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Find the least number of square tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad.
Question

Find the least number of square tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad.

A.

902

B.

800

C.

814

D.

None of these

Correct option is C

Given:
Length of room =15 m 17 cm=1517 cm= 15 \text{ m } 17 \text{ cm} = 1517 \text{ cm} \\​​
Breadth of room =9 m 2 cm=902 cm= 9 \text{ m } 2 \text{ cm} = 902 \text{ cm} \\[10pt]​​
Concept used:
To find the least number of square tiles to cover the floor,
we use the largest square tile that divides both dimensions exactly.
This side length is the HCF of length and breadth.
 HCF of 1517 and 902 using Euclidean algorithm:
​1517÷902=1 remainder 615902÷615=1 remainder 287615÷287=2 remainder 41287÷41=7 remainder 0=>HCF=41 cm1517 \div 902 = 1 \text{ remainder } 615 \\902 \div 615 = 1 \text{ remainder } 287 \\615 \div 287 = 2 \text{ remainder } 41 \\287 \div 41 = 7 \text{ remainder } 0 \\\Rightarrow \text{HCF} = 41 \text{ cm} \\[10pt]​​
Area Calculations
Area of floor =1517×902=1367834 cm2 = 1517 \times 902 = 1367834 \text{ cm}^2 \\​​
Area of one tile =412=1681 cm2 = 41^2 = 1681 \text{ cm}^2 \\[10pt]​​
Number of tiles =13678341681=814 = \dfrac{1367834}{1681} = 814 \\[10pt]​​
Crrect answer is (C) 814.

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