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 :

Solution (By Examveda Team)

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