Question

What is the least number of square tiles required to pave the floor of a room $9\text{ m 99 cm}$ long and $4\text{ m 7 cm}$ broad?
A. $247$
B. $277$
C. $297$
D. $307$

Answer 1

Hint: We have given length and width of the floor, as floor is rectangular in shape so first we find the area of the floor using the formula
\[\text{Area = length}\times \text{width}\]
Then, we calculate the maximum permissible size of tile by calculating the HCF of length and width of the floor given in the question and divide the area of floor by area of one tile to get the number of tiles.

Complete step by step answer:
We have given that the floor of a room is $9\text{ m 99 cm}$ long and $4\text{ m 7 cm}$ broad.

We have to find the least number of square tiles required to pave the floor.
We know that a room is rectangular in shape. So, the area of room will be
\[\text{Area = length}\times \text{width}\]
We have been given that
 $\begin{align}
  & length=9\text{ m 99 cm = 999 cm} \\
 & width=4\text{ m 7 cm =407 cm} \\
\end{align}$
So, area of the floor will be
\[\begin{align}
  & Area=9\text{ m 99 cm}\times 4\text{ m 7 cm} \\
 &\Rightarrow Area=999\times 407\text{ cm} \\
 & \Rightarrow \text{Area=406593 c}{{\text{m}}^{2}} \\
\end{align}\]
Now, we know that the maximum permissible size of tiles is equal to the HCF of $\text{999 }\!\!\And\!\!\text{ 407}$.
So, we will calculate the HCF of $\text{999 }\!\!\And\!\!\text{ 407}$ by using the prime factorization method.
$\begin{align}
  & \Rightarrow 999=3\times 3\times 3\times 37 \\
 & \Rightarrow 407=11\times 37 \\
\end{align}$
Now, the common factors of both the numbers are $37$
So, we get the HCF $37$.
Now, the area of one tile $=37\times 37=1369\text{ c}{{\text{m}}^{2}}$
If we divide the area of the floor by the area of one tile, it gives a number of tiles.
Now, Number of tiles required $=\dfrac{\text{Area of floor}}{\text{Area of one tile}}$.
So, we get Number of tiles required $=\dfrac{406593}{1369}$
Number of tiles required $=297$
So the number of tiles required to pave the floor of a room $9\text{ m 99 cm}$ long and $4\text{ m 7 cm}$ broad is $297$.

So, the correct answer is “Option C”.

Note: If we have given in the question the area of one tile then, we directly calculate the number of tiles required.
Number of tiles required $=\dfrac{\text{Area of floor}}{\text{Area of one tile}}$.
If a measure of the side of tile is given, we calculate the area of one tile using the formula of area of square, as given the tile is square in shape.