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 total area of the four walls of the room will

• A. remain the same
• B. decrease by $30\%$
• C. decrease by $15\%$
• D. decrease by $18.75\%$

Answer 1

Answer: (B)

decrease by $30\%$

Let $l=3x$, $b=2x$, $h=x$

Area of four walls $=2(l+b)h=2(3x+2x)x=10x^2$

Now, $l^1=6x,b^1=x,h^1=x/2$

New area $=2(6x+x)\times \frac{x}{2}=7x^2$

$\therefore$ % decrease in area $=\frac{{10x}^2-{7x}^2}{{10x}^2}\times 100=30$%