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The length, breadth and height of a room are in the ration 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

1. remain the same.
2. decrease by 13.64%
3. decrease by 15%
4. decrease by 18.75%
5. decrease by 30%

Let  l = 3x, b = 2x and h = x

Area of 4 walls = 2(lh + bh) = 2(3x2 + 2x2) = 10x2

New dimensions are as follows,

l' = 2l = 6x, b' = $\frac{b}{2}$ = x and h' = $\frac{h}{2}$ = 0.5x

Area of 4 walls = 2(l'h' + b'h') = 2(6x * 0.5x + x * 0.5x) = 7x2

So we can see that area has decreased.

% decrease  = $\frac{10x^{2} - 7x^{2}}{10x^{2}}$ * 100 = 30%

Option 5 is correct