Question

The cost of carpeting a room 15 m long with a carpet of width 75 m at Rs 80 per metre is Rs 19200. Find the width of the room.

Answer 1

Hint: We will consider the carpet of width 75 m as a strip and count the number of strips needed to cover the width of the room. First we will calculate the cost for covering the length of the room by carpet. Then we will find the number of strips of carpet of width 75 m that are required to cover the entire room. Then we will compute the length of the room by adding the width of all the strips of carpet required.

Complete step-by-step answer:
The cost per metre of carpet is given as Rs 80. The length of the room is 15 m. So, the cost to cover the length of the room with carpet of width 75 m can be calculated in the following manner,
$\begin{align}
  & \text{cost of covering the length of room with carpet = 15 }\times \text{ 80} \\
 & \therefore \text{cost of covering the length of room with carpet = 1200 Rs} \\
\end{align}$
Now, the total cost of carpeting the room is Rs 19200. We have to calculate the number of strips of carpet of width 75 m required to cover the entire room. To calculate this, we will divide the cost of carpeting the entire room by the cost of carpeting the length of the room. So, the number of strips needed to cover the width of the room are
$\begin{align}
  & \text{number of strips of carpet = }\dfrac{19200}{1200} \\
 & \therefore \text{number of strips of carpet = 16 } \\
\end{align}$
Hence, the number of strips needed to cover the width of the room is 16. Now, each strip of carpet is of 75 m. So, the width of the room is
$\begin{align}
  & \text{width of the room = 16 }\times \text{ 75} \\
 & \therefore \text{width of the room = 1200 m} \\
\end{align}$
Therefore, the width of the room is 1200 metres.

Note: We should interpret the question carefully and make sense of the relations between the given dimensions correctly. The calculations in this question are tricky and need to be done explicitly. So that we can avoid making any minor mistakes in the calculations and obtain the correct answer. It might be useful to quickly visualize the room with its length and breadth using a rough diagram.