A rectangular courtyard is 4m 95cm long and 16m 65cm broad. It is to be paved with square tiles of the same size. Find the least number of such square tiles required to pave the rectangular courtyard.

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Accepted Answer

Step 1: Convert the dimensions into a consistent unit (cm).
- Length = 4m 95cm = 400cm + 95cm = 495cm
- Breadth = 16m 65cm = 1600cm + 65cm = 1665cm

Step 2: Find the side length of the largest square tile that can exactly fit both dimensions. This is the HCF of 495 and 1665.

Step 3: Calculate HCF(495, 1665):
- 1665 ÷ 495 = 3 remainder 180
- 495 ÷ 180 = 2 remainder 135
- 180 ÷ 135 = 1 remainder 45
- 135 ÷ 45 = 3 remainder 0

So, HCF = 45 cm.

Step 4: Calculate the number of tiles along length and breadth:
- Number along length = 495 ÷ 45 = 11
- Number along breadth = 1665 ÷ 45 = 37

Step 5: Total number of tiles = 11 × 37 = 407

Step 6: Check options: 407 is option 4, but the correct answer should be 407.

Rechecking the options, 407 is option 4, so the correct answer is 407.

Correction: The correct answer is 407, option 4.

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