Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
A room is half as long again as it is broad. The cost of carpeting the room at ₹ 5 per sq. m is ₹ 270 and the cost of papering the four walls at ₹ 10 per m$^2$ is ₹ 1720. If a door and 2 windows occupy 8 sq. m, find the dimensions of the room.
Answer
Answer (as printed):
Explanation
Let breadth $=x$ metres, length $=\frac{3x}{2}$ metres, height $=H$ metres. $$\begin{aligned} & \text{Area of the floor}=\left(\frac{\text{Total cost of carpeting}}{\text{Rate}/\text{m}^2}\right)\text{m}^2=\left(\frac{270}{5}\right)\text{m}^2=54\text{ m}^2. \\ & \therefore x \times \frac{3x}{2}=54 \Leftrightarrow x^2=\left(54\times\frac{2}{3}\right)=36 \Leftrightarrow x=6. \end{aligned}$$ So, breadth = 6 m and length $=\left(\frac{3}{2}\times 6\right)$ m $=9$ m. Now, papered area $=\left(\frac{1720}{10}\right)$ m$^2=172$ m$^2$. Area of 1 door and 2 windows $=8$ m$^2$. Total area of 4 walls $=(172+8)$ m$^2=180$ m$^2$. $$\therefore 2(9+6)\times H=180 \Leftrightarrow H=\left(\frac{180}{30}\right)=6\text{ m}.$$
Explanation as extracted from the printed page; notation may be imperfect.