Correct Answer: 35 metres

Solution : The circumference of a circle is given by the formula $C = 2\pi r$, where $r$ is the radius of the circle.
Given that the ratio of the outer and the inner circumferences of the circular path is 11 : 7.
$⇒\frac{C_{\text{outer}}}{C_{\text{inner}}} = \frac{11}{7}$
$⇒\frac{2\pi r_{\text{outer}}}{2\pi r_{\text{inner}}} = \frac{11}{7}$
$⇒\frac{r_{\text{outer}}}{r_{\text{inner}}} = \frac{11}{7}$
Given that the width of the path (which is the difference between the outer and inner radii) is 20 metres.
$⇒r_{\text{outer}} - r_{\text{inner}} = 20$
Substituting the first equation into this gives:
$⇒r_{\text{inner}} \times \frac{11}{7} - r_{\text{inner}} = 20$
$\therefore r_{\text{inner}} = \frac{20 \times 7}{4} = 35$ metres
Hence, the correct answer is 35 metres.