Question

Find the cost of carpeting a room \[13m\] by \[9m\] with a carpet of width \[75cm\] at the rate of \[Rs.105\] per meter.
A. \[16380\]
B. \[10080\]
C. \[14580\]
D. \[10000\]

Answer 1

Hint:Here, find the area of the room and equate it with area of carpet assuming length of carpet as L m. Convert the unit of width of carpet in meters. Then, multiply the obtained length of carpet with the given rate of carpet to get the final result as the width of the carpet is fixed.

Complete step by step answer:
Given is the rectangular room of dimensions \[13m\] by \[9m\]. We know that area of rectangle is given by the formula \[Length \times Breadth\]
\[{A_{room}} = 13m \times 9m = 117sq.m\]
Width of the carpet is in cm. But we need the dimensions in meters. So let’s convert it in meters. We know that, \[1m = 100cm\]
Width of carpet = \[\dfrac{{75cm}}{{100}} = 0.75m{\text{ }}\;\]
The length of carpet is L m.
Then, area of carpet \[ = 0.75 \times L{\text{ sq}}{\text{.m}}{\text{.}}\]

If a room is carpeted, then the area of the room is equal to the area of carpet.
\[117 = 75 \times L\]
Then the length of the carpet will be,
\[L = \dfrac{{117}}{{0.75}}\]
\[L = \dfrac{{11700}}{{75}}\]
On dividing we get,
\[L = 156m\]
Length of carpet = \[156m\]
Given that rate of per meter carpet is \[Rs.105\]
Required cost = \[156 \times 105 = Rs.16380\].

Hence, option A is correct.

Note:In these types of questions, assume unknown length or breadth of carpet and equate it with the given area. As we know that the area is the region enclosed by boundaries. In the above question, room is carpeted means room is fully covered with carpet, so we calculated the area of room and carpet here. To find the cost of the carpet, multiply the length with the given rate as the width of the carpet is fixed.