Question

The dimensions of a rectangular box are in the ratio $1:2:4$ and the difference between the costs of covering it with the cloth and sheet at the rate of $Rs.20$ and $Rs.20.50$ per square metre, respectively is $Rs.126$. Find the dimensions of the box.

• A. $4cm,7cm$ and $10cm$
• B. $2cm,4cm$ and $11cm$
• C. $3cm,6cm$ and $12cm$
• D. $7cm,8cm$ and $13cm$

Answer 1

The correct option is C $3cm,6cm$ and $12cm$

Let length$=x$, breadth $=2x$ and height $=4x$.
Area of the box $=2(lb+bh+lh)$

$=2(2x^2+8x^2+4x^2)=28x^2$
Given, $20.5\times 28x^2-20\times 28x^2=126$

$\Rightarrow 28x^2\times 0.5=216$

$\Rightarrow x^2=9$

$\Rightarrow x=3$
$\therefore$ The dimensions are $3cm,6cm$ and $12cm$.