Question

The cost of preparing the walls of a room \[12m\] long at the rate of $Rs.1.35$ per square meter is $Rs.340.20$ and the cost of matting the floor at $85$ paise per square metre is $Rs.91.80$. Find the height of the room.

Answer 1

Hint: Here, we need to prepare the walls of a room. First, we shall analyze the given information so that it will be easy for us to obtain the required answer.
It is given that the length of the room is \[12m\] and the total cost of matting the floor is $Rs.91.80$ where the cost of matting the floor per square meter is $85$ paise.
Also, it is given that the total cost of preparing the walls of a room is $Rs.340.20$ where the cost of preparing the walls of a room per square meter is $Rs.1.35$.
We are asked to calculate the height of the room. Before getting into the height of the room, we shall calculate the breadth of the room using the given information.
Formula used:
area of the floor of the room$ = l \times b$
Area of walls of the room \[ = 2h\left( {l + b} \right)\]
Where
 $l$ is the length of the room, $b$ is the breadth of the room, and $h$ is the height of the room.

Complete step by step answer:
Let the length of the room be $l$, breadth of the room be $b$ and the height of the room be $h$.
It is given that the length of the room, $l = 12m$
We need to calculate the area of the floor of the room. The area of the floor of the room is the product of the length and breadth of the room.
Hence, the area of the floor of the room$ = l \times b$
$
   = 12 \times b \\
   = 12b{m^2} \\
 $
We know that the total cost of matting the floor is $Rs.91.80$ where the cost of matting the floor per square meter is $85$ paise.
We shall convert the above costs into the same unit.
So, the cost of matting the floor per square meter $ = 85paise$
$
   = Rs.\dfrac{{85}}{{100}} \\
   = Rs.0.85 \\
 $
Therefore, the total cost of matting floor$ = $ cost of matting the floor per square meter $ \times $ area of the floor of the room
 We get,
 $Rs.91.80$\[ = Rs.0.85 \times 12b\]
\[12b = \dfrac{{91.80}}{{0.85}}\]
\[ \Rightarrow 12b = \dfrac{{91.80}}{{0.85}} \times \dfrac{{100}}{{100}}\]
\[ \Rightarrow 12b = \dfrac{{9180}}{{85}}\]
\[ \Rightarrow 12b = 108\]
\[b = \dfrac{{108}}{{12}}\]
$ \Rightarrow b = 9$
Hence, the breadth of the room, \[b = 9m\]
 Now, the area of the walls of the room \[ = 2h\left( {l + b} \right)\]
 \[ = 2h\left( {12m + 9{\text{ }}m} \right)\]
Also, it is given that the total cost of preparing the walls of a room is $Rs.340.20$ where the cost of preparing the walls of a room per square meter is $Rs.1.35$.
Therefore, the total cost of preparing the walls of a room $ = $ cost of preparing the walls of a room per square meter $ \times $ area of the walls of the room
We get,
\[Rs.340.20 = Rs.1.35 \times 42h\]
\[ \Rightarrow 42h = \dfrac{{340.20}}{{1.35}}\]
\[ \Rightarrow 42h = \dfrac{{340.20}}{{1.35}} \times \dfrac{{100}}{{100}}\]
\[ \Rightarrow 42h = \dfrac{{34020}}{{135}}\]
\[ \Rightarrow 42h = 252\]
\[ \Rightarrow h = \dfrac{{252}}{{42}}\]
$ \Rightarrow h = 6$
Therefore, the required height of the room is $6cm$

Note: We are asked to calculate the height of the room. Before getting into the height of the room, we need to calculate the breadth of the room using the given information. Also, never forget to convert the dimensions into the same unit.