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CAT 2006 | Question: 54

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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 $30\%$
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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

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