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1. 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.

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

Solution:

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{aligned} ∴ 52 x^{2} = \frac{1248}{1.50} \\ \Rightarrow 52 x^{2} = 832 \\ \Rightarrow x^{2} = \frac{832}{52} \\ \Rightarrow x^{2} = 16 \\ \Rightarrow x = 4 \end{aligned}

Hence, the diameter of the box are 8 m, 12 m and 16 m

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