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