Question

The least number of square tiles required to pave the ceiling of a room $15m17cm$ long and $9m2cm$ broad is:

• A. $906$
• B. $656$
• C. $738$
• D. $814$

Answer 1

The correct option is D

$814$

Step 1: Convert meter into centimeter:

Length of the ceiling $=1517cm$ $[\because 1m=100cm]$

Breadth of the ceiling$=902cm$

Step 2: Find Side of the largest tile:

Factors of $1517=37\times 41$

Factors of $902=2\times 11\times 41$

$\mathrm{Here},\mathrm{HCF}=41$

$\therefore$Side of the largest tile$=41\mathrm{cm}$

Step 3: Calculate the area of one tile and the area of the ceiling of the room:

Area of one tile$=41cm\times 41cm\mathbf{[}\mathbf{}\mathbf{\because }\mathit{A}\mathit{r}\mathit{e}\mathit{a}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{s}\mathit{q}\mathit{u}\mathit{a}\mathit{r}\mathit{e}\mathbf{=}\mathbf{}\mathit{S}\mathit{i}\mathit{d}\mathit{e}\mathbf{}\mathbf{\times }\mathbf{}\mathit{S}\mathit{i}\mathit{d}\mathit{e}\mathbf{]}$

$=1681c{m}^2$

Area of ceiling $=1517cm\times 902cm$ $\mathbf{[}\mathbf{}\mathbf{\because }\mathit{A}\mathit{r}\mathit{e}\mathit{a}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{r}\mathit{e}\mathit{c}\mathit{t}\mathit{a}\mathit{n}\mathit{g}\mathit{l}\mathit{e}\mathbf{=}\mathbf{}\mathit{l}\mathit{e}\mathit{n}\mathit{g}\mathit{t}\mathit{h}\mathbf{}\mathbf{\times }\mathbf{}\mathit{w}\mathit{i}\mathit{d}\mathit{t}\mathit{h}\mathbf{]}$

$=1,368,334c{m}^2$

Step 4: Divide area of ceiling by area of one tile to get the number of tiles:

$$\begin{gathered} No.oftiles=\frac{Areaofceiling}{Areaofonetile} \\ =\frac{1368334c{m}^2}{1681c{m}^2} \\ =\mathbf{814} \end{gathered}$$

Hence, option D is correct answer.