Answer :

Ratio of dimensions of rectangular box = 2:3:4

Let length of box = 2x m

Breadth of box = 3x m

Height of box = 4x m

Area of sheet of paper required for covering it = total surface area of cuboid

= 2(lb × bh × hl)

=2(6x^{2} + 12x^{2} + 8x^{2})

= 2×26x^{2}

=52 x^{2} m^{2}

Cost of covering it with sheet of paper at Rs.9.50 /m^{2}

= 52 x^{2} × 9.50

=Rs.494 x^{2}

Cost of covering it with sheet of paper at rate Rs.8/m^{2} = 52x^{2} × 8

=Rs.416 x^{2}

= 494x^{2}-416x^{2}=1248 Given

= 78x^{2}=1248

= x^{2}=1248/78=16

= x= √16=4

So,

Length of box = 2x = 2×4 = 8 m

Breadth of box = 3x = 3×4 = 12 m

Height of box = 4x = 4×4 = 16 m

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