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    Question

    A rectangular courtyard is 4m 95cm long and 16m 65cm

    broad. It is to be paved with the square tiles of the same size. Find the least number of such square tiles required to pave the rectangular courtyard. 
    A 877 Correct Answer Incorrect Answer
    B 944 Correct Answer Incorrect Answer
    C 388 Correct Answer Incorrect Answer
    D 407 Correct Answer Incorrect Answer

    Solution

    Length (L) = 4 m 95 cm = 495 cm Width (W) = 16 m 65 cm = 1665 cm The largest square tile that can fit both dimensions is the GCD of 495 and 1665. 1665 ÷ 495 = 3 with remainder 180 495÷180 = 2 with remainder 135 180÷135 = 1 with remainder 45 135 ÷ 45 = 3 with remainder 0 So, the GCD = 45 cm. Now, calculate the number of tiles: Tiles along length = 495÷45 = 11 Tiles along width = 1665÷45=37 Total tiles = 11× 37 = 407

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