Question : The ratio of the outer and the inner circumferences of a circular path is 11 : 7. If the path is 20 metres wide, then what is the radius of the inner circle?
Option 1: 20 metres
Option 2: 55 metres
Option 3: 65 metres
Option 4: 35 metres
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.
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