The length of a room is double its breadth. The cost of colouring the ceiling at Rs. 25 per sq. meter is Rs. 5000 and the cost of painting the four walls at Rs. 240 per sq. metre is Rs. 64800. Find the height of the room :

Let the breadth and height of the room be b metres and h metres respectively.
Then, length of the room = (2b) metres
Area of the ceiling :
$$\eqalign{ & = \left( {2b \times b} \right)m \cr & = \left( {2{b^2}} \right){m^2} \cr} $$
$$\eqalign{ & 2{b^2} = \frac{{5000}}{{25}} \cr & 2{b^2} = 200 \cr & {b^2} = 100 \cr & b = 10 \cr} $$
So, length = 20 m, breadth = 10 m
Area of 4 walls :
$$\eqalign{ & = \left[ {2\left( {20 + 10} \right) \times h} \right]{m^2} \cr & = \left( {60h} \right){m^2} \cr} $$
$$\eqalign{ & \therefore 60h = \frac{{64800}}{{240}} \cr & \Rightarrow 60h = 270 \cr & \Rightarrow h = \frac{{270}}{{60}} \cr & \Rightarrow h = 4.5\,m \cr} $$