Question

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

Answer 1

Answer :

Given : The length, breadth and height of a room are in the ratio 3 : 2 : 1 .

Let ratio coefficient = x
So,
Length = 3x
Breadth = 2x
And
Height = x

And Area of walls = 2 ( Length + Breadth ) Height , So

Area of walls = 2 ( 3x + 2x ) x = 10x² unit
Now
the breadth and height are halved while the length is doubled, So

Length = 6x
Breadth = x
And
Height = $\frac{x}{2}$
So,
Area of walls = 2 ( 6x + x ) $\frac{x}{2}$ = 7x² unit
So,
Area of walls decreased = 10x² - 7x² = 3x² unit
So,
Area of walls decreased in percentage = $\frac{3x^2}{10x^2}\times 100=\frac{3}{10}\times 100=\mathbf{30}\mathbf{\%}$ ( Ans )