Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
The dimensions of a rectangular box are in the ratio 2 : 3 : 4 and the difference between the cost of covering it with sheet of paper at the rate of ₹ 8 and ₹ 9.50 per square metre is ₹ 1248. Find the dimensions of the box in meters.
(a)2 m, 12 m, 8 m
(b)4 m, 9 m, 16 m
(c)8 m, 12 m, 16 m
(d)None of these
Answer
Answer (as printed): C
Explanation
Let the length, breadth and height of the box be $2 x, 3 x$ and $4 x$ respectively. Then, surface area of the box $=2[2 x .3 x+3 x .4 x+2 x .4 x]$ $$\begin{aligned} & =\left[2\left(6 x^{2}+12 x^{2}+8 x^{2}\right)\right]=52 x^{2} . \\ & \therefore 52 x^{2}=\frac{1248}{1.50}=832 \Rightarrow x^{2}=\frac{832}{52}=16 \Rightarrow x=\sqrt{16}=4 . \end{aligned}$$ Hence, the dimensions of the box are 8 m, 12 m and 16 m.
Explanation as extracted from the printed page; notation may be imperfect.