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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 of covering 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

## Ratio in the dimensions of a cuboidal box=2:3:4 Let length (l)=4x Breadth (b)=3x and height (h)=2x ∴ Total surface area= 2[lb+bh+hl] =2[4x×3x+3x×2x+2x×4x] cm2 =2[12x2+6x2+8x2]=2×26x2 =52x2 Now, rate of covering it with paper=Rs 8 per m2Therefore, cost of covering it with paper =8×52x2 Also, rate of covering it with paper=Rs 9.50 per m2Therefore, cost of covering it with paper =9.50×52x2 ∴ Difference in the cost, =Rs (52x2×9.50−52x2×8) =Rs (494x2−416x2)=78x2Now, according to the question, ⇒78x2=1248⇒ x2=124878=16 ⇒x=√16=4 ∴ Dimensions are,h= 2×4=8 m b=3×4=12 m l=4×4=16 m

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