TNPSC - வினாவும் விளக்கமும் - 67 | ஒரு அறையின் தளத்தை அமைக்கத் தேவையான சதுர ஓடுகளின் குறைந்தபட்ச எண்ணிக்கை (DOE-28.09.2025)

 The least number of square tiles required to pave the ceiling is (B) 814.

 To determine the least number of square tiles needed to pave a room, follow these steps:

Step 1: Convert all dimensions to a single unit (centimeters).

• The room's length is 15 meters and 17 centimeters.
  • Since 1 meter equals 100 centimeters, the length in centimeters is (15 * 100) + 17 = 1517 cm.
• The room's breadth is 9 meters and 2 centimeters.
  • In centimeters, this is (9 * 100) + 2 = 902 cm.

Step 2: Find the Highest Common Factor (HCF) of the room's dimensions.

The side length of each square tile must be the HCF of the room's length and breadth to find the least number of tiles.

• First, find the prime factorization of 1517 and 902:
  • 1517 = 37 × 41
  • 902 = 2 × 11 × 41
• The HCF of 1517 and 902 is 41. Therefore, the side of each square tile will be 41 cm.

Step 3: Calculate the number of tiles along the length and breadth.

• Number of tiles along the length = (Length of room) / (Side of tile) = 1517 cm / 41 cm = 37 tiles.
• Number of tiles along the breadth = (Breadth of room) / (Side of tile) = 902 cm / 41 cm = 22 tiles.

Step 4: Calculate the total number of tiles.

The total number of square tiles required is the product of the number of tiles along the length and the number of tiles along the breadth:

• Total tiles = 37 × 22 = 814 tiles.

Answer: The least number of square tiles required is (B) 814.

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