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.

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
$$\eqalign{ & \therefore 52{x^2} = \frac{{1248}}{{1.50}} \cr & \Rightarrow 52{x^2} = 832 \cr & \Rightarrow {x^2} = \frac{{832}}{{52}} \cr & \Rightarrow {x^2} = 16 \cr & \Rightarrow x = 4 \cr} $$
Hence, the diameter of the box are 8 m, 12 m and 16 m