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