Question

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 total area of the four walls of the room will,

• A. Remain the same
• B. Decrease by $30\%$
• C. Decrease by $15\%$
• D. Decrease by $18.75\%$

Answer 1

The correct option is B

Decrease by $30\%$

The explanation for the correct option.

Since the length breadth and height of a room are in the ratio $3:2:1$.

Let us consider that, length$\left(l\right)$, breadth $\left(b\right)$, and height $\left(h\right)$ are $3\mathrm{x},2\mathrm{x}\mathrm{and}\mathrm{x}$ respectively.

The area of the walls is computed as,

$$\begin{gathered} A_1=2(l+b)\times h \\ \Rightarrow =2(3x+2x)x \\ \Rightarrow =10x^2 \end{gathered}$$

When the breadth and height are halved while the length is doubled, then the total area of the four walls is computed as,

$$\begin{gathered} A_2=2(6x+x)\frac{x}{2} \\ \Rightarrow =7x^2 \end{gathered}$$

The percent decrease in area is computed as,

$$\begin{gathered} \mathrm{Decrease}=\frac{A_1-A_2}{A_1}\times 100 \\ \Rightarrow =\frac{10x^2-7x^2}{10x^2}\times 100 \\ \Rightarrow =\frac{3}{10}\times 100 \\ \Rightarrow =30\% \end{gathered}$$

Thus, the total area is decreased by $30\%$.

Hence, the option $B$is correct.