question_answer

The ratio of the outer and the inner perimeters 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 :

Let the shaded portion be the circular path.

Let the inner radius be r metres.

\[\therefore \]      Outer radius R = (r + 5) m

\[\frac{2\pi R}{2\pi r}=\frac{23}{22}\Rightarrow \frac{R}{r}=\frac{23}{22}\]

\[\Rightarrow \]   \[\frac{r+5}{r}=\frac{23}{22}\Rightarrow 23r=22r+110\]

\[\Rightarrow \]   \[r=110\,\,\text{m}\]

\[\therefore \] Daimeter \[=2\times 110=220\,\,\text{m}\]