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
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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