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.

Answer 1

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`