The dimensions of a rectangular box are in the ratio of 2: 3: 4 and the difference between the cost of covering it

Question:

The dimensions of a rectangular box are in the ratio of $2: 3: 4$ and the difference between the cost of covering it with a sheet of paper at the rates of Rs 8 and Rs $9.50$ per $m^{2}$ is Rs 1248 . Find the dimensions of the box.

Solution:

Let the ratio be ‘x’

Length (l) = 2x

Breadth (b) = 3x

Height (h) = 4x

Therefore, Total Surface area = 2[lb + bh + hl]

$=2\left(6 x^{2}+12 x^{2}+8 x^{2}\right)$

$=52 x^{2} \mathrm{~m}^{2}$

When the cost is at Rs. 8 per $\mathrm{m}^{2}$

Therefore, the total cost of $52 x^{2}=8 * 52 x^{2}$

$=\operatorname{Rs} \cdot 494 x^{2}$

Therefore, the Difference in cost $=$ Rs. $494 x^{2}-$ Rs. $416 x^{2}$

$1248=\operatorname{Rs} .78 x^{2}$

$x^{2}=1248 / 78$

$x^{2}=16$

x = 4

 

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