It is required to construct a big rectangular hall to accommodate 500 persons, allowing 22.5 m³ space per… · ABC26GN4800
Subject: General Aptitude · Chapter: Volume and Surface Area
It is required to construct a big rectangular hall to accommodate 500 persons, allowing $22.5 \mathrm{m}^{3}$ space per person. The height of the hall is to be kept at 7.5 m, while the total inner surface area of the walls must be 1200 sq. m. Then the length and breadth of the hall respectively are
(a)40 m and 30 m
(b)45 m and 35 m
(c)50 m and 30 m
(d)60 m and 20 m
Answer
Answer (as printed): C
Explanation
Volume of the hall $=(500 \times 22.5) \mathrm{m}^{3}=11250 \mathrm{m}^{3}$. Let the length and breadth of the hall be $l$ and $b$ metres respectively. $$\text { Then, } l \times b \times h=11250 \Rightarrow l b=\frac{11250}{7.5}=1500 \text { And, } 2(l+b) \times h=1200 \Rightarrow 2(l+b)=\frac{1200}{7.5}=160$$ Putting $b=(80-l)$ in (i), we get: $$\begin{aligned} & l(80-l)=1500 \Rightarrow l^{2}-80 l+1500=0 \Rightarrow(l-30)(l-50) \\ & =0 \Rightarrow l=50 . \end{aligned}$$ Hence, length $=50 \mathrm{m}$, breadth $=30 \mathrm{m}$.