A) 7
B) 11
C) 9
D) 21
E) 14
Correct Answer: A
Solution :
Total expenses on path construction = Rs. 1848 Rate = Rs. 4 per sq. metre \[\therefore \]Area of path \[=\frac{1848}{4}\]= 462 sq. metre If the width of path be r metre, then \[\pi {{(7+r)}^{2}}-\pi \times {{7}^{2}}=462\] \[\Rightarrow \]\[\frac{22}{7}({{(7+r)}^{2}}-{{7}^{2}})=462\] \[\Rightarrow \]\[(49+{{r}^{2}}+14r-49)=\frac{462\times 7}{22}\] \[\Rightarrow \]\[{{r}^{2}}+14r=147\] \[\Rightarrow \]\[{{r}^{2}}+14r=147=0\] \[\Rightarrow \]\[{{r}^{2}}+21r-7r-147=0\] \[\Rightarrow \]\[r(r+21)-7(r+21)=0\] \[\Rightarrow \]\[(r-7)(r+21)=0\] \[\Rightarrow \]\[r=7\,\text{because}\,\text{r}\ne -21\]You need to login to perform this action.
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