Question : The ratio of the outer and the inner circumference of a circular path is 5 : 4. If the path is 50 metres wide, then what is the radius of the inner circle?
Option 1: 250 metres
Option 2: 300 metres
Option 3: 200 metres
Option 4: 210 metres
Correct Answer: 200 metres
Solution :
Let the radius of the inner and outer circumference be $r$ and $R$.
According to the question,
$\frac{2\pi R}{2\pi r}=\frac{5}{4}$
⇒ $\frac{2\pi(r+50)}{2\pi r}=\frac54$
⇒ $4(r+50)=5(r)$
⇒ $4r+200=5r$
⇒ $r = 200$ metres
Hence, the correct answer is 200 metres.
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