Question

The length, breadth and height of a room are in the ratio 4:3:2. If the breadth and height are halved
while the length is doubled, then the total area of the four walls of the room will
remains the same,
decrease by 13.64%
decrease by 15%
decrease by 32%​

Answer 1

Answer:

30%

step by step

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)×

2

x

=7x

2

∴ % decrease in area =

10x

2

10x

2

−7x

2

×100=30%

Answer 2

Given:

The ratio of the length, breadth and height of the room = 4:3:2

To find:

If the breadth and height are halved while the length is doubled. Then what will be the correct option.

Solution:

Let us assume that the length, breadth and height of the room are 4x, 3x and 2x.

The area of the four walls of the room will be:

= 2(4x*2x + 3x*2x)

= 2(8x² + 6x²)

= 2*14x²

= 28x²

On making the required changes, the final length, breadth and height will be 8x, 1.5x and x.

The final area of the four walls of the room will be:

= 2(8x*x + 1.5x*x)

= 2(8x² + 1.5x²)

= 2*9.5x²

= 19x²

Thus, the area of the four walls have decreased by:

(28x²- 19x²)/ 28x² * 100

= 9x²/ 28x² * 100

= 32%

Thus, the correct option is D, i.e. the area of the four walls of the room decreases by 32%.