Geometry & Mensuration
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Q.

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

 A.

remains the same.

 B.

decrease by \(13.64\%\)

 C.

decrease by \(15\%\)

 D.

decrease by \(30\%\)

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Solution:
Option(D) is correct

Let the original length, breadth and height of the room be $3x$, $2x$ and $x$ respectively.

Therefore, the new length, breadth and height are $6x$, $x$ and $x/2$ respectively.

Area of four walls = (2 × length × height) + (2 × breadth × height)

Original area of four walls,

\(=(2 \times 3x \times x)+(2 \times 2x \times x)\)

\(= 6x^2 + 4x^2 = 10x^2\)

New area of four walls,

\(=(2 \times 6x \times \frac{x}{2})+(2 \times x \times \frac{x}{2})\)

 \( =6x^2 + x^2 = 7x^2\)

Therefore, Area of wall decreases by

\( =\left[\dfrac{10x^2 - 7x^2}{10x^2} \right] \times 100\)

\(= 30\%\)

Edit: A typo in the final step has been corrected based on the input from KARTIK.


(4) Comment(s)


Amit
 ()

in this question u have not mentioned which four walls are to be considered .


Alia
 ()

A room has only four walls. Other two surfaces are called 'roof' and 'floor'. So, I believe the question is okay and does not need any correction.


KARTIK
 ()

last step : $10x^2$ instead of $10^2$ :)


Deepak
 ()

Thank you Kartik, corrected the mistake.