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Question
The dimensions of a rectangular box are in the ratio of 2 : 3 : 4 and the difference between the cost ofcovering it with sheet of paper at the rates of Rs. 8 and Rs. 9.50 per m2 is Rs.1248. Find the dimensions of the box.
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Solution
Let the ratio be x
∴length = 2x
Breath = 3x
Height = 4x
∴Total surface area = `2[lb+bh+hl]`
`=2[6x^2+12x^2+8x^2]`
`=52x^2m^2`
When cost is at `Rs. 9.51 per m^2`
`∴Total cost of 52x^2m^2=Rs.8xx52x^2`
`= Rs. 416x^2`
And when the cost is at `95 per m^2`
`∴Total cost of 52x^2m^2=Rs.9.5xx52x^2`
`=Rs.499x^2`
`∴"different in cost"= Rs.494x^2-Rs.416x^2`
`⇒1248=494x^2-416x^2`
`⇒78x^2=1248`
`⇒x^2=16`
`⇒x=4`
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