in inches of the tile required that has to be cut and how many such tiles are required?

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a

24 inches; 20

b

20 inches; 24

c

20 inches; 20

d

24 inches; 24

answer is A.

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Detailed Solution

Given size of the bathroom = 10ft by 8ft.
The highest common factor (HCF) for two or more numbers is the largest number that divides them.
The maximum number can be calculated using HCF and the minimum number can be calculated using LCM.
Calculate the minimum size of titles.

1 f t = 12 inches . 10 f t = 10 × 12 = 120 inches 8 f t = 8 × 12 = 96 inches

Calculate HCF of 120 and 96.

120 = 2 × 3 × 2 × 2 × 5 96 = 2 × 2 × 2 × 2 × 2 × 3

The HCF of 120 and 96 = 24.
Hence, the size of tile is 24 inches.

Number of square marble = area of bathroom area of tiles ⇒ 120 × 96 24 × 24 ⇒ 20

Therefore, the size in inches of the tile required is 24 inches and the number of tiles is 20.
Hence the correct option is 1.

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