Previous Year Questions

We are given a rectangular courtyard with dimensions:

· Length = 4 m 95 cm

· Breadth = 16 m 65 cm

· We need to find the least number of square tiles required to completely pave the rectangular courtyard.

Step 1: Convert the dimensions to a consistent unit (centimeters)

· Length = 4 m 95 cm=495 cm (since 1 meter = 100 cm)

· Breadth = 16 m 65 cm=1665 cm

Step 2: Find the side length of the largest square tile

The side length of the largest square tile that can tile the courtyard exactly will be the greatest common divisor (GCD) of the length and breadth of the courtyard, because the GCD represents the largest possible side length that can divide both dimensions without leaving a remainder.

Now, find the GCD of 495 cm and 1665 cm

Using the Euclidean algorithm to find the GCD:

1665÷495≈3(quotient)1665

1665−3 X 495=1665−1485=180

495÷180≈2(quotient)

495−2 X 180=495−360=135

180÷135≈1(quotient)180

180−1 X 135=180−135=45

135÷45=3(quotient)

Since the remainder is now 0, the GCD is 45 cm.

Step 3: Find the area of the courtyard

The area of the courtyard is:

Area of the courtyard=495 cm X 1665 cm=823,575 cm²

Step 4: Find the area of one square tile

The area of one square tile with side length 45 cm is:

Area of one square tile=45 cm X 45 cm=2025 cm²

Step 5: Find the number of tiles required

To find the number of tiles required, divide the area of the courtyard by the area of one square tile:

Number of tiles=Area of the courtyard/Area of one square tile=823,575/2025=407

Step 6: Conclusion

Thus, the least number of square tiles required to pave the courtyard is 407.

The correct answer is d) 407.