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

$$\eqalign{ & \frac{{2\pi {R_1}}}{{2\pi {R_2}}} = \frac{{23}}{{22}} \cr & \Rightarrow \frac{{{R_1}}}{{{R_2}}} = \frac{{23}}{{22}} \cr & \Rightarrow {R_1} = \frac{{23{R_2}}}{{22}} \cr & {\text{Also, }}{R_1} - {R_2} = 5\,m \cr & \Rightarrow \frac{{23{R_2}}}{{22}} - {R_2} = 5 \cr & \Rightarrow {R_2} = 110 \cr} $$
∴ Diameter of inner circle :
= (2 × 110) m
= 220 m