Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
The ratio of the height of a room to its semi-perimeter is 2 : 5. It costs ₹ 260 to paper the walls of the room with paper 50 cm wide at ₹ 2 per metre allowing an area of 15 sq. m for doors and windows. The height of the room is
(a)2.6 m
(b)3.9 m
(c)4 m
(d)4.2 m
Answer
Answer (as printed): C
Explanation
Let $h=2 x$ metres and $(l+b)=5 x$ metres. Length of the paper $=\frac{\text { Total cost }}{\text { Rate per } \mathrm{m}}=\frac{260}{2} \mathrm{m}=130 \mathrm{m}$. Area of the paper $=\left(130 \times \frac{50}{100}\right) \mathrm{m}^{2}=65 \mathrm{m}^{2}$. Total area of 4 walls $=(65+15) \mathrm{m}^{2}=80 \mathrm{m}^{2}$. $$\begin{aligned} \therefore 2(l+b) \times h=80 & \Leftrightarrow 2 \times 5 x \times 2 x=80 \\ & \Leftrightarrow x^{2}=4 \Leftrightarrow x=2 . \end{aligned}$$ Height of the room $=4 \mathrm{m}$.