Question

Find the cost of carpeting a room 13 m by 9 m width a carpet of width 75 cm at the rate of Rs. 105 per metre.
(a) Rs. 16380
(b) Rs. 10080
(c) Rs. 14580
(d) Rs. 10000

Answer 1

Hint:Here, we can first find the length of the carpet using the given data. We can assume the length of the carpet to be ‘L’ and then we can equate the area of the floor of the room to the area of the carpet to get the value of L. We can find the cost of carpeting by multiplying L with the rate per metre.

Complete step-by-step answer:
We know that carpeting is done on the floor of the room and the floor is in the form of a rectangle.
The length of the rectangular room is 13 m and breadth is 9 m.
We know that the formula for the area of the rectangle is given as:
$Area=length\times breadth...........\left( 1 \right)$
On putting the values of length and breadth in equation (1), we get the area of floor as:
$Area=13m\times 9m=117{{m}^{2}}$
It is given that the carpet used for carpeting the floor is of width 75 cm.
Since, the area of the floor is in ${{m}^{2}}$, so we have to convert the width of the carpet in metres.
We know that 1m = 100cm.
Therefore, $75cm=\dfrac{1}{100}\times 75m=0.75m$
Let us assume that the total length of the carpet required is = L
So, the total area of the carpet required will be given as:
$A=L\times 0.75{{m}^{2}}$
The area of the floor of the room must be equal to the total area of the carpet. Therefore, we can write:
$\begin{align}
  & L\times 0.75{{m}^{2}}=117{{m}^{2}} \\
 & L=\dfrac{117}{0.75}m=156m \\
\end{align}$
So, the length of the carpet comes out to be 156 m.
It is given that the cost of 1 m carpet is = Rs. 105
So, total cost of 156 m of carpet = $Rs.105\times 156=Rs.16,380$
Hence, option (a) is the correct answer.

Note: Students should note here that the cost of carpet is always given as its cost per metre of length of the carpet. Thus, it is necessary to find the length of the carpet first and then calculate the total cost.Students should convert the parameters into same units before simplification and also remember the definitions and formulas related to rectangle for solving these types of questions.