The length, breadth and height of the room are in the ratio 3 : 2 : 1. The breadth and height of the room are halved and length of the room is doubled. The area of the four walls of the room will :

Answer: Option D

Let the length, breadth and height of the room be 3x, 2x and x respectively.
Area of 4 walls :
$$\begin{array}{rl}& =2\left(l+b\right)\times h\\ & =2\left(3x+2x\right)\times x\\ & =10x^2\end{array}$$
New length = 6x
New breadth = x
New height = $$\frac{x}{2}$$
New area of four walls :
$$\begin{array}{rl}& =\left[2\left(6x+x\right)\frac{x}{2}\right]\\ & =7x^2\end{array}$$
Decrease in area :
$$\begin{array}{rl}& =\left(10x^2-7x^2\right)\\ & =3x^2\end{array}$$
∴ Decrease% :
$$\begin{array}{rl}& =\left(\frac{3x^2}{10x^2}\times 100\right)\%\\ & =30\%\end{array}$$