There is a square field whose side is 44 m. A square flower bed i… - Vidyadip

Question

There is a square field whose side is $44\ m.$ A square flower bed is prepared in its centre leaving a gravel path all round the flower bed. The total cost of laying the flower bed and graving the path at $Rs\ 2. 75$ and $Rs. 1.5$ per square metre, respectively, is $Rs. 4,904.$ Find the width of the gravel path.

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Answer

Let the side of flower bed be $a$ and that of gravel path be $b$.
Then $a+2 b=44$ (as $44$ is overall size of field and it contains side of flower bed and double side of gravel path) .... (i)
Area of Flower bed $=a^2$
Area of Gravel path $=$ Area of Square - Area of flower bed $=44 \times 44-a^2$
$\Rightarrow$ Area of Gravel path $=1936- a ^2$
Cost of laying flower bed + Gravel path $=$ Area $x$ cost of laying per sq.m
$\Rightarrow 4904=\left(a^2 \times 2.75\right)+\left(1936-a^2\right) \times 1.5 $
$\Rightarrow 4904=2.75 a^2-1.5 a^2+2904 $
$\Rightarrow 1.25 a^2=2000 $
$\Rightarrow a^2=1600, \text { Hence } a=40 .$
Hence gravel path width $=\frac{44-40}{2} m =2 m$

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