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 Rs. 8 and Rs. 9.50 per square metre is Rs. 1248. Find the dimensions of the box in metres.

Answer: Option C

Let the length, breadth and height of the box be 2x, 3x and 4x respectively
Then, surface area of the box :
= 2 [2x.3x + 3x.4x + 2x.4x]
= [2(6x² + 12x² + 8x²)]
= 52x²
$$\begin{array}{rl}& \therefore 52x^2=\frac{1248}{1.50}\\ & \Rightarrow 52x^2=832\\ & \Rightarrow x^2=\frac{832}{52}\\ & \Rightarrow x^2=16\\ & \Rightarrow x=4\end{array}$$
Hence, the diameter of the box are 8 m, 12 m and 16 m