A rectangular plot of land measures 95m by 72m. Inside the plot, … - Vidyadip

Question

A rectangular plot of land measures $95m$ by $72m.$ Inside the plot, a path of uniform width of $3.5m$ is to be constructed all around. The rest of the plot is to be laid with grass. Find the total expenses involved in constructing the path at $Rs.80$ per $m^2$ and laying the grass at $Rs.40$ per $m^2$.

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Answer

Outer length of the plot $(\mathrm{L})=95 \mathrm{~m}$
and breadth $(B)=72 \mathrm{~m}$
Width of path $=3.5 \mathrm{~m}$

Inner length $(l)=95-2 \times 3.5=95-7=88 \mathrm{~m}$
and breadth $=72-2 \times 3.5=72-7=65 \mathrm{~m}$
Outer area $=\mathrm{L} \times \mathrm{B}=95 \times 72 \mathrm{~m}^2=6840 \mathrm{~m}^2$
and inner area $=\mathrm{l} \times \mathrm{b}=88 \times 65 \mathrm{~m}^2=5720 \mathrm{~m}^2$
Area of path $=$ outer area $-$ inner area $=6840-5720=1120 \mathrm{~m}^2$
Rate of constructing it $= Rs. 80 per \mathrm{m}^2$
Total cost $= Rs. 1120 \times 80= Rs. 89600$
and rate of laying grass $= Rs. 40$ per $\mathrm{m}^2$
Total cost $= Rs. 40 \times 5720= Rs. 228800$
Total cost $= Rs. 89600 + Rs. 228800= Rs. 318400$

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