question_answer

The ratio of the outer and the inner perimeter of a circular path is 23 : 22. If the path is 5 m wide, the diameter of the inner circle is

A)  110 m             

B)  55 m

C)  220 m 

D)  230 m

Correct Answer: C

Solution :

\[\therefore \]      \[\frac{2\pi {{r}_{2}}}{2\pi {{r}_{1}}}=\frac{23}{22}\] \[\Rightarrow \]   \[\frac{{{r}_{2}}}{{{r}_{1}}}=\frac{23}{22}\]  Let        \[{{r}_{1}}=22x\,m\] and       \[{{r}_{2}}=23x\,m\] \[\therefore \]      \[{{r}_{1}}-{{r}_{2}}=5\] \[\Rightarrow \]   \[x=5\,m\] \[\therefore \] Inner radius \[=22\times 5=110\,m\] \[\therefore \] Required diameter \[=110\times 2=220\,m\]