Question

The dimensions of a reactangular box are in the ratio 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 $m^2$ is Rs. 1,248. Find the dimensions of the box.

Answer 1

Ratio in the dimensions of a box
= 2:3:4
Difference in total cost= Rs 1,248
Difference in rates = Rs. 9.50-rs.8 =Rs. 1.50
Let length (l) = 2x
Then breadth (b) = 3x
and height (h) = 4x
\therefore Surface area = $2(l\times b+b\times h+h\times l)$
= $2(2x\times 3x+3x\times 4x+4x\times 2x)$
= $2(6x^2+12x^2+8x^2)=2\times 26x^2=52x^2$
First rate of paper = Rs. 9.50 per $m^2$
and second rate = 8.00 per $m^2$
$\therefore$ First cost = Rs. $52x^2\times 9.50$
and second cost = Rs $52x^2\times 8$
$\therefore 52x^2\times 9.50-52x^2\times 8$
$\Rightarrow 52x^2$ (9.50-8)= 1248
$\Rightarrow 52x^2$ (1.50) = 1248
$\Rightarrow x^2=\frac{1248}{52\times 1.50}=\frac{1248\times 100}{52\times 150}=16$
$\Rightarrow x=\sqrt{16}4$
$\therefore$ Length = 2x= $2\times$ 4 = 8 m
Breadth = 3x=$3\times 4$ = 12 m
Height = 4x= $4\times 4$ = 16 m