# Difficult Geometry & Mensuration Solved QuestionAptitude Discussion

 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 $30\%$

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.