Question

Find the cost of flooring a square room of 10m with marble titles \[25cm{\text{ }} \times {\text{ }}20cm\] at the rate INR 7.50 per title.

Answer 1

Hint: The room is in the shape of a square which means all sides of the room will be 10 meters. A square is a regular quadrilateral in which all four sides are equal, the four interior angles are at \[{90^ \circ }\]and four opposite sides are parallel. To find the cost of flooring, find the number of tiles to be used by dividing the floor size with the size of a tile. The size of the floor refers to the area of the floor and is represented as area\[A = {\left( {side} \right)^2}\]. Since the sizes of the tiles are given, find the number of tiles to be used in the room.

Complete step by step answer:
Given the side of the room is 10 meters so, \[side = 10m\].
As the room is a square room then all the sides of the room will be \[10m\]
Hence, the area of the floor will be:
\[
  {A_F} = {\left( {side} \right)^2} \\
   = {\left( {10} \right)^2} \\
   = 100{m^2} \\
 \]
Now we know that a total of \[100{m^2}\] is the area where flooring is to be done with the tiles.
Now, find the size of the tile which is to be used whose dimension is given as \[25cm{\text{ }} \times {\text{ }}20cm\] in the same measuring dimension of the room.
\[
  25cm{\text{ }} \times {\text{ }}20cm = \dfrac{{25}}{{100}}m \times \dfrac{{20}}{{100}}m. \\
   = 0.25m \times 0.2m \\
 \]
Hence, the area of a title will be:
\[{A_T} = 0.25m \times 0.2m = 0.05{m^2}\]
Now find the number of title to be used:
\[\dfrac{{{A_F}}}{{{A_T}}} = \dfrac{{100}}{{0.05}} = \dfrac{{10000}}{5} = 2000\]
Hence the total number of tiles required for flooring @7.50 per title will be 2000.
Now, to calculate the total cost of flooring, multiply the number of tiles with the cost per piece of a tile.
Therefore, total cost of flooring is:
\[
  {\text{Cost = }}2000 \times 7.50 \\
   = 15000 \\
 \]
Hence, the cost of flooring a square room of side 10m with marble titles \[25cm{\text{ }} \times {\text{ }}20cm\] at the rate INR 7.50 per title is INR. 15000.

Note: To find the total cost of flooring find the number of tiles required for flooring. It should be kept in mind the measuring unit of the room as well as the tiles must be the same