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# 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. - CBSE Class 9 - Mathematics

ConceptSurface Area of a Cuboid and a Cube

#### 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.

#### 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

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Solution for Mathematics for Class 9 by R D Sharma (2018-19 Session) (2018 to Current)
Chapter 18: Surface Areas and Volume of a Cuboid and Cube
Ex.18.10 | Q: 16 | Page no. 15
Solution 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. Concept: Surface Area of a Cuboid and a Cube.
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