question_answer

The ratio of the outer and inner perimeters of a circular path is\[23:22\]. If the path is 5 metres wide, the diameter of the inner circle is

A)  \[55\,m\]                                 

B)  \[110\,m\]                   

C) \[220\text{ }m\]        

D)         \[~230\text{ }m\]      

Correct Answer: C

Solution :

Let radius of inner and outer circle be \[{{r}_{1}}\] and  \[{{r}_{2}}\]respectively.                  \[\therefore \]        \[{{r}_{2}}=({{r}_{1}}+5)\]                  .....(i)       According to question         \[\frac{2\pi {{r}_{2}}}{2\pi {{r}_{1}}}=\frac{23}{22}\,\Rightarrow \,\frac{{{r}_{1}}+5}{{{r}_{1}}}=\frac{23}{22}\] \[\Rightarrow \]            \[{{r}_{1}}=110\,n.\] Diameter of inner circle \[=2\times {{r}_{1}}=2\times 110=220m\]