Question : The ratio of the outer and the inner circumference of a circular path is 17 : 15. If the path is 40 metres wide, then what is the radius of the inner circle?
Option 1: 280 metres
Option 2: 340 metres
Option 3: 360 metres
Option 4: 300 metres
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Correct Answer: 300 metres
Solution : Let the radius of the inner and outer circumference be $r$ and $R$. $R=r+40$ According to the question, $\frac{2\pi R}{2\pi r}=\frac{17}{15}$ $⇒\frac{(r+40)}{r}=\frac{17}{15}$ $⇒15r+600=17r$ $⇒2r=600$ $\therefore r = 300$ metres Hence, the correct answer is 300 metres.
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