The cost of preparing the walls of a room 12 m long at the rate of Rs 1.35 per square metre 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.

#### Solution

\[\text { The cost of preparing 4 walls of a room whose length is 12 m is Rs 340 . 20 at a rate of Rs } 1 . 35/ m^2 . \]

\[ \therefore { \text { Area of the four walls of the room } = }\frac{\text { total cost }}{\text { rate }} = \frac{Rs 340 . 20}{Rs 1 . 35} = 252 m^2 \]

\[\text { Also, the cost of matting the floor at 85 paise }/ m^2 is Rs 91 . 80 . \]

\[ \therefore \text { Area of the floor } = \frac{\text { total cost }}{\text { rate }} = \frac{Rs 91 . 80}{Rs 0 . 85} = 108 m^2 \]

\[\text { Hence, breadth of the room = } \frac{\text { area of the floor }}{\text { length }}=\frac{108}{12} = 9 m\]

\[\text { Suppose that the height of the room is h m . }\hspace{0.167em} \text { Then, we have: }\]

\[\text { Area of four walls = } 2 \times \text { (length }\times\text { height + breadth } \times\text { height) }\]

\[ \Rightarrow 252 = 2 \times (12 \times h + 9 \times h)\]

\[ \Rightarrow 252 = 2 \times (21h)\]

\[ \Rightarrow 21h = \frac{252}{2} = 126\]

\[ \Rightarrow h = \frac{126}{21} = 6 m\]

\[ \therefore\text { The height of the room is 6 m }.\]